Toniolo and Linder, Equation (3b), real
Time bar (total: 12.9s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 3 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 4 |
| 25% | 25% | 74.9% | 0.1% | 0% | 0% | 0% | 5 |
| 43.8% | 43.7% | 56.2% | 0.1% | 0% | 0% | 0% | 6 |
| 43.8% | 43.7% | 56.2% | 0.1% | 0% | 0% | 0% | 7 |
| 53.1% | 53% | 46.8% | 0.1% | 0% | 0% | 0% | 8 |
| 60.9% | 60.8% | 39% | 0.1% | 0% | 0% | 0% | 9 |
| 60.9% | 60.8% | 39% | 0.1% | 0% | 0% | 0% | 10 |
| 64.8% | 64.7% | 35.1% | 0.1% | 0% | 0% | 0% | 11 |
| 68.4% | 68.3% | 31.6% | 0.1% | 0% | 0% | 0% | 12 |
Compiled 18 to 14 computations (22.2% saved)
| 1.4s | 8 256× | 0 | valid |
ival-sin: 674.0ms (60.2% of total)ival-pow2: 209.0ms (18.7% of total)ival-sqrt: 66.0ms (5.9% of total)ival-mult: 62.0ms (5.5% of total)ival-div: 52.0ms (4.6% of total)ival-add: 44.0ms (3.9% of total)ival-true: 7.0ms (0.6% of total)ival-assert: 5.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 20 | 0 | - | 2 | (-4.338907324505202e-297 2.4343272063481398e-158 -1.2737176725849601e-219) | (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
| 0 | 0 | - | 0 | - | (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
| 0 | 0 | - | 0 | - | (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | (sin.f64 kx) |
| 0 | 0 | - | 0 | - | (sin.f64 th) |
| 0 | 0 | - | 0 | - | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 0 | 0 | - | 0 | - | th |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 0 | 0 | - | 0 | - | (sin.f64 ky) |
| 0 | 0 | - | 0 | - | ky |
| 0 | 0 | - | 0 | - | kx |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
sqrt.f64 | (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) | uflow-rescue | 18 | 0 |
| ↳ | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) | underflow | 65 | |
| ↳ | (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) | underflow | 69 | |
| ↳ | (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) | underflow | 18 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 18 | 2 |
| - | 0 | 236 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 18 | 0 | 2 |
| - | 0 | 0 | 236 |
| number | freq |
|---|---|
| 0 | 238 |
| 1 | 18 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 115.0ms | 512× | 0 | valid |
Compiled 218 to 56 computations (74.3% saved)
ival-pow2: 46.0ms (48.3% of total)ival-sin: 36.0ms (37.8% of total)ival-sqrt: 4.0ms (4.2% of total)ival-div: 3.0ms (3.1% of total)ival-mult: 3.0ms (3.1% of total)ival-add: 2.0ms (2.1% of total)ival-true: 1.0ms (1% of total)ival-assert: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 153 |
| 1 | 101 | 147 |
| 2 | 211 | 147 |
| 3 | 383 | 147 |
| 4 | 845 | 147 |
| 5 | 1976 | 147 |
| 6 | 2541 | 147 |
| 7 | 2802 | 147 |
| 8 | 2914 | 147 |
| 9 | 2966 | 147 |
| 10 | 2981 | 147 |
| 11 | 2981 | 147 |
| 0 | 13 | 16 |
| 0 | 22 | 16 |
| 1 | 28 | 16 |
| 2 | 32 | 16 |
| 3 | 33 | 16 |
| 0 | 33 | 11 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(abs kx)
(negabs th)
(negabs ky)
Compiled 16 to 13 computations (18.8% saved)
Compiled 0 to 3 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 92.6% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
Compiled 16 to 13 computations (18.8% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sin.f64 ky) | |
| cost-diff | 0 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) | |
| cost-diff | 7424 | (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 66 |
| 0 | 22 | 66 |
| 1 | 28 | 66 |
| 2 | 32 | 66 |
| 3 | 33 | 66 |
| 0 | 33 | 51 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
(sin.f64 ky) |
ky |
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
(sin.f64 kx) |
kx |
#s(literal 2 binary64) |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
(sin.f64 th) |
th |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(sin.f64 ky) |
ky |
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
(sin.f64 kx) |
kx |
#s(literal 2 binary64) |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
(sin.f64 th) |
th |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.15625 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) | |
| accuracy | 0.21322250976844204 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) | |
| accuracy | 0.221035009768442 | (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) | |
| accuracy | 4.441519330968751 | (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
| 93.0ms | 256× | 0 | valid |
Compiled 134 to 28 computations (79.1% saved)
ival-sin: 51.0ms (61.6% of total)ival-pow2: 22.0ms (26.6% of total)ival-mult: 4.0ms (4.8% of total)ival-sqrt: 2.0ms (2.4% of total)ival-div: 1.0ms (1.2% of total)ival-add: 1.0ms (1.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
(sin.f64 ky) |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
(pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| Outputs |
|---|
(sin ky) |
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) |
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky)))))) |
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky)))))) |
(sin th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
1 |
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(pow kx 2) |
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(pow (sin kx) 2) |
(sin kx) |
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx)))) |
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx)))))) |
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx)))))) |
(/ (* ky (sin th)) (sin kx)) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(/ ky (sin kx)) |
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(pow ky 2) |
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3)))) |
(pow (sin ky) 2) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 25.0ms | ky | @ | inf | ((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2)) |
| 6.0ms | ky | @ | 0 | ((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2)) |
| 4.0ms | th | @ | -inf | ((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2)) |
| 4.0ms | kx | @ | inf | ((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2)) |
| 3.0ms | kx | @ | 0 | ((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 317 | 1402 |
| 1 | 1011 | 1353 |
| 2 | 3865 | 1261 |
| 3 | 7812 | 1261 |
| 0 | 8115 | 1188 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sin ky) |
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) |
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky)))))) |
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky)))))) |
(sin th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
1 |
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(pow kx 2) |
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(pow (sin kx) 2) |
(sin kx) |
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx)))) |
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx)))))) |
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx)))))) |
(/ (* ky (sin th)) (sin kx)) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(/ ky (sin kx)) |
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(pow ky 2) |
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3)))) |
(pow (sin ky) 2) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
| Outputs |
|---|
(sin ky) |
(sin.f64 ky) |
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) |
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)) |
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky)))))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (*.f64 kx (/.f64 kx (sin.f64 ky))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (*.f64 kx kx) (sin.f64 ky)) |
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky)))))) |
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (*.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) |
(sin th) |
(sin.f64 th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(fma.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) #s(literal 1/2 binary64)) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (sin.f64 th) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 kx kx) (sin.f64 th)) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (*.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (fma.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64)) |
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) #s(literal 1/2 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64)) |
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(fma.f64 (fma.f64 (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64)) |
(pow kx 2) |
(*.f64 kx kx) |
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) |
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 kx kx)) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) |
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx)) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) |
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx)) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))) |
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) |
(pow (sin kx) 2) |
(pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
(sin kx) |
(sin.f64 kx) |
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx)))) |
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)) |
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx)))))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (*.f64 ky (/.f64 ky (sin.f64 kx))) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx)) |
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx)))))) |
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (*.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (*.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 kx))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx))) |
(/ (* ky (sin th)) (sin kx)) |
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (*.f64 (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)))) (*.f64 ky ky) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) (fma.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) #s(literal -1/12 binary64) (*.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (*.f64 (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th))))) (*.f64 ky ky) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky) |
(/ ky (sin kx)) |
(/.f64 ky (sin.f64 kx)) |
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(fma.f64 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (+.f64 (fma.f64 (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (*.f64 ky ky) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (/.f64 ky (sin.f64 kx))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (fma.f64 (sin.f64 kx) (fma.f64 #s(literal -1/12 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (*.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (-.f64 (/.f64 #s(literal -1/5040 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (+.f64 (fma.f64 (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)))) (*.f64 ky ky) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (/.f64 ky (sin.f64 kx))) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 ky ky) #s(literal -1/6 binary64)) ky) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 ky ky) #s(literal 1/120 binary64)) (*.f64 ky ky) #s(literal -1/6 binary64)) ky) |
(pow ky 2) |
(*.f64 ky ky) |
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))) |
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 ky ky)) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))) |
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (*.f64 ky ky)) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3)))) |
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (*.f64 ky ky) #s(literal -1/3 binary64)) (*.f64 ky ky)) |
(pow (sin ky) 2) |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 th th)) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
(*.f64 (fma.f64 (pow.f64 th #s(literal 4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) (sin.f64 ky)))) th) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 49 |
| 0 | 22 | 49 |
| 1 | 62 | 49 |
| 2 | 344 | 49 |
| 3 | 2978 | 49 |
| 0 | 8260 | 34 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
(sin.f64 ky) |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
(pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))) |
(*.f64 (sqrt.f64 (/.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (+.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(*.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (pow.f64 (pow.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))) #s(literal -1 binary64)))) |
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(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 ky)) |
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal 1 binary64)) |
(*.f64 (sin.f64 ky) (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1 binary64))) |
(pow.f64 (*.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) #s(literal 2 binary64)) |
(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal 1 binary64)) |
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64)) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(/.f64 (/.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(/.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) |
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))) |
(/.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1 binary64)) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(/.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))) |
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) |
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(exp.f64 (-.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (neg.f64 (log.f64 (sin.f64 ky))))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal -1 binary64)) (neg.f64 (log.f64 (sin.f64 ky))))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (neg.f64 (log.f64 (sin.f64 ky))))) |
(exp.f64 (neg.f64 (log.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) |
(exp.f64 (+.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (log.f64 (sin.f64 ky)))) |
(exp.f64 (fma.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal -1 binary64) (log.f64 (sin.f64 ky)))) |
(exp.f64 (fma.f64 (log.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (log.f64 (sin.f64 ky)))) |
(exp.f64 (+.f64 (log.f64 (sin.f64 ky)) (neg.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))) |
(exp.f64 (+.f64 (log.f64 (sin.f64 ky)) (*.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal -1 binary64)))) |
(exp.f64 (+.f64 (log.f64 (sin.f64 ky)) (*.f64 (log.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) |
(exp.f64 (-.f64 (log.f64 (sin.f64 ky)) (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (sin.f64 ky))) |
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 ky))) |
(*.f64 #s(literal 1 binary64) (sin.f64 ky)) |
(*.f64 (sin.f64 ky) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (sin.f64 ky))) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sqrt.f64 (sin.f64 ky)))) |
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (sin.f64 ky) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) |
(neg.f64 (neg.f64 (sin.f64 ky))) |
(sin.f64 ky) |
(sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 ky))) |
(exp.f64 (neg.f64 (neg.f64 (log.f64 (sin.f64 ky))))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (sin.f64 ky))) #s(literal -1 binary64))) |
(exp.f64 (log.f64 (sin.f64 ky))) |
(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64)) #s(literal 4 binary64))) |
(*.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) (sqrt.f64 (sin.f64 ky))) |
(*.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64))) |
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 2 binary64))) |
(*.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(*.f64 (sin.f64 ky) (sin.f64 ky)) |
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 (sin.f64 ky))) |
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))) #s(literal -1 binary64)) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 ky))) |
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64)) |
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64)))))) (exp.f64 (log.f64 #s(literal 2 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))) |
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (cos.f64 ky) #s(literal 4 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))))) |
(/.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 3 binary64)))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))) #s(literal -2 binary64)) |
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))) |
(-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64))) |
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 ky)))) |
(exp.f64 (log.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(+.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))) |
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 ky)) (cos.f64 ky))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))) |
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 1/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 1/4 binary64)) #s(literal 4 binary64))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 kx))) |
(*.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) (sqrt.f64 (sin.f64 kx))) |
(*.f64 (sqrt.f64 (sin.f64 kx)) (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (sin.f64 kx)) (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64))) |
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64)) |
(*.f64 (sin.f64 kx) (sin.f64 kx)) |
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) |
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 (sin.f64 kx))) |
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -1 binary64)) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 kx))) |
(pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 4 binary64)) |
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (exp.f64 (log.f64 #s(literal 2 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))) |
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (cos.f64 kx) #s(literal 4 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))) |
(/.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -2 binary64)) |
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) |
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) |
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 kx)))) |
(exp.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) |
(+.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))) |
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 kx)) (cos.f64 kx))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) |
Compiled 9 472 to 1 772 computations (81.3% saved)
18 alts after pruning (18 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 352 | 18 | 370 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 353 | 18 | 371 |
| Status | Accuracy | Program |
|---|---|---|
| 99.4% | (/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) | |
| 95.0% | (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) | |
| ▶ | 99.7% | (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
| ▶ | 99.0% | (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))) |
| 99.6% | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) | |
| ▶ | 71.2% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
| 49.7% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) | |
| 80.9% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) | |
| ▶ | 56.5% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 34.7% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th)) | |
| 32.8% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th)) | |
| 34.2% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) | |
| 99.4% | (*.f64 (neg.f64 (sin.f64 ky)) (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) | |
| 22.1% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th)) | |
| 31.7% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) | |
| 44.9% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) | |
| 90.3% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))) | |
| ▶ | 28.3% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
Compiled 732 to 570 computations (22.1% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (hypot.f64 (sin.f64 ky) (sin.f64 kx)) | |
| cost-diff | 0 | (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) | |
| cost-diff | 0 | (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)) | |
| cost-diff | 704 | (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) | |
| cost-diff | 128 | (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) | |
| cost-diff | 384 | (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) | |
| cost-diff | 384 | (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) | |
| cost-diff | 0 | (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (sin.f64 ky) | |
| cost-diff | 0 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) | |
| cost-diff | 0 | (sin.f64 th) | |
| cost-diff | 0 | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) | |
| cost-diff | 0 | (hypot.f64 (sin.f64 ky) (sin.f64 kx)) | |
| cost-diff | 0 | (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) | |
| cost-diff | 0 | (sin.f64 th) | |
| cost-diff | 0 | (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 331 |
| 0 | 73 | 324 |
| 1 | 103 | 319 |
| 2 | 150 | 319 |
| 3 | 252 | 309 |
| 4 | 509 | 309 |
| 5 | 846 | 309 |
| 6 | 1288 | 309 |
| 7 | 1696 | 309 |
| 8 | 1899 | 309 |
| 9 | 1970 | 309 |
| 0 | 1970 | 303 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(sin.f64 th) |
th |
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(sin.f64 ky) |
ky |
(sin.f64 kx) |
kx |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
(sin.f64 th) |
th |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
(sin.f64 ky) |
ky |
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
#s(approx (pow (sin kx) 2) (*.f64 kx kx)) |
(*.f64 kx kx) |
kx |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sin.f64 th) |
th |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) |
(sin.f64 ky) |
ky |
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)) |
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) |
#s(literal 1 binary64) |
(cos.f64 (*.f64 ky #s(literal 2 binary64))) |
(*.f64 ky #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(*.f64 #s(literal 2 binary64) kx) |
kx |
(sin.f64 th) |
th |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))) |
#s(literal 1 binary64) |
(/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)) |
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(sin.f64 ky) |
ky |
(sin.f64 kx) |
kx |
(sin.f64 th) |
th |
| Outputs |
|---|
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(sin.f64 th) |
th |
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(sin.f64 kx) |
kx |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
(sin.f64 th) |
th |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))) |
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))) |
(sin.f64 ky) |
ky |
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))) |
(+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))) |
#s(approx (pow (sin kx) 2) (*.f64 kx kx)) |
(*.f64 kx kx) |
kx |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sin.f64 th) |
th |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sin.f64 th)) (sqrt.f64 (fma.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal -2 binary64) #s(literal 4 binary64)))) |
(/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) |
(/.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 (fma.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal -2 binary64) #s(literal 4 binary64)))) |
(sin.f64 ky) |
ky |
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)) |
(/.f64 (sqrt.f64 (fma.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal -2 binary64) #s(literal 4 binary64))) #s(literal 2 binary64)) |
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(sqrt.f64 (fma.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal -2 binary64) #s(literal 4 binary64))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(fma.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal -2 binary64) #s(literal 4 binary64)) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
#s(literal 1 binary64) |
(cos.f64 (*.f64 ky #s(literal 2 binary64))) |
(cos.f64 (*.f64 #s(literal 2 binary64) ky)) |
(*.f64 ky #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) ky) |
#s(literal 2 binary64) |
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(fma.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(*.f64 #s(literal 2 binary64) kx) |
kx |
(sin.f64 th) |
th |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
#s(literal 1 binary64) |
(/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)) |
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)) |
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(sin.f64 kx) |
kx |
(sin.f64 th) |
th |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.046875 | (hypot.f64 (sin.f64 ky) (sin.f64 kx)) | |
| accuracy | 0.11947250976844201 | (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) | |
| accuracy | 0.19759750976844204 | (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)) | |
| accuracy | 0.5576634531310115 | (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))) | |
| accuracy | 0.15625 | (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) | |
| accuracy | 4.432331053242653 | (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) | |
| accuracy | 15.751578029588966 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) | |
| accuracy | 17.8247072510061 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) | |
| accuracy | 0.15625 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) | |
| accuracy | 0.221035009768442 | (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) | |
| accuracy | 4.441519330968751 | (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) | |
| accuracy | 27.233281993713618 | #s(approx (pow (sin kx) 2) (*.f64 kx kx)) | |
| accuracy | 0.00390625 | (sin.f64 th) | |
| accuracy | 45.90212724970163 | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) | |
| accuracy | 0.00390625 | (sin.f64 kx) | |
| accuracy | 0.046875 | (hypot.f64 (sin.f64 ky) (sin.f64 kx)) | |
| accuracy | 0.11947250976844201 | (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) | |
| accuracy | 0.1640625 | (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
| 109.0ms | 112× | 2 | valid |
| 71.0ms | 91× | 1 | valid |
| 46.0ms | 53× | 0 | valid |
Compiled 695 to 78 computations (88.8% saved)
ival-cos: 41.0ms (23.2% of total)ival-hypot: 32.0ms (18.1% of total)ival-sin: 23.0ms (13% of total)ival-div: 19.0ms (10.7% of total)adjust: 16.0ms (9% of total)ival-mult: 16.0ms (9% of total)ival-pow2: 10.0ms (5.6% of total)ival-add: 8.0ms (4.5% of total)ival-sqrt: 7.0ms (4% of total)ival-sub: 5.0ms (2.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(sin.f64 th) |
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
(sin.f64 ky) |
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))) |
(/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)) |
(sin.f64 kx) |
#s(approx (pow (sin kx) 2) (*.f64 kx kx)) |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) |
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
| Outputs |
|---|
(sin th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
1 |
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(sin ky) |
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) |
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky)))))) |
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky)))))) |
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (sin ky)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(* 2 (- 1 (cos (* 2 ky)))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* 4 (pow kx 2))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3))))) |
(* 4 (pow kx 2)) |
(* (pow kx 2) (+ 4 (* -4/3 (pow kx 2)))) |
(* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3)))) |
(* (pow kx 2) (+ 4 (* (pow kx 2) (- (* (pow kx 2) (+ 8/45 (* -4/315 (pow kx 2)))) 4/3)))) |
(* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(/ 1 (sin th)) |
(+ (* 1/2 (/ (pow kx 2) (* (pow (sin ky) 2) (sin th)))) (/ 1 (sin th))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (* (pow (sin ky) 2) (sin th)))) (* 1/2 (/ 1 (* (pow (sin ky) 2) (sin th)))))) (/ 1 (sin th))) |
(+ (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (* (pow (sin ky) 2) (sin th)))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (* (pow (sin ky) 2) (sin th)))))) (* 1/2 (/ 1 (* (pow (sin ky) 2) (sin th)))))) (/ 1 (sin th))) |
kx |
(* kx (+ 1 (* -1/6 (pow kx 2)))) |
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6)))) |
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6)))) |
(pow kx 2) |
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) |
(* 2 (pow kx 2)) |
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) |
(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))) |
(* 2 (- 1 (cos (* 2 kx)))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(sin kx) |
(pow (sin kx) 2) |
(- 1 (cos (* 2 kx))) |
(sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky)))))) |
(/ (* ky (sin th)) (sin kx)) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(/ (sin kx) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky) |
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx)))) |
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx)))))) |
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx)))))) |
(/ ky (sin kx)) |
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(* 2 (* (* ky (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 4 (pow ky 2))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* -4/3 (pow ky 2))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* (pow ky 2) (- (* 8/45 (pow ky 2)) 4/3))))) |
(* 2 (* (* ky (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(/ (sin kx) (* ky (sin th))) |
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) ky) |
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (+ (* 1/2 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 7/360 (/ (sin kx) (sin th))) (* 1/12 (/ 1 (* (sin kx) (sin th)))))))))) (/ (sin kx) (sin th))) ky) |
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (+ (* 1/2 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 7/360 (/ (sin kx) (sin th))) (+ (* 1/12 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 31/15120 (/ (sin kx) (sin th))) (+ (* 7/720 (/ 1 (* (sin kx) (sin th)))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (* (sin kx) (sin th))))))))))))))) (/ (sin kx) (sin th))) ky) |
(pow ky 2) |
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3)))) |
(* 2 (pow ky 2)) |
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2)))) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3)))) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) |
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(pow (sin ky) 2) |
(- 1 (cos (* 2 ky))) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
th |
(* th (+ 1 (* -1/6 (pow th 2)))) |
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6)))) |
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6)))) |
(* 2 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* th (+ (* -1/3 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/2520 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))))) |
(* (/ 1 (* th (sin ky))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/ (+ (* 1/6 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) th) |
(/ (+ (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 7/360 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/6 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) th) |
(/ (+ (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 1/6 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* 31/15120 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 7/360 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) th) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 19.0ms | ky | @ | 0 | ((/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (* 2 (- 1 (cos (* 2 kx)))) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ 1 (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th))) (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2) (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))))) |
| 12.0ms | th | @ | inf | ((/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (* 2 (- 1 (cos (* 2 kx)))) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ 1 (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th))) (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2) (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))))) |
| 10.0ms | kx | @ | inf | ((/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (* 2 (- 1 (cos (* 2 kx)))) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ 1 (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th))) (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2) (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))))) |
| 9.0ms | kx | @ | 0 | ((/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (* 2 (- 1 (cos (* 2 kx)))) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ 1 (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th))) (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2) (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))))) |
| 7.0ms | ky | @ | inf | ((/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (* 2 (- 1 (cos (* 2 kx)))) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ 1 (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th))) (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2) (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 870 | 5422 |
| 1 | 2872 | 5030 |
| 2 | 7448 | 5022 |
| 0 | 8027 | 4738 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sin th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
1 |
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(sin ky) |
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) |
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky)))))) |
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky)))))) |
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (sin ky)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(* 2 (- 1 (cos (* 2 ky)))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* 4 (pow kx 2))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3))))) |
(* 4 (pow kx 2)) |
(* (pow kx 2) (+ 4 (* -4/3 (pow kx 2)))) |
(* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3)))) |
(* (pow kx 2) (+ 4 (* (pow kx 2) (- (* (pow kx 2) (+ 8/45 (* -4/315 (pow kx 2)))) 4/3)))) |
(* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(/ 1 (sin th)) |
(+ (* 1/2 (/ (pow kx 2) (* (pow (sin ky) 2) (sin th)))) (/ 1 (sin th))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (* (pow (sin ky) 2) (sin th)))) (* 1/2 (/ 1 (* (pow (sin ky) 2) (sin th)))))) (/ 1 (sin th))) |
(+ (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (* (pow (sin ky) 2) (sin th)))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (* (pow (sin ky) 2) (sin th)))))) (* 1/2 (/ 1 (* (pow (sin ky) 2) (sin th)))))) (/ 1 (sin th))) |
kx |
(* kx (+ 1 (* -1/6 (pow kx 2)))) |
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6)))) |
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6)))) |
(pow kx 2) |
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) |
(* 2 (pow kx 2)) |
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) |
(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))) |
(* 2 (- 1 (cos (* 2 kx)))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(sin kx) |
(pow (sin kx) 2) |
(- 1 (cos (* 2 kx))) |
(sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky)))))) |
(/ (* ky (sin th)) (sin kx)) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(/ (sin kx) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky) |
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx)))) |
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx)))))) |
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx)))))) |
(/ ky (sin kx)) |
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(* 2 (* (* ky (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 4 (pow ky 2))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* -4/3 (pow ky 2))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* (pow ky 2) (- (* 8/45 (pow ky 2)) 4/3))))) |
(* 2 (* (* ky (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(/ (sin kx) (* ky (sin th))) |
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) ky) |
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (+ (* 1/2 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 7/360 (/ (sin kx) (sin th))) (* 1/12 (/ 1 (* (sin kx) (sin th)))))))))) (/ (sin kx) (sin th))) ky) |
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (+ (* 1/2 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 7/360 (/ (sin kx) (sin th))) (+ (* 1/12 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 31/15120 (/ (sin kx) (sin th))) (+ (* 7/720 (/ 1 (* (sin kx) (sin th)))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (* (sin kx) (sin th))))))))))))))) (/ (sin kx) (sin th))) ky) |
(pow ky 2) |
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3)))) |
(* 2 (pow ky 2)) |
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2)))) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3)))) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) |
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(pow (sin ky) 2) |
(- 1 (cos (* 2 ky))) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
th |
(* th (+ 1 (* -1/6 (pow th 2)))) |
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6)))) |
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6)))) |
(* 2 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* th (+ (* -1/3 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/2520 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))))) |
(* (/ 1 (* th (sin ky))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/ (+ (* 1/6 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) th) |
(/ (+ (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 7/360 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/6 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) th) |
(/ (+ (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 1/6 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* 31/15120 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 7/360 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) th) |
| Outputs |
|---|
(sin th) |
(sin.f64 th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(fma.f64 (/.f64 (*.f64 (*.f64 kx kx) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (sin.f64 th)) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th)) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (*.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)))) (*.f64 kx kx) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)) |
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(fma.f64 (fma.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64)) |
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64)) |
(sin ky) |
(sin.f64 ky) |
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (*.f64 kx kx) (sin.f64 ky)) |
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky)))))) |
(fma.f64 (fma.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (*.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (*.f64 kx kx) (sin.f64 ky)) |
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (*.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 ky))) (*.f64 kx kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (*.f64 kx kx) (sin.f64 ky)) |
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64)) |
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))) (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64)) |
(* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(+ (* -1 (* (/ (* (pow kx 2) (sin ky)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(fma.f64 (neg.f64 (/.f64 (*.f64 (*.f64 kx kx) (sin.f64 ky)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(fma.f64 (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))))) (/.f64 (sin.f64 ky) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (*.f64 (*.f64 (*.f64 kx kx) (sin.f64 ky)) (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (-.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (/.f64 (sin.f64 ky) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (*.f64 (fma.f64 (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) (/.f64 #s(literal 2/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64))))) (sin.f64 ky)) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64)))))) (*.f64 kx kx) (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(* 2 (- 1 (cos (* 2 ky)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* 4 (pow kx 2))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 4 binary64) (*.f64 kx kx))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 kx kx) #s(literal 4 binary64)) (*.f64 kx kx))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3))))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal 8/45 binary64) (*.f64 kx kx) #s(literal -4/3 binary64)) (*.f64 kx kx) #s(literal 4 binary64)) (*.f64 kx kx))) |
(* 4 (pow kx 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 kx kx)) |
(* (pow kx 2) (+ 4 (* -4/3 (pow kx 2)))) |
(*.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 kx kx) #s(literal 4 binary64)) (*.f64 kx kx)) |
(* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 8/45 binary64) (*.f64 kx kx) #s(literal -4/3 binary64)) (*.f64 kx kx) #s(literal 4 binary64)) (*.f64 kx kx)) |
(* (pow kx 2) (+ 4 (* (pow kx 2) (- (* (pow kx 2) (+ 8/45 (* -4/315 (pow kx 2)))) 4/3)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -4/315 binary64) (*.f64 kx kx) #s(literal 8/45 binary64)) (*.f64 kx kx) #s(literal -4/3 binary64)) (*.f64 kx kx) #s(literal 4 binary64)) (*.f64 kx kx)) |
(* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(fma.f64 (neg.f64 (/.f64 (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (*.f64 kx kx)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
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(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
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(/ 1 (sin th)) |
(/.f64 #s(literal 1 binary64) (sin.f64 th)) |
(+ (* 1/2 (/ (pow kx 2) (* (pow (sin ky) 2) (sin th)))) (/ 1 (sin th))) |
(fma.f64 (/.f64 (*.f64 kx kx) (sin.f64 th)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 th))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (* (pow (sin ky) 2) (sin th)))) (* 1/2 (/ 1 (* (pow (sin ky) 2) (sin th)))))) (/ 1 (sin th))) |
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(+ (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (* (pow (sin ky) 2) (sin th)))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (* (pow (sin ky) 2) (sin th)))))) (* 1/2 (/ 1 (* (pow (sin ky) 2) (sin th)))))) (/ 1 (sin th))) |
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kx |
(* kx (+ 1 (* -1/6 (pow kx 2)))) |
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) |
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) kx) |
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 kx kx) #s(literal 1/120 binary64)) (*.f64 kx kx) #s(literal -1/6 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) kx) |
(pow kx 2) |
(*.f64 kx kx) |
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) |
(*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx)) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx)) |
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx)) |
(* 2 (pow kx 2)) |
(*.f64 (*.f64 kx kx) #s(literal 2 binary64)) |
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2)))) |
(*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx)) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx)) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -2/315 binary64) (*.f64 kx kx) #s(literal 4/45 binary64)) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx)) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(fma.f64 (/.f64 (*.f64 (*.f64 kx kx) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 4/3 binary64)) (*.f64 kx (/.f64 kx (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 kx kx) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 4/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 8/45 binary64)) (*.f64 kx (/.f64 kx (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 4/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 kx kx) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (*.f64 kx kx) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))) |
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) |
(* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))) |
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(* 2 (- 1 (cos (* 2 kx)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)) |
(sin kx) |
(sin.f64 kx) |
(pow (sin kx) 2) |
(pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
(- 1 (cos (* 2 kx))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky)))))) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(/ (* ky (sin th)) (sin kx)) |
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(*.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (sin.f64 th)) (fma.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (fma.f64 #s(literal -1/240 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/5040 binary64)) (sin.f64 kx))))) (*.f64 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (/.f64 (*.f64 (sin.f64 th) #s(literal 1/12 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky) |
(/ (sin kx) ky) |
(/.f64 (sin.f64 kx) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky) |
(/.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx)) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (sin.f64 kx)) #s(literal -1/2 binary64) (fma.f64 #s(literal 7/360 binary64) (sin.f64 kx) (/.f64 #s(literal 1/12 binary64) (sin.f64 kx)))) (*.f64 ky ky) (fma.f64 #s(literal 1/6 binary64) (sin.f64 kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)))) (*.f64 ky ky) (sin.f64 kx)) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (sin.f64 kx)) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (sin.f64 kx)) #s(literal -1/12 binary64) (fma.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (sin.f64 kx)) #s(literal 1/2 binary64) (fma.f64 #s(literal 31/15120 binary64) (sin.f64 kx) (/.f64 #s(literal 7/720 binary64) (sin.f64 kx))))) (*.f64 ky ky) (fma.f64 #s(literal 7/360 binary64) (sin.f64 kx) (/.f64 #s(literal 1/12 binary64) (sin.f64 kx))))) (*.f64 ky ky) (fma.f64 #s(literal 1/6 binary64) (sin.f64 kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)))) (*.f64 ky ky) (sin.f64 kx)) ky) |
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx)))) |
(fma.f64 (*.f64 ky (/.f64 ky (sin.f64 kx))) #s(literal 1/2 binary64) (sin.f64 kx)) |
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx)))))) |
(fma.f64 (fma.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (*.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx)) |
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (*.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 kx))) (*.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx)) |
(/ ky (sin kx)) |
(/.f64 ky (sin.f64 kx)) |
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (*.f64 ky ky))) ky) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(fma.f64 (*.f64 (-.f64 (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (*.f64 ky ky)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (*.f64 ky ky)) ky (/.f64 ky (sin.f64 kx))) |
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx)))) |
(fma.f64 (*.f64 (-.f64 (*.f64 (+.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (*.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))))) (+.f64 (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx)))) (*.f64 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (*.f64 ky ky)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (*.f64 ky ky)) ky (/.f64 ky (sin.f64 kx))) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky) |
(* 2 (* (* ky (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 1/2 binary64))))) ky) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
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(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
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(+ (* 2 (- 1 (cos (* 2 kx)))) (* 4 (pow ky 2))) |
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(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* -4/3 (pow ky 2))))) |
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(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* (pow ky 2) (- (* 8/45 (pow ky 2)) 4/3))))) |
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(* 2 (* (* ky (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
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(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
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(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
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(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
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(/ (sin kx) (* ky (sin th))) |
(/.f64 (/.f64 (sin.f64 kx) ky) (sin.f64 th)) |
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) ky) |
(/.f64 (fma.f64 (fma.f64 (sin.f64 kx) (/.f64 #s(literal 1/6 binary64) (sin.f64 th)) (/.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 th)) (sin.f64 kx))) (*.f64 ky ky) (/.f64 (sin.f64 kx) (sin.f64 th))) ky) |
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (+ (* 1/2 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 7/360 (/ (sin kx) (sin th))) (* 1/12 (/ 1 (* (sin kx) (sin th)))))))))) (/ (sin kx) (sin th))) ky) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sin.f64 th)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (sin.f64 kx)) (fma.f64 (sin.f64 kx) (/.f64 #s(literal 7/360 binary64) (sin.f64 th)) (/.f64 (/.f64 #s(literal 1/12 binary64) (sin.f64 th)) (sin.f64 kx)))) (*.f64 ky ky) (fma.f64 (sin.f64 kx) (/.f64 #s(literal 1/6 binary64) (sin.f64 th)) (/.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 th)) (sin.f64 kx)))) (*.f64 ky ky) (/.f64 (sin.f64 kx) (sin.f64 th))) ky) |
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (+ (* 1/2 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 7/360 (/ (sin kx) (sin th))) (+ (* 1/12 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 31/15120 (/ (sin kx) (sin th))) (+ (* 7/720 (/ 1 (* (sin kx) (sin th)))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (* (sin kx) (sin th))))))))))))))) (/ (sin kx) (sin th))) ky) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (sin.f64 th)) (fma.f64 (fma.f64 (/.f64 #s(literal -1/12 binary64) (sin.f64 th)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (sin.f64 kx)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 th)) (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (sin.f64 kx)) (fma.f64 (sin.f64 kx) (/.f64 #s(literal 31/15120 binary64) (sin.f64 th)) (/.f64 (/.f64 #s(literal 7/720 binary64) (sin.f64 th)) (sin.f64 kx))))) (*.f64 ky ky) (fma.f64 (sin.f64 kx) (/.f64 #s(literal 7/360 binary64) (sin.f64 th)) (/.f64 (/.f64 #s(literal 1/12 binary64) (sin.f64 th)) (sin.f64 kx))))) (*.f64 ky ky) (fma.f64 (sin.f64 kx) (/.f64 #s(literal 1/6 binary64) (sin.f64 th)) (/.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 th)) (sin.f64 kx)))) (*.f64 ky ky) (/.f64 (sin.f64 kx) (sin.f64 th))) ky) |
(pow ky 2) |
(*.f64 ky ky) |
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))) |
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)) |
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (*.f64 ky ky) #s(literal -1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)) |
(* 2 (pow ky 2)) |
(*.f64 (*.f64 ky ky) #s(literal 2 binary64)) |
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2)))) |
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky)) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) (*.f64 ky ky) #s(literal 2 binary64)) (*.f64 ky ky)) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) (*.f64 ky ky) #s(literal -2/3 binary64)) (*.f64 ky ky) #s(literal 2 binary64)) (*.f64 ky ky)) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(fma.f64 (/.f64 (*.f64 (*.f64 ky ky) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (*.f64 ky (/.f64 ky (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 8/45 binary64)) (*.f64 ky (/.f64 ky (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 ky ky) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(pow (sin ky) 2) |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
(- 1 (cos (* 2 ky))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (*.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 th th) (sin.f64 ky))))) (*.f64 th th) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th) |
th |
(* th (+ 1 (* -1/6 (pow th 2)))) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th) |
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th) |
(* 2 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(* th (+ (* -1/3 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (*.f64 #s(literal 2 binary64) (sin.f64 ky)))) th) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal 1/60 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (*.f64 #s(literal -1/3 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) th) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/2520 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal 1/60 binary64) (sin.f64 ky) (*.f64 #s(literal -1/2520 binary64) (*.f64 (*.f64 th th) (sin.f64 ky))))) (*.f64 th th) (*.f64 (*.f64 #s(literal -1/3 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 th th) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) th) |
(* (/ 1 (* th (sin ky))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)) |
(/ (+ (* 1/6 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) th) |
(/.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th (/.f64 th (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) th) |
(/ (+ (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 7/360 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/6 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) th) |
(/.f64 (fma.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (fma.f64 #s(literal 7/360 binary64) (*.f64 th (/.f64 th (sin.f64 ky))) (/.f64 #s(literal 1/6 binary64) (sin.f64 ky)))) (*.f64 th th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th) |
(/ (+ (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 1/6 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* 31/15120 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 7/360 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) th) |
(/.f64 (fma.f64 (fma.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (fma.f64 #s(literal 31/15120 binary64) (*.f64 th (/.f64 th (sin.f64 ky))) (/.f64 #s(literal 7/360 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 th th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 236 |
| 0 | 73 | 215 |
| 1 | 264 | 212 |
| 2 | 1727 | 199 |
| 0 | 9314 | 199 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(sin.f64 th) |
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
(sin.f64 ky) |
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))) |
(/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)) |
(sin.f64 kx) |
#s(approx (pow (sin kx) 2) (*.f64 kx kx)) |
(pow.f64 (sin.f64 ky) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) |
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
| Outputs |
|---|
(*.f64 (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 (sin.f64 th) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (sin.f64 th) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) (/.f64 (neg.f64 (sin.f64 ky)) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (sin.f64 th) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) (/.f64 (sin.f64 ky) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64))) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal 1 binary64)) (/.f64 (neg.f64 (sin.f64 ky)) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 th) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 (neg.f64 (sin.f64 ky)) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 (sin.f64 ky) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (sin.f64 th) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) #s(literal 1/2 binary64)) (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 (pow.f64 (pow.f64 (neg.f64 (sin.f64 th)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) (/.f64 (sin.f64 th) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) #s(literal -2 binary64)) |
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(literal 1 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) |
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th)) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (pow.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (pow.f64 (pow.f64 (neg.f64 (sin.f64 th)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (neg.f64 (sin.f64 th))) |
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (neg.f64 (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sin.f64 th) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sin.f64 th) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64))))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) #s(literal 1 binary64)) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 ky) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (sin.f64 ky) #s(literal 1 binary64)) (/.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (sin.f64 ky) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) #s(literal 1/2 binary64)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 (pow.f64 (sin.f64 th) #s(literal 1 binary64)) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 #s(literal 2 binary64) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 (sin.f64 th) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (/.f64 (pow.f64 (sin.f64 th) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (sin.f64 th) #s(literal 1 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 th)) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64))))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) (sin.f64 th)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (*.f64 (sin.f64 ky) (sin.f64 th))) |
(*.f64 (neg.f64 (sin.f64 th)) (/.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)))) |
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) #s(literal 1 binary64)) |
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th))) |
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(pow.f64 (exp.f64 (log.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)))) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) #s(literal 1 binary64)) |
(/.f64 (neg.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) #s(literal -1/2 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 th)))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 (sin.f64 ky) (sin.f64 th)))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 th)))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (sin.f64 ky) (sin.f64 th)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))) |
(/.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(literal 1/2 binary64)) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (sin.f64 ky) (sin.f64 th))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))) |
(/.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (neg.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (neg.f64 (pow.f64 (sin.f64 th) #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) |
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (sin.f64 th) #s(literal -1 binary64))) |
(/.f64 (neg.f64 (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))) |
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky))) (sin.f64 th))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(neg.f64 (/.f64 (neg.f64 (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))) (/.f64 (neg.f64 (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))) #s(literal -1 binary64))) |
(sin.f64 th) |
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) |
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(/.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
(/.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 2 binary64)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 3 binary64))) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 2 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 3 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 3 binary64))))) |
(fma.f64 #s(literal -1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)) |
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (/.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(-.f64 (pow.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 2 binary64)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)))) |
(-.f64 (pow.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 3 binary64)) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(+.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) #s(literal 4 binary64)))) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)) #s(literal 8 binary64) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)) #s(literal 8 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64))))) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)) #s(literal 8 binary64) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)) #s(literal 8 binary64)))) (pow.f64 (pow.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64))))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)) #s(literal 8 binary64) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)) #s(literal 8 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))))))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)) #s(literal 8 binary64) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)) #s(literal 8 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))))))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)) #s(literal 8 binary64) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)) #s(literal 8 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) #s(literal 4 binary64) (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))))))) |
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)) #s(literal 8 binary64) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)) #s(literal 8 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64))))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) #s(literal 4 binary64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64))))) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)) #s(literal 8 binary64) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)) #s(literal 8 binary64)))))) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 1/2 binary64))) |
Compiled 33 954 to 4 581 computations (86.5% saved)
41 alts after pruning (39 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 981 | 33 | 1 014 |
| Fresh | 7 | 6 | 13 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 0 | 0 |
| Total | 991 | 41 | 1 032 |
| Status | Accuracy | Program |
|---|---|---|
| 54.8% | (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))) | |
| 55.4% | (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) | |
| 71.1% | (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) | |
| 31.7% | (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) | |
| ▶ | 50.0% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
| 31.4% | (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) | |
| 28.0% | (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) | |
| 70.7% | (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (sin.f64 th)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) | |
| 45.4% | (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) | |
| 71.0% | (*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(literal 2 binary64)) | |
| 71.2% | (*.f64 (/.f64 (*.f64 (sin.f64 ky) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) | |
| ▶ | 99.6% | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
| 71.2% | (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 (sin.f64 ky) #s(literal 1/2 binary64))) | |
| 71.1% | (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) | |
| 70.9% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 36.6% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 38.2% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 31.0% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) | |
| ▶ | 30.7% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
| 30.9% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 49.7% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) | |
| ✓ | 56.5% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 30.8% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 46.7% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) | |
| 32.0% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) | |
| 34.7% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th)) | |
| 32.8% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th)) | |
| 34.2% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) | |
| 27.2% | (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 99.5% | (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) | |
| 30.9% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) | |
| ▶ | 26.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
| 31.7% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) | |
| 30.7% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) | |
| 26.5% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) | |
| 70.9% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) | |
| 36.5% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) | |
| ✓ | 28.3% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
| 16.3% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| 16.2% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| ▶ | 16.4% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
Compiled 2 333 to 1 757 computations (24.7% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 th th) | |
| cost-diff | 0 | (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) | |
| cost-diff | 384 | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) | |
| cost-diff | 0 | (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| cost-diff | 0 | (sin.f64 ky) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) | |
| cost-diff | 384 | (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) | |
| cost-diff | 0 | (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) | |
| cost-diff | 0 | #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) | |
| cost-diff | 0 | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) | |
| cost-diff | 0 | (*.f64 th th) | |
| cost-diff | 0 | (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) | |
| cost-diff | 0 | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| cost-diff | 0 | (hypot.f64 (sin.f64 ky) (sin.f64 kx)) | |
| cost-diff | 0 | (sin.f64 th) | |
| cost-diff | 0 | (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 483 |
| 0 | 93 | 478 |
| 1 | 135 | 466 |
| 2 | 203 | 466 |
| 3 | 342 | 448 |
| 4 | 556 | 448 |
| 5 | 846 | 448 |
| 6 | 1253 | 448 |
| 7 | 1674 | 448 |
| 8 | 1887 | 448 |
| 9 | 1965 | 448 |
| 10 | 1966 | 448 |
| 0 | 1966 | 436 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(sin.f64 th) |
th |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(sin.f64 ky) |
ky |
(sin.f64 kx) |
kx |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(*.f64 th th) |
th |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
#s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
ky |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
#s(literal 1 binary64) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(*.f64 #s(literal 2 binary64) kx) |
kx |
(sin.f64 th) |
th |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) |
(sin.f64 ky) |
ky |
(/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) |
#s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
#s(literal 1 binary64) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(*.f64 #s(literal 2 binary64) kx) |
#s(literal 2 binary64) |
kx |
(sqrt.f64 #s(literal 2 binary64)) |
(sin.f64 th) |
th |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(*.f64 th th) |
th |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(sin.f64 ky) |
ky |
(sin.f64 kx) |
kx |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th)) |
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(sin.f64 th) |
th |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(sin.f64 kx) |
kx |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) |
(*.f64 th th) |
th |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64)))) (sin.f64 th)) |
#s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
#s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
ky |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) |
#s(literal 1 binary64) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(*.f64 #s(literal 2 binary64) kx) |
kx |
(sin.f64 th) |
th |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sin.f64 th)) #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) |
(/.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(sin.f64 ky) |
ky |
(/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)) |
#s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
#s(literal 1 binary64) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(*.f64 #s(literal 2 binary64) kx) |
#s(literal 2 binary64) |
kx |
(sqrt.f64 #s(literal 2 binary64)) |
(sin.f64 th) |
th |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(*.f64 #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) |
(*.f64 th th) |
th |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(sin.f64 kx) |
kx |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.06640625 | (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) | |
| accuracy | 0.11947250976844201 | (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) | |
| accuracy | 0.1640625 | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) | |
| accuracy | 31.893200456091343 | #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) | |
| accuracy | 0.457695019536884 | (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))) | |
| accuracy | 15.417151017429484 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) | |
| accuracy | 17.8247072510061 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) | |
| accuracy | 33.69329853099764 | #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) | |
| accuracy | 0.421875 | (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) | |
| accuracy | 15.873885102544394 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) | |
| accuracy | 17.8247072510061 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) | |
| accuracy | 36.563990987778865 | #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) | |
| accuracy | 0.046875 | (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) | |
| accuracy | 0.06640625 | (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) | |
| accuracy | 31.893200456091343 | #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) | |
| accuracy | 45.90212724970163 | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| accuracy | 0.00390625 | (sin.f64 kx) | |
| accuracy | 0.046875 | (hypot.f64 (sin.f64 ky) (sin.f64 kx)) | |
| accuracy | 0.24609375 | (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) | |
| accuracy | 0.24609375 | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
| 124.0ms | 63× | 1 | valid |
| 86.0ms | 63× | 2 | valid |
| 77.0ms | 118× | 0 | valid |
| 16.0ms | 12× | 3 | valid |
Compiled 897 to 110 computations (87.7% saved)
ival-sin: 98.0ms (37.8% of total)ival-cos: 38.0ms (14.7% of total)ival-mult: 33.0ms (12.7% of total)ival-div: 16.0ms (6.2% of total)ival-sqrt: 16.0ms (6.2% of total)adjust: 14.0ms (5.4% of total)const: 13.0ms (5% of total)ival-pow2: 11.0ms (4.2% of total)ival-hypot: 8.0ms (3.1% of total)ival-add: 5.0ms (1.9% of total)ival-sub: 4.0ms (1.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(sin.f64 th) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(*.f64 th th) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
#s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) |
(/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(sin.f64 ky) |
(/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(sin.f64 kx) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) |
#s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) |
| Outputs |
|---|
(sin th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
(/ (sin th) (sin ky)) |
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (/ (sin th) (sin ky))) |
(sin ky) |
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) |
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky)))))) |
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky)))))) |
(* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (sin ky)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(* 2 (/ (* ky (pow (sqrt 1/2) 2)) kx)) |
(/ (+ (* 1/6 (* (pow kx 2) ky)) (* 2 (* ky (pow (sqrt 1/2) 2)))) kx) |
(/ (+ (* 2 (* ky (pow (sqrt 1/2) 2))) (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (* ky (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))))))) kx) |
(/ (+ (* 2 (* ky (pow (sqrt 1/2) 2))) (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (+ (* ky (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (* (pow kx 2) (* ky (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))))))))) kx) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/4 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/4 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
kx |
(* kx (+ 1 (* -1/6 (pow kx 2)))) |
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6)))) |
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6)))) |
(* 2 (pow kx 2)) |
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3)))) |
(/ (sqrt 1/2) kx) |
(/ (+ (sqrt 1/2) (* 1/12 (/ (pow kx 2) (sqrt 1/2)))) kx) |
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) |
(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(* kx (sqrt 2)) |
(* kx (+ (sqrt 2) (* -1/3 (/ (pow kx 2) (sqrt 2))))) |
(* kx (+ (sqrt 2) (* (pow kx 2) (- (* 1/2 (/ (* (pow kx 2) (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/3 (/ 1 (sqrt 2))))))) |
(* kx (+ (sqrt 2) (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 2/315 (* -1/3 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/3 (/ 1 (sqrt 2))))))) |
(* kx (pow (sqrt 2) 2)) |
(* kx (+ (* -1/3 (pow kx 2)) (pow (sqrt 2) 2))) |
(* kx (+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))))) 1/3)) (pow (sqrt 2) 2))) |
(* kx (+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (+ 2/315 (* -1/3 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (* 1/2 (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2))))))) 1/3)) (pow (sqrt 2) 2))) |
1 |
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* 2 (* (* ky (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* 1/2 (sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))) |
(sin kx) |
(- 1 (cos (* 2 kx))) |
(sqrt (/ 1 (- 1 (cos (* 2 kx))))) |
(sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky)))))) |
(sqrt (- 1 (cos (* 2 kx)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) |
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/ (* ky (sin th)) (sin kx)) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(/ (sin th) (sin kx)) |
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx))) |
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx))) |
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))) (/ (sin th) (sin kx))) |
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx)))) |
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx)))))) |
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx)))))) |
(* 2 (* (* ky (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(* 2 (* ky (sqrt 1/2))) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/4 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (sqrt 1/2)) |
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(/ (sin kx) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) |
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))) |
th |
(* th (+ 1 (* -1/6 (pow th 2)))) |
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6)))) |
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6)))) |
(+ 1 (* -1/6 (pow th 2))) |
(pow th 2) |
(* 2 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* th (+ (* -1/3 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/2520 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))))) |
(* -1/6 (pow th 2)) |
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6)) |
(* -1/6 (pow th 3)) |
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6)) |
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2))))) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 22.0ms | ky | @ | 0 | ((* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* th th) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* 2 (* (sqrt 1/2) ky)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin kx) (* (+ (* (* th th) -1/6) 1) th) (- 1 (cos (* 2 kx))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* (sqrt 1/2) ky) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt (- 1 (cos (* 2 kx)))) (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) |
| 18.0ms | kx | @ | 0 | ((* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* th th) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* 2 (* (sqrt 1/2) ky)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin kx) (* (+ (* (* th th) -1/6) 1) th) (- 1 (cos (* 2 kx))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* (sqrt 1/2) ky) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt (- 1 (cos (* 2 kx)))) (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) |
| 7.0ms | kx | @ | inf | ((* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* th th) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* 2 (* (sqrt 1/2) ky)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin kx) (* (+ (* (* th th) -1/6) 1) th) (- 1 (cos (* 2 kx))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* (sqrt 1/2) ky) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt (- 1 (cos (* 2 kx)))) (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) |
| 7.0ms | kx | @ | -inf | ((* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* th th) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* 2 (* (sqrt 1/2) ky)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin kx) (* (+ (* (* th th) -1/6) 1) th) (- 1 (cos (* 2 kx))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* (sqrt 1/2) ky) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt (- 1 (cos (* 2 kx)))) (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) |
| 6.0ms | ky | @ | -inf | ((* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* th th) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* 2 (* (sqrt 1/2) ky)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin kx) (* (+ (* (* th th) -1/6) 1) th) (- 1 (cos (* 2 kx))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* (sqrt 1/2) ky) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt (- 1 (cos (* 2 kx)))) (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 850 | 5570 |
| 1 | 2797 | 4961 |
| 2 | 7300 | 4801 |
| 0 | 8025 | 4572 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sin th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
(/ (sin th) (sin ky)) |
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (/ (sin th) (sin ky))) |
(sin ky) |
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) |
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky)))))) |
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky)))))) |
(* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (sin ky)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(* 2 (/ (* ky (pow (sqrt 1/2) 2)) kx)) |
(/ (+ (* 1/6 (* (pow kx 2) ky)) (* 2 (* ky (pow (sqrt 1/2) 2)))) kx) |
(/ (+ (* 2 (* ky (pow (sqrt 1/2) 2))) (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (* ky (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))))))) kx) |
(/ (+ (* 2 (* ky (pow (sqrt 1/2) 2))) (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (+ (* ky (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (* (pow kx 2) (* ky (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))))))))) kx) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/4 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/4 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
kx |
(* kx (+ 1 (* -1/6 (pow kx 2)))) |
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6)))) |
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6)))) |
(* 2 (pow kx 2)) |
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3)))) |
(/ (sqrt 1/2) kx) |
(/ (+ (sqrt 1/2) (* 1/12 (/ (pow kx 2) (sqrt 1/2)))) kx) |
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) |
(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(* kx (sqrt 2)) |
(* kx (+ (sqrt 2) (* -1/3 (/ (pow kx 2) (sqrt 2))))) |
(* kx (+ (sqrt 2) (* (pow kx 2) (- (* 1/2 (/ (* (pow kx 2) (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/3 (/ 1 (sqrt 2))))))) |
(* kx (+ (sqrt 2) (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 2/315 (* -1/3 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/3 (/ 1 (sqrt 2))))))) |
(* kx (pow (sqrt 2) 2)) |
(* kx (+ (* -1/3 (pow kx 2)) (pow (sqrt 2) 2))) |
(* kx (+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))))) 1/3)) (pow (sqrt 2) 2))) |
(* kx (+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (+ 2/315 (* -1/3 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (* 1/2 (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2))))))) 1/3)) (pow (sqrt 2) 2))) |
1 |
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* 2 (* (* ky (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* 1/2 (sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))) |
(sin kx) |
(- 1 (cos (* 2 kx))) |
(sqrt (/ 1 (- 1 (cos (* 2 kx))))) |
(sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky)))))) |
(sqrt (- 1 (cos (* 2 kx)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) |
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/ (* ky (sin th)) (sin kx)) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(/ (sin th) (sin kx)) |
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx))) |
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx))) |
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))) (/ (sin th) (sin kx))) |
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx)))) |
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx)))))) |
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx)))))) |
(* 2 (* (* ky (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(* 2 (* ky (sqrt 1/2))) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/4 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (sqrt 1/2)) |
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(/ (sin kx) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) |
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))) |
th |
(* th (+ 1 (* -1/6 (pow th 2)))) |
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6)))) |
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6)))) |
(+ 1 (* -1/6 (pow th 2))) |
(pow th 2) |
(* 2 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* th (+ (* -1/3 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/2520 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))))) |
(* -1/6 (pow th 2)) |
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6)) |
(* -1/6 (pow th 3)) |
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6)) |
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2))))) |
| Outputs |
|---|
(sin th) |
(sin.f64 th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(fma.f64 (/.f64 (*.f64 (*.f64 kx kx) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (sin.f64 th)) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th)) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (*.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)))) (*.f64 kx kx) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th)) |
(/ (sin th) (sin ky)) |
(/.f64 (sin.f64 th) (sin.f64 ky)) |
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky))) |
(fma.f64 (/.f64 (*.f64 (*.f64 kx kx) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (sin.f64 ky))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (sin.f64 ky)) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (*.f64 kx kx) (/.f64 (sin.f64 th) (sin.f64 ky))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (/ (sin th) (sin ky))) |
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(sin ky) |
(sin.f64 ky) |
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) |
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(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky)))))) |
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(* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
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(+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
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(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
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(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
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(* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(+ (* -1 (* (/ (* (pow kx 2) (sin ky)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
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(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
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(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (*.f64 (fma.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (sin.f64 ky)) (*.f64 (*.f64 (*.f64 kx kx) (sin.f64 ky)) (fma.f64 (/.f64 (fma.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) (/.f64 #s(literal 2/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))))))) (*.f64 kx kx) (*.f64 (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))))) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(* 2 (/ (* ky (pow (sqrt 1/2) 2)) kx)) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)) |
(/ (+ (* 1/6 (* (pow kx 2) ky)) (* 2 (* ky (pow (sqrt 1/2) 2)))) kx) |
(/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx) |
(/ (+ (* 2 (* ky (pow (sqrt 1/2) 2))) (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (* ky (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))))))) kx) |
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(/ (+ (* 2 (* ky (pow (sqrt 1/2) 2))) (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (+ (* ky (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (* (pow kx 2) (* ky (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))))))))) kx) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) ky (*.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 31/15120 binary64))) (*.f64 kx kx) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
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(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
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(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/4 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))) |
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(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/4 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (fma.f64 #s(literal 1/4 binary64) (*.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 4/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 8/45 binary64)) (*.f64 kx (/.f64 kx (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 4/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 kx kx) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
kx |
(* kx (+ 1 (* -1/6 (pow kx 2)))) |
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) |
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) kx) |
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 kx kx) #s(literal 1/120 binary64)) (*.f64 kx kx) #s(literal -1/6 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) kx) |
(* 2 (pow kx 2)) |
(*.f64 (*.f64 kx kx) #s(literal 2 binary64)) |
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2)))) |
(*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx)) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx)) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -2/315 binary64) (*.f64 kx kx) #s(literal 4/45 binary64)) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx)) |
(/ (sqrt 1/2) kx) |
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx) |
(/ (+ (sqrt 1/2) (* 1/12 (/ (pow kx 2) (sqrt 1/2)))) kx) |
(/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx) |
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
(/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 #s(literal 7/360 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx) |
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 #s(literal 31/15120 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) (/.f64 #s(literal 7/720 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 kx kx) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(fma.f64 (/.f64 (*.f64 (*.f64 kx kx) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 4/3 binary64)) (*.f64 kx (/.f64 kx (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 kx kx) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 4/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 8/45 binary64)) (*.f64 kx (/.f64 kx (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 4/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 kx kx) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (*.f64 kx kx) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(* kx (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) kx) |
(* kx (+ (sqrt 2) (* -1/3 (/ (pow kx 2) (sqrt 2))))) |
(*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx (/.f64 kx (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) kx) |
(* kx (+ (sqrt 2) (* (pow kx 2) (- (* 1/2 (/ (* (pow kx 2) (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/3 (/ 1 (sqrt 2))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (/.f64 #s(literal 1/30 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1/3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 kx kx) (sqrt.f64 #s(literal 2 binary64))) kx) |
(* kx (+ (sqrt 2) (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 2/315 (* -1/3 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/3 (/ 1 (sqrt 2))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (/.f64 #s(literal 1/1260 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/60 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 kx kx) (/.f64 #s(literal -1/3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 kx kx) (sqrt.f64 #s(literal 2 binary64))) kx) |
(* kx (pow (sqrt 2) 2)) |
(*.f64 #s(literal 2 binary64) kx) |
(* kx (+ (* -1/3 (pow kx 2)) (pow (sqrt 2) 2))) |
(*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) kx) |
(* kx (+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))))) 1/3)) (pow (sqrt 2) 2))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/30 binary64) (*.f64 kx kx)) #s(literal 1/2 binary64) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) kx) |
(* kx (+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (+ 2/315 (* -1/3 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (* 1/2 (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2))))))) 1/3)) (pow (sqrt 2) 2))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/1260 binary64) (*.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/60 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) kx) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)) |
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(fma.f64 (fma.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64)) |
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64)) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))) |
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(* 2 (* (* ky (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(* 1/2 (sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(literal 1/2 binary64)) |
(sin kx) |
(sin.f64 kx) |
(- 1 (cos (* 2 kx))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(sqrt (/ 1 (- 1 (cos (* 2 kx))))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky)))))) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(sqrt (- 1 (cos (* 2 kx)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))) |
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) |
(/ (* ky (sin th)) (sin kx)) |
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(*.f64 (fma.f64 (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)))) (*.f64 ky ky) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (sin.f64 th)) (fma.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))) (*.f64 ky ky)))) (*.f64 ky ky) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky) |
(/ (sin th) (sin kx)) |
(/.f64 (sin.f64 th) (sin.f64 kx)) |
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx))) |
(fma.f64 (*.f64 (*.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (sin.f64 kx))) |
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 ky ky)) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (sin.f64 kx)) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) |
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))) (/ (sin th) (sin kx))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 ky ky)) (*.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (sin.f64 th)) (sin.f64 kx)))) (*.f64 ky ky) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) |
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx)))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 ky ky) (sin.f64 kx)) |
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx)))))) |
(fma.f64 (fma.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (*.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx)) |
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (*.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 kx))) (*.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx)) |
(* 2 (* (* ky (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))))) ky) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) (*.f64 ky ky) (fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (*.f64 ky ky) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) ky) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (*.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -1 binary64) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64) (/.f64 #s(literal 2/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 #s(literal -1/12 binary64) (*.f64 (fma.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 1/2 binary64)))))) (fma.f64 (/.f64 (*.f64 #s(literal -1/240 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) (*.f64 ky ky) (fma.f64 (*.f64 (*.f64 (fma.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))))) (*.f64 ky ky) (*.f64 (fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(literal 2 binary64))) (*.f64 ky ky))) ky) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 1/2 binary64))))) ky) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
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(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
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(* 2 (* ky (sqrt 1/2))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64)) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 ky ky) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (*.f64 ky (/.f64 ky (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 ky ky))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/4 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal 1/4 binary64) (*.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 8/45 binary64)) (*.f64 ky (/.f64 ky (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 ky ky) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(* ky (sqrt 1/2)) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) |
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(fma.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 ky ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (*.f64 ky (/.f64 ky (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 8/45 binary64)) (*.f64 ky (/.f64 ky (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 ky ky) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(/ (sin kx) ky) |
(/.f64 (sin.f64 kx) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky) |
(/.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx)) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (sin.f64 kx)) #s(literal -1/2 binary64) (fma.f64 #s(literal 7/360 binary64) (sin.f64 kx) (/.f64 #s(literal 1/12 binary64) (sin.f64 kx)))) (*.f64 ky ky) (fma.f64 #s(literal 1/6 binary64) (sin.f64 kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)))) (*.f64 ky ky) (sin.f64 kx)) ky) |
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (sin.f64 kx)) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (sin.f64 kx)) #s(literal -1/12 binary64) (fma.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (sin.f64 kx)) #s(literal 1/2 binary64) (fma.f64 #s(literal 31/15120 binary64) (sin.f64 kx) (/.f64 #s(literal 7/720 binary64) (sin.f64 kx))))) (*.f64 ky ky) (fma.f64 #s(literal 7/360 binary64) (sin.f64 kx) (/.f64 #s(literal 1/12 binary64) (sin.f64 kx))))) (*.f64 ky ky) (fma.f64 #s(literal 1/6 binary64) (sin.f64 kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)))) (*.f64 ky ky) (sin.f64 kx)) ky) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (*.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 th th) (sin.f64 ky))))) (*.f64 th th) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th) |
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) |
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) |
(*.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th) |
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 th th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th) |
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/6 binary64))) (*.f64 th th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th) |
th |
(* th (+ 1 (* -1/6 (pow th 2)))) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th) |
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th) |
(+ 1 (* -1/6 (pow th 2))) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(pow th 2) |
(*.f64 th th) |
(* 2 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(* th (+ (* -1/3 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (*.f64 #s(literal 2 binary64) (sin.f64 ky)))) th) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal 1/60 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (*.f64 #s(literal -1/3 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) th) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/2520 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal 1/60 binary64) (sin.f64 ky) (*.f64 #s(literal -1/2520 binary64) (*.f64 (*.f64 th th) (sin.f64 ky))))) (*.f64 th th) (*.f64 (*.f64 #s(literal -1/3 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 th th) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) th) |
(* -1/6 (pow th 2)) |
(*.f64 (*.f64 th th) #s(literal -1/6 binary64)) |
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6)) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(* -1/6 (pow th 3)) |
(*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)) |
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6)) |
(*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))) |
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2))))) |
(*.f64 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 th th)))) (pow.f64 th #s(literal 3 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 386 |
| 0 | 93 | 376 |
| 1 | 310 | 357 |
| 2 | 1880 | 331 |
| 0 | 8739 | 317 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(sin.f64 th) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(*.f64 th th) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
#s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) |
(/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(sin.f64 ky) |
(/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(sin.f64 kx) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) |
#s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) |
| Outputs |
|---|
(*.f64 (/.f64 (neg.f64 (sin.f64 th)) #s(literal -1 binary64)) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 ky) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64))) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) #s(literal 1 binary64)) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 th) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sin.f64 th) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sin.f64 th) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (sin.f64 ky) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (/.f64 (sin.f64 ky) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))) |
(*.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) (sin.f64 th))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 th)) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (sin.f64 ky))) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 ky) (neg.f64 (sin.f64 th)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (sin.f64 ky) (sin.f64 th)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 ky) #s(literal 1 binary64))) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))) |
(/.f64 (*.f64 (neg.f64 (sin.f64 th)) (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (*.f64 (sin.f64 ky) (neg.f64 (sin.f64 th))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
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(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) |
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (sin.f64 ky))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sqrt.f64 (sin.f64 ky))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (sin.f64 ky))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 (sin.f64 ky)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 (sin.f64 ky))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (sin.f64 ky)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) #s(literal 1/4 binary64)) (sin.f64 ky)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sin.f64 ky))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sqrt.f64 (sin.f64 ky)))) |
(*.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sqrt.f64 (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sin.f64 ky)))) |
(*.f64 (/.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) (/.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky)))) |
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(*.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) |
(*.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal 1 binary64)) |
(pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 1 binary64))) (neg.f64 (sin.f64 ky))) |
(/.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 1 binary64)) (sin.f64 ky)) |
(/.f64 (neg.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (neg.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) (neg.f64 (*.f64 (sin.f64 ky) #s(literal -2 binary64)))) |
(/.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (neg.f64 (*.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (*.f64 (sin.f64 ky) #s(literal -2 binary64))) |
(/.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky))))) |
(/.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (*.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (neg.f64 (sin.f64 ky)))) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) |
(neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (sin.f64 ky) #s(literal -2 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (*.f64 (sin.f64 ky) #s(literal -2 binary64)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 ky))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (log.f64 (sin.f64 ky)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(literal -1 binary64))) |
Compiled 42 696 to 4 420 computations (89.6% saved)
64 alts after pruning (61 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 969 | 38 | 1 007 |
| Fresh | 11 | 23 | 34 |
| Picked | 3 | 2 | 5 |
| Done | 1 | 1 | 2 |
| Total | 984 | 64 | 1 048 |
| Status | Accuracy | Program |
|---|---|---|
| 55.4% | (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) | |
| 71.1% | (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) | |
| 31.7% | (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) | |
| 27.1% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) | |
| ▶ | 36.6% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
| 36.5% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) | |
| 17.2% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) | |
| 31.4% | (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) | |
| 28.0% | (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) | |
| 70.7% | (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (sin.f64 th)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) | |
| 45.4% | (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) | |
| 71.2% | (*.f64 (/.f64 (*.f64 (sin.f64 ky) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) | |
| ✓ | 99.6% | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
| 55.4% | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) | |
| 63.6% | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) | |
| ▶ | 71.2% | (*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
| 28.2% | (*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) | |
| 70.9% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 36.6% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 38.2% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 31.0% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) | |
| ▶ | 15.8% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
| 26.5% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 30.7% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 26.6% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 30.8% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 46.7% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) | |
| 32.0% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) | |
| 30.9% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) | |
| 30.7% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) | |
| 50.0% | (*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) | |
| 27.2% | (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 26.6% | (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 34.2% | (*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) | |
| 30.9% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) | |
| 26.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1/2 binary64)))) (sin.f64 th)) | |
| 26.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) | |
| ✓ | 26.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
| 13.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| 13.6% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| 13.6% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 38.1% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) | |
| 21.3% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) | |
| 19.2% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) | |
| 20.8% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) | |
| 26.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -1/2 binary64))))) (sin.f64 th)) | |
| ▶ | 21.6% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
| 25.6% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) | |
| 20.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) | |
| 21.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) | |
| 25.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) | |
| 31.7% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) | |
| 26.5% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) | |
| 70.9% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) | |
| 36.5% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) | |
| ✓ | 28.3% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
| 16.3% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| 16.2% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| 16.4% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) | |
| 16.4% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 15.7% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) | |
| ▶ | 10.7% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
| 6.8% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) | |
| 10.7% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
Compiled 4 655 to 3 327 computations (28.5% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) | |
| cost-diff | 0 | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) | |
| cost-diff | 128 | (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) | |
| cost-diff | 192 | (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) | |
| cost-diff | 0 | (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| cost-diff | 0 | (sin.f64 ky) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| cost-diff | 384 | (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) | |
| cost-diff | 0 | (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx))) | |
| cost-diff | 0 | #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) | |
| cost-diff | 0 | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) | |
| cost-diff | 0 | #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th) | |
| cost-diff | 0 | #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)) | |
| cost-diff | 0 | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) | |
| cost-diff | 0 | (sin.f64 th) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) | |
| cost-diff | 128 | (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) | |
| cost-diff | 192 | (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 77 | 826 |
| 0 | 119 | 814 |
| 1 | 188 | 814 |
| 2 | 310 | 778 |
| 3 | 546 | 772 |
| 4 | 858 | 772 |
| 5 | 1285 | 772 |
| 6 | 1678 | 772 |
| 7 | 1961 | 772 |
| 8 | 2040 | 772 |
| 9 | 2046 | 772 |
| 10 | 2047 | 772 |
| 0 | 2047 | 745 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) |
(sin.f64 th) |
th |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
#s(literal 2 binary64) |
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
#s(literal 1 binary64) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(*.f64 #s(literal 2 binary64) kx) |
kx |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(cos.f64 (*.f64 #s(literal 2 binary64) ky)) |
(*.f64 #s(literal 2 binary64) ky) |
ky |
#s(literal 1/2 binary64) |
(sin.f64 ky) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)) |
(*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th) |
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) |
(*.f64 (*.f64 th th) #s(literal -1/6 binary64)) |
(*.f64 th th) |
th |
#s(literal -1/6 binary64) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
#s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
ky |
#s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)) |
(/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx) |
(fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
#s(literal 1/12 binary64) |
(*.f64 kx kx) |
kx |
(sin.f64 th) |
th |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) |
(sin.f64 ky) |
ky |
(/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) |
#s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
#s(literal 1 binary64) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(*.f64 #s(literal 2 binary64) kx) |
#s(literal 2 binary64) |
kx |
(sqrt.f64 #s(literal 2 binary64)) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(*.f64 th th) |
th |
#s(literal -1/6 binary64) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(*.f64 th th) |
th |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky)) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
#s(literal 2 binary64) |
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(*.f64 #s(literal 2 binary64) kx) |
kx |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(cos.f64 (*.f64 #s(literal 2 binary64) ky)) |
(*.f64 #s(literal 2 binary64) ky) |
ky |
#s(literal 1/2 binary64) |
(sin.f64 ky) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(/.f64 (*.f64 (/.f64 (sin.f64 th) #s(literal 1/2 binary64)) (sin.f64 ky)) (sqrt.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)))) |
(/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) |
(/.f64 (/.f64 (sin.f64 th) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)))) |
(sin.f64 th) |
th |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)))) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(sqrt.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64))) |
(*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
(fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) |
#s(literal 2 binary64) |
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) |
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) |
#s(literal 1 binary64) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(cos.f64 (*.f64 kx #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) kx) |
(*.f64 kx #s(literal 2 binary64)) |
kx |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) |
(cos.f64 (*.f64 #s(literal 2 binary64) ky)) |
(cos.f64 (*.f64 ky #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) ky) |
(*.f64 ky #s(literal 2 binary64)) |
ky |
#s(literal 1/2 binary64) |
(sin.f64 ky) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)) |
(*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th) |
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) |
(*.f64 (*.f64 th th) #s(literal -1/6 binary64)) |
(*.f64 th th) |
th |
#s(literal -1/6 binary64) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal 1/12 binary64) kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64)))) (sin.f64 th)) |
#s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) |
#s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal 1/12 binary64) kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx))) |
(*.f64 #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal 1/12 binary64) kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
ky |
#s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)) |
#s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal 1/12 binary64) kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)) |
(/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx) |
(/.f64 (fma.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal 1/12 binary64) kx) (sqrt.f64 #s(literal 1/2 binary64))) kx) |
(fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) |
(fma.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal 1/12 binary64) kx) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
#s(literal 1/12 binary64) |
(*.f64 kx kx) |
kx |
(sin.f64 th) |
th |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 (*.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))) #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) |
(/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) |
(/.f64 (*.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) |
(sin.f64 ky) |
ky |
(/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))))))) #s(literal 2 binary64)) |
#s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))))))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) |
#s(literal 1 binary64) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(cos.f64 (*.f64 kx #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) kx) |
(*.f64 kx #s(literal 2 binary64)) |
#s(literal 2 binary64) |
kx |
(sqrt.f64 #s(literal 2 binary64)) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(*.f64 th th) |
th |
#s(literal -1/6 binary64) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 (*.f64 (/.f64 (sin.f64 ky) #s(literal 1/2 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))) (sqrt.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)))) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(*.f64 th th) |
th |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)))) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(sqrt.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64))) |
(*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
(fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) |
#s(literal 2 binary64) |
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) |
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) |
(cos.f64 (*.f64 #s(literal 2 binary64) kx)) |
(cos.f64 (*.f64 kx #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) kx) |
(*.f64 kx #s(literal 2 binary64)) |
kx |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) |
(cos.f64 (*.f64 #s(literal 2 binary64) ky)) |
(cos.f64 (*.f64 ky #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) ky) |
(*.f64 ky #s(literal 2 binary64)) |
ky |
#s(literal 1/2 binary64) |
(sin.f64 ky) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 4.432331053242653 | (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) | |
| accuracy | 15.751578029588966 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) | |
| accuracy | 17.8247072510061 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) | |
| accuracy | 31.893200456091343 | #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) | |
| accuracy | 15.417151017429484 | (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) | |
| accuracy | 17.8247072510061 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) | |
| accuracy | 31.893200456091343 | #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) | |
| accuracy | 33.69329853099764 | #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) | |
| accuracy | 1.0 | (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) | |
| accuracy | 13.376061736487113 | (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx) | |
| accuracy | 26.563431610847967 | #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)) | |
| accuracy | 36.563990987778865 | #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) | |
| accuracy | 0.15234375 | (*.f64 (*.f64 th th) #s(literal -1/6 binary64)) | |
| accuracy | 31.044919334916923 | #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) | |
| accuracy | 31.893200456091343 | #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)) | |
| accuracy | 45.90212724970163 | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) | |
| accuracy | 0.24609375 | (*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) | |
| accuracy | 4.432331053242653 | (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) | |
| accuracy | 15.751578029588966 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) | |
| accuracy | 17.8247072510061 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
| 254.0ms | 116× | 2 | valid |
| 88.0ms | 75× | 1 | valid |
| 38.0ms | 53× | 0 | valid |
| 21.0ms | 12× | 3 | valid |
Compiled 1 455 to 141 computations (90.3% saved)
ival-cos: 132.0ms (39.7% of total)ival-mult: 51.0ms (15.3% of total)adjust: 29.0ms (8.7% of total)ival-div: 28.0ms (8.4% of total)ival-sqrt: 23.0ms (6.9% of total)ival-sin: 23.0ms (6.9% of total)const: 15.0ms (4.5% of total)ival-add: 14.0ms (4.2% of total)ival-sub: 9.0ms (2.7% of total)ival-pow2: 9.0ms (2.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) |
(*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(sin.f64 th) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)) |
(*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th) |
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
#s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) |
(/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(sin.f64 ky) |
(/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(*.f64 (*.f64 th th) #s(literal -1/6 binary64)) |
#s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)) |
(/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx) |
(/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
#s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
| Outputs |
|---|
(- 1 (cos (* 2 ky))) |
(- (+ 1 (* 2 (pow kx 2))) (cos (* 2 ky))) |
(- (+ 1 (* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))) (cos (* 2 ky))) |
(- (+ 1 (* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))) (cos (* 2 ky))) |
(* 2 (- 1 (cos (* 2 ky)))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* 4 (pow kx 2))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3))))) |
(* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (- 1 (cos (* 2 ky))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(sin th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
(* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (sin ky)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(* 2 (/ (* ky (pow (sqrt 1/2) 2)) kx)) |
(/ (+ (* 1/6 (* (pow kx 2) ky)) (* 2 (* ky (pow (sqrt 1/2) 2)))) kx) |
(/ (+ (* 2 (* ky (pow (sqrt 1/2) 2))) (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (* ky (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))))))) kx) |
(/ (+ (* 2 (* ky (pow (sqrt 1/2) 2))) (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (+ (* ky (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (* (pow kx 2) (* ky (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))))))))) kx) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/4 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/4 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(* 2 (pow kx 2)) |
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (* (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sqrt 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/2 (* (* (sqrt 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 ky)))))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (* (pow kx 2) (* (sqrt 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))) (- 1 (cos (* 2 ky)))))))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(/ (sqrt 1/2) kx) |
(/ (+ (sqrt 1/2) (* 1/12 (/ (pow kx 2) (sqrt 1/2)))) kx) |
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(* kx (sqrt 2)) |
(* kx (+ (sqrt 2) (* -1/3 (/ (pow kx 2) (sqrt 2))))) |
(* kx (+ (sqrt 2) (* (pow kx 2) (- (* 1/2 (/ (* (pow kx 2) (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/3 (/ 1 (sqrt 2))))))) |
(* kx (+ (sqrt 2) (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 2/315 (* -1/3 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/3 (/ 1 (sqrt 2))))))) |
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))) |
(* 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))) |
(* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* 2 (* (* ky (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* 1/2 (sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))) |
(- 1 (cos (* 2 kx))) |
(* (sqrt 2) (sqrt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))) |
(sqrt (/ 1 (- 1 (cos (* 2 kx))))) |
(* 1/12 (/ kx (sqrt 1/2))) |
(* kx (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) (pow kx 2)))) |
(sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky)))))) |
(sqrt (- 1 (cos (* 2 kx)))) |
(* -1 (* kx (- (* -1 (/ (sqrt 1/2) (pow kx 2))) (* 1/12 (/ 1 (sqrt 1/2)))))) |
(- (+ 1 (* 2 (pow ky 2))) (cos (* 2 kx))) |
(- (+ 1 (* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))) (cos (* 2 kx))) |
(- (+ 1 (* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))) (cos (* 2 kx))) |
(* 2 (- 1 (cos (* 2 kx)))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 4 (pow ky 2))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* -4/3 (pow ky 2))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* (pow ky 2) (- (* 8/45 (pow ky 2)) 4/3))))) |
(* 2 (* (/ (* ky (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(/ (* ky (sin th)) (sin kx)) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(* 2 (* (* ky (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(* 2 (* ky (sqrt 1/2))) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/4 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* 2 (pow ky 2)) |
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2)))) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3)))) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (* (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (* (sqrt 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (* (sqrt 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx)))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (* (pow ky 2) (* (sqrt 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(sin ky) |
(* 2 (* (/ (* th (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) |
(* th (+ (* -1/3 (* (/ (* (pow th 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))) |
(* th (+ (* 2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/3 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/60 (* (/ (* (pow th 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))))) |
(* th (+ (* 2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/3 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/2520 (* (/ (* (pow th 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/60 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))))))) |
th |
(* th (+ 1 (* -1/6 (pow th 2)))) |
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6)))) |
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6)))) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
1 |
(+ 1 (* -1/6 (pow th 2))) |
(* 2 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* th (+ (* -1/3 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/2520 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))))) |
(* -1/6 (pow th 2)) |
(* -1/6 (pow th 3)) |
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6)) |
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6)) |
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2))))) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 34.0ms | ky | @ | inf | ((+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* 2 (* (sqrt 1/2) ky)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (/ (sin th) (/ (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2) (sin ky))) (sin th) (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))) (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (* (* th th) -1/6) (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (/ 1/12 (sqrt 1/2)) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt (- 1 (cos (* 2 kx))))) |
| 26.0ms | kx | @ | -inf | ((+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* 2 (* (sqrt 1/2) ky)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (/ (sin th) (/ (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2) (sin ky))) (sin th) (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))) (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (* (* th th) -1/6) (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (/ 1/12 (sqrt 1/2)) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt (- 1 (cos (* 2 kx))))) |
| 8.0ms | kx | @ | inf | ((+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* 2 (* (sqrt 1/2) ky)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (/ (sin th) (/ (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2) (sin ky))) (sin th) (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))) (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (* (* th th) -1/6) (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (/ 1/12 (sqrt 1/2)) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt (- 1 (cos (* 2 kx))))) |
| 8.0ms | ky | @ | 0 | ((+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* 2 (* (sqrt 1/2) ky)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (/ (sin th) (/ (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2) (sin ky))) (sin th) (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))) (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (* (* th th) -1/6) (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (/ 1/12 (sqrt 1/2)) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt (- 1 (cos (* 2 kx))))) |
| 8.0ms | ky | @ | -inf | ((+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* 2 (* (sqrt 1/2) ky)) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (/ (sin th) (/ (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2) (sin ky))) (sin th) (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))) (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (* (* th th) -1/6) (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (/ 1/12 (sqrt 1/2)) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt (- 1 (cos (* 2 kx))))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 904 | 6412 |
| 1 | 3057 | 5778 |
| 0 | 8008 | 5566 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- 1 (cos (* 2 ky))) |
(- (+ 1 (* 2 (pow kx 2))) (cos (* 2 ky))) |
(- (+ 1 (* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))) (cos (* 2 ky))) |
(- (+ 1 (* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))) (cos (* 2 ky))) |
(* 2 (- 1 (cos (* 2 ky)))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* 4 (pow kx 2))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3))))) |
(* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (- 1 (cos (* 2 ky))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(sin th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
(* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -1 (* (/ (* (pow kx 2) (sin ky)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(* 2 (/ (* ky (pow (sqrt 1/2) 2)) kx)) |
(/ (+ (* 1/6 (* (pow kx 2) ky)) (* 2 (* ky (pow (sqrt 1/2) 2)))) kx) |
(/ (+ (* 2 (* ky (pow (sqrt 1/2) 2))) (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (* ky (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))))))) kx) |
(/ (+ (* 2 (* ky (pow (sqrt 1/2) 2))) (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (+ (* ky (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (* (pow kx 2) (* ky (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))))))))) kx) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/4 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/4 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(* 2 (pow kx 2)) |
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3)))) |
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (* (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sqrt 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/2 (* (* (sqrt 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 ky)))))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (* (pow kx 2) (* (sqrt 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))) (- 1 (cos (* 2 ky)))))))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(/ (sqrt 1/2) kx) |
(/ (+ (sqrt 1/2) (* 1/12 (/ (pow kx 2) (sqrt 1/2)))) kx) |
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))))) |
(* kx (sqrt 2)) |
(* kx (+ (sqrt 2) (* -1/3 (/ (pow kx 2) (sqrt 2))))) |
(* kx (+ (sqrt 2) (* (pow kx 2) (- (* 1/2 (/ (* (pow kx 2) (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/3 (/ 1 (sqrt 2))))))) |
(* kx (+ (sqrt 2) (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 2/315 (* -1/3 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/45 (* 1/9 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/3 (/ 1 (sqrt 2))))))) |
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))) |
(* 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))) |
(* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* 2 (* (* ky (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* 1/2 (sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))) |
(- 1 (cos (* 2 kx))) |
(* (sqrt 2) (sqrt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))) |
(sqrt (/ 1 (- 1 (cos (* 2 kx))))) |
(* 1/12 (/ kx (sqrt 1/2))) |
(* kx (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) (pow kx 2)))) |
(sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky)))))) |
(sqrt (- 1 (cos (* 2 kx)))) |
(* -1 (* kx (- (* -1 (/ (sqrt 1/2) (pow kx 2))) (* 1/12 (/ 1 (sqrt 1/2)))))) |
(- (+ 1 (* 2 (pow ky 2))) (cos (* 2 kx))) |
(- (+ 1 (* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))) (cos (* 2 kx))) |
(- (+ 1 (* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))) (cos (* 2 kx))) |
(* 2 (- 1 (cos (* 2 kx)))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 4 (pow ky 2))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* -4/3 (pow ky 2))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* (pow ky 2) (- (* 8/45 (pow ky 2)) 4/3))))) |
(* 2 (* (/ (* ky (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(/ (* ky (sin th)) (sin kx)) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(* 2 (* (* ky (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(* 2 (* ky (sqrt 1/2))) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/4 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* 2 (pow ky 2)) |
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2)))) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3)))) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3)))) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (* (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (* (sqrt 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (* (sqrt 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx)))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (* (pow ky 2) (* (sqrt 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(sin ky) |
(* 2 (* (/ (* th (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) |
(* th (+ (* -1/3 (* (/ (* (pow th 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))) |
(* th (+ (* 2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/3 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/60 (* (/ (* (pow th 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))))) |
(* th (+ (* 2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/3 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/2520 (* (/ (* (pow th 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/60 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))))))) |
th |
(* th (+ 1 (* -1/6 (pow th 2)))) |
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6)))) |
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6)))) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
1 |
(+ 1 (* -1/6 (pow th 2))) |
(* 2 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* th (+ (* -1/3 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/2520 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))))) |
(* -1/6 (pow th 2)) |
(* -1/6 (pow th 3)) |
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6)) |
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6)) |
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2))))) |
| Outputs |
|---|
(- 1 (cos (* 2 ky))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(- (+ 1 (* 2 (pow kx 2))) (cos (* 2 ky))) |
(-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(- (+ 1 (* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))) (cos (* 2 ky))) |
(-.f64 (fma.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(- (+ 1 (* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))) (cos (* 2 ky))) |
(-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(* 2 (- 1 (cos (* 2 ky)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* 4 (pow kx 2))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 4 binary64) (*.f64 kx kx))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 kx kx) #s(literal 4 binary64)) (*.f64 kx kx))) |
(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3))))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal 8/45 binary64) (*.f64 kx kx) #s(literal -4/3 binary64)) (*.f64 kx kx) #s(literal 4 binary64)) (*.f64 kx kx))) |
(* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(fma.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 kx kx) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(+ (* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
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(+ (* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (- 1 (cos (* 2 ky))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
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(sin th) |
(sin.f64 th) |
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) |
(fma.f64 (/.f64 (*.f64 (*.f64 kx kx) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (sin.f64 th)) |
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) |
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(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) |
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(* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
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(+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(fma.f64 (neg.f64 (/.f64 (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (*.f64 kx kx)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 kx kx) (sin.f64 ky)) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 1/2 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (*.f64 (neg.f64 (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))))) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(+ (* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (* (sin ky) (sin th)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (fma.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (sin.f64 th)) (/.f64 (sin.f64 ky) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 (*.f64 (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) (/.f64 #s(literal 2/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))))) (*.f64 kx (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64)))))))) (*.f64 kx kx) (*.f64 (neg.f64 (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))))) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(+ (* -1 (* (/ (* (pow kx 2) (sin ky)) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(fma.f64 (neg.f64 (/.f64 (*.f64 (*.f64 kx kx) (sin.f64 ky)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))) |
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(+ (* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1 (* (/ (sin ky) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))) (* (/ (* (sin ky) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 ky)))))))))) |
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(* (sqrt 2) (sqrt (- 1 (cos (* 2 ky))))) |
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(/ (sqrt 1/2) kx) |
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(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx) |
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(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 ky)))))) |
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(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))) |
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(* 2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) |
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
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(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
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(* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
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(* 2 (* (* ky (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
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(* 1/2 (sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))) |
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(- 1 (cos (* 2 kx))) |
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(* (sqrt 2) (sqrt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))) |
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(sqrt (/ 1 (- 1 (cos (* 2 kx))))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(* 1/12 (/ kx (sqrt 1/2))) |
(*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)) |
(* kx (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) (pow kx 2)))) |
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(sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky)))))) |
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(sqrt (- 1 (cos (* 2 kx)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(* -1 (* kx (- (* -1 (/ (sqrt 1/2) (pow kx 2))) (* 1/12 (/ 1 (sqrt 1/2)))))) |
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(- (+ 1 (* 2 (pow ky 2))) (cos (* 2 kx))) |
(-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(- (+ 1 (* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))) (cos (* 2 kx))) |
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(- (+ 1 (* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))) (cos (* 2 kx))) |
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(* 2 (- 1 (cos (* 2 kx)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 4 (pow ky 2))) |
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(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* -4/3 (pow ky 2))))) |
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(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* (pow ky 2) (- (* 8/45 (pow ky 2)) 4/3))))) |
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(* 2 (* (/ (* ky (sin th)) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
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(* ky (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
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(* ky (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
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(* ky (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
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(/ (* ky (sin th)) (sin kx)) |
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) |
(*.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (/.f64 (*.f64 (sin.f64 th) #s(literal 1/12 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky) |
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (sin.f64 th)) (fma.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (fma.f64 #s(literal -1/240 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/5040 binary64)) (sin.f64 kx))))) (*.f64 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (/.f64 (*.f64 (sin.f64 th) #s(literal 1/12 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky) |
(* 2 (* (* ky (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 ky ky) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) ky) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (*.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) (*.f64 ky ky) (fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (*.f64 ky ky) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) ky) |
(* ky (+ (* 2 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* (sin th) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ (sin th) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 #s(literal -1/12 binary64) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 1/2 binary64)))))) (fma.f64 (/.f64 (*.f64 #s(literal -1/240 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) (*.f64 ky ky) (fma.f64 (*.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))))) (*.f64 ky ky) (*.f64 (fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(literal 2 binary64))) (*.f64 ky ky) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) ky) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 ky ky) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) ky) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 1/120 binary64) (fma.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))))))) (*.f64 ky ky) (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (*.f64 ky ky) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) ky) |
(* ky (+ (* 2 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -1/2 (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/240 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/12 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 1/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 1/2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))) |
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(* 2 (* ky (sqrt 1/2))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky) #s(literal 2 binary64)) |
ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky) |
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 ky ky) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky) |
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 ky ky) #s(literal 1/120 binary64)) (*.f64 ky ky) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky) |
(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 ky ky) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (*.f64 ky (/.f64 ky (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 ky ky))) |
(+ (* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/4 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/4 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal 1/4 binary64) (*.f64 (-.f64 #s(literal 8/45 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (*.f64 ky (/.f64 ky (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 ky ky) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(* 2 (pow ky 2)) |
(*.f64 (*.f64 ky ky) #s(literal 2 binary64)) |
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2)))) |
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky)) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) (*.f64 ky ky) #s(literal 2 binary64)) (*.f64 ky ky)) |
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) (*.f64 ky ky) #s(literal -2/3 binary64)) (*.f64 ky ky) #s(literal 2 binary64)) (*.f64 ky ky)) |
(* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (* (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(fma.f64 (*.f64 (*.f64 ky ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (* (sqrt 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (+.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 ky ky)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 ky ky) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (* (sqrt 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx)))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (* (pow ky 2) (* (sqrt 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 ky ky) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/45 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 ky ky) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
(fma.f64 (/.f64 (*.f64 (*.f64 ky ky) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (*.f64 ky (/.f64 ky (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 8/45 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (*.f64 ky (/.f64 ky (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 4/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 ky ky) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(sin ky) |
(sin.f64 ky) |
(* 2 (* (/ (* th (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) |
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(* th (+ (* -1/3 (* (/ (* (pow th 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal 2 binary64) (/.f64 (sin.f64 ky) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1/3 binary64) (/.f64 (*.f64 (*.f64 th th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))))) th) |
(* th (+ (* 2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/3 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/60 (* (/ (* (pow th 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal 1/60 binary64) (/.f64 (*.f64 (*.f64 th th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 th th) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) th) |
(* th (+ (* 2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/3 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/2520 (* (/ (* (pow th 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/60 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (fma.f64 #s(literal 1/60 binary64) (/.f64 (sin.f64 ky) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1/2520 binary64) (/.f64 (*.f64 (*.f64 th th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 th th) (*.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (*.f64 th th) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) th) |
th |
(* th (+ 1 (* -1/6 (pow th 2)))) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th) |
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th) |
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) |
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th) |
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (*.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 th th) (sin.f64 ky))))) (*.f64 th th) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/6 (pow th 2))) |
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(* 2 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(* th (+ (* -1/3 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (*.f64 #s(literal 2 binary64) (sin.f64 ky)))) th) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal 1/60 binary64) (*.f64 (*.f64 th th) (sin.f64 ky)) (*.f64 #s(literal -1/3 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) th) |
(* th (+ (* 2 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/3 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/2520 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) (* 1/60 (* (sin ky) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal 1/60 binary64) (sin.f64 ky) (*.f64 #s(literal -1/2520 binary64) (*.f64 (*.f64 th th) (sin.f64 ky))))) (*.f64 th th) (*.f64 (*.f64 #s(literal -1/3 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 th th) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) th) |
(* -1/6 (pow th 2)) |
(*.f64 (*.f64 th th) #s(literal -1/6 binary64)) |
(* -1/6 (pow th 3)) |
(*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)) |
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6)) |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))) |
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6)) |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th)) |
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2))))) |
(*.f64 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 th th)))) (pow.f64 th #s(literal 3 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 77 | 539 |
| 0 | 119 | 523 |
| 1 | 395 | 519 |
| 2 | 2356 | 519 |
| 0 | 8602 | 504 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) |
(*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(sin.f64 th) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)) |
(*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th) |
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
#s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) |
(/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(sin.f64 ky) |
(/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(*.f64 (*.f64 th th) #s(literal -1/6 binary64)) |
#s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)) |
(/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx) |
(/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
#s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
| Outputs |
|---|
(*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64))) (pow.f64 (+.f64 (expm1.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx))))) (cos.f64 (+.f64 ky ky))) #s(literal -1 binary64))) |
(*.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (+.f64 (expm1.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx))))) (cos.f64 (+.f64 ky ky))) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (+.f64 (expm1.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx))))) (cos.f64 (+.f64 ky ky)))) (*.f64 (+.f64 (expm1.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx))))) (cos.f64 (+.f64 ky ky))) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64)))) (*.f64 (+.f64 (expm1.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx))))) (cos.f64 (+.f64 ky ky))) (+.f64 (expm1.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx))))) (cos.f64 (+.f64 ky ky))))) |
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(/.f64 (-.f64 (*.f64 (expm1.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) (+.f64 (pow.f64 (cos.f64 ky) #s(literal 4 binary64)) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (cos.f64 ky) (sin.f64 ky)) #s(literal 2 binary64))))) (*.f64 (expm1.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx))))) (-.f64 (pow.f64 (cos.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (*.f64 (expm1.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx))))) (+.f64 (pow.f64 (cos.f64 ky) #s(literal 4 binary64)) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (cos.f64 ky) (sin.f64 ky)) #s(literal 2 binary64)))))) |
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(/.f64 (*.f64 (neg.f64 (sin.f64 th)) (sin.f64 ky)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
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#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) |
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(pow.f64 (*.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))) |
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(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) #s(literal 1 binary64))) |
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(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))) #s(literal 2 binary64)) |
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(/.f64 (fabs.f64 (sin.f64 (*.f64 kx #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 kx kx)))))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)))) (sqrt.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sqrt.f64 #s(literal -1 binary64))) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 kx)) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) (pow.f64 (sin.f64 (*.f64 kx #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)))))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 kx)) #s(literal -1 binary64))) |
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) |
(hypot.f64 (sin.f64 kx) (sin.f64 kx)) |
(exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))) |
Compiled 73 930 to 6 239 computations (91.6% saved)
86 alts after pruning (81 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 192 | 37 | 1 229 |
| Fresh | 12 | 44 | 56 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 3 | 3 |
| Total | 1 207 | 86 | 1 293 |
| Status | Accuracy | Program |
|---|---|---|
| 36.4% | (/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) | |
| 55.4% | (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) | |
| 31.7% | (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) | |
| 71.0% | (/.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sin.f64 th)))) | |
| 27.1% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) | |
| 36.6% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) | |
| 20.9% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) | |
| 16.1% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) | |
| 15.8% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) | |
| 16.1% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) | |
| 15.8% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) | |
| 36.5% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) | |
| 17.2% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) | |
| 31.4% | (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) | |
| 28.0% | (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) | |
| ✓ | 99.6% | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
| 55.4% | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) | |
| 63.6% | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) | |
| 71.0% | (*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64)) (cos.f64 (+.f64 kx kx))))) #s(literal 1/2 binary64))) (sin.f64 ky)) | |
| 71.1% | (*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64))) (sin.f64 ky)) | |
| 28.5% | (*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) | |
| 31.0% | (*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) | |
| 30.7% | (*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) | |
| 31.0% | (*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) | |
| 30.7% | (*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) | |
| 28.2% | (*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) | |
| 13.8% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 26.5% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 15.3% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 30.7% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 26.6% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 30.8% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 46.7% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) | |
| 32.0% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) | |
| 30.9% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) | |
| 16.1% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 15.8% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 50.0% | (*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) | |
| 27.2% | (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 26.6% | (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 13.4% | (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 36.6% | (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 70.9% | (*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) | |
| 36.6% | (*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) | |
| 36.5% | (*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) | |
| 36.4% | (*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) | |
| 71.1% | (*.f64 (sin.f64 th) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky))) | |
| 34.2% | (*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) | |
| 21.6% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) | |
| 30.9% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) | |
| 26.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1/2 binary64)))) (sin.f64 th)) | |
| 26.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) | |
| ✓ | 26.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
| 13.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| 13.6% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| 13.6% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 38.1% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) | |
| 19.2% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) | |
| 20.8% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) | |
| 26.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -1/2 binary64))))) (sin.f64 th)) | |
| ✓ | 21.6% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
| 10.8% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| 10.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| 10.9% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 25.6% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) | |
| 8.9% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) | |
| 20.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) | |
| 21.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) | |
| 25.7% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) | |
| 31.7% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) | |
| 26.6% | #s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) | |
| 30.7% | #s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) | |
| 26.5% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) | |
| 70.9% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) | |
| 36.5% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) | |
| ✓ | 28.3% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
| 16.3% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) | |
| 16.4% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) | |
| 16.4% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 15.7% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) | |
| 8.2% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) | |
| ✓ | 10.7% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
| 10.7% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) | |
| 16.6% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) | |
| 6.8% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) | |
| 10.7% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
Compiled 7 862 to 3 053 computations (61.2% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
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#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -1/2 binary64))))) (sin.f64 th)) |
(*.f64 (sin.f64 th) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky))) |
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64)) (cos.f64 (+.f64 kx kx))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (*.f64 (sin.f64 ky) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(literal 2 binary64)) |
(/.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sin.f64 th)))) |
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 (sin.f64 ky) #s(literal 1/2 binary64))) |
(/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (sin.f64 th)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(*.f64 (neg.f64 (sin.f64 ky)) (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) |
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) |
(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))) |
| Outputs |
|---|
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
9 calls:
| 45.0ms | (sin.f64 ky) |
| 43.0ms | kx |
| 38.0ms | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 37.0ms | (sin.f64 th) |
| 37.0ms | th |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | kx |
| 99.7% | 1 | ky |
| 99.7% | 1 | th |
| 99.7% | 1 | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 99.7% | 1 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 99.7% | 1 | (sin.f64 ky) |
| 99.7% | 1 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 99.7% | 1 | (sin.f64 kx) |
| 99.7% | 1 | (sin.f64 th) |
Compiled 42 to 51 computations (-21.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
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#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
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(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -1/2 binary64))))) (sin.f64 th)) |
(*.f64 (sin.f64 th) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky))) |
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64)) (cos.f64 (+.f64 kx kx))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (*.f64 (sin.f64 ky) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(literal 2 binary64)) |
(/.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sin.f64 th)))) |
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 (sin.f64 ky) #s(literal 1/2 binary64))) |
(/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (sin.f64 th)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
9 calls:
| 61.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 46.0ms | (sin.f64 th) |
| 37.0ms | kx |
| 37.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 36.0ms | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | th |
| 99.6% | 1 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 99.6% | 1 | kx |
| 99.6% | 1 | ky |
| 99.6% | 1 | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 99.6% | 1 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 99.6% | 1 | (sin.f64 ky) |
| 99.6% | 1 | (sin.f64 kx) |
| 99.6% | 1 | (sin.f64 th) |
Compiled 42 to 51 computations (-21.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
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#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -1/2 binary64))))) (sin.f64 th)) |
(*.f64 (sin.f64 th) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky))) |
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64)) (cos.f64 (+.f64 kx kx))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (*.f64 (sin.f64 ky) #s(literal 2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(literal 2 binary64)) |
(/.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sin.f64 th)))) |
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 (sin.f64 ky) #s(literal 1/2 binary64))) |
(/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (sin.f64 th)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
| Outputs |
|---|
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
9 calls:
| 37.0ms | (sin.f64 th) |
| 35.0ms | (sin.f64 kx) |
| 35.0ms | kx |
| 33.0ms | th |
| 33.0ms | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 2 | kx |
| 99.4% | 2 | ky |
| 84.5% | 2 | th |
| 88.6% | 7 | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 99.5% | 4 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 99.5% | 3 | (sin.f64 ky) |
| 99.4% | 2 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 99.4% | 3 | (sin.f64 kx) |
| 87.3% | 4 | (sin.f64 th) |
Compiled 42 to 51 computations (-21.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
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#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -1/2 binary64))))) (sin.f64 th)) |
(*.f64 (sin.f64 th) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky))) |
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
| Outputs |
|---|
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
(*.f64 (sin.f64 th) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky))) |
1 calls:
| 30.0ms | ky |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 2 | ky |
Compiled 1 to 3 computations (-200% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
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(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -1/2 binary64))))) (sin.f64 th)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
6 calls:
| 316.0ms | ky |
| 46.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 34.0ms | (sin.f64 kx) |
| 33.0ms | kx |
| 33.0ms | (sin.f64 ky) |
| Accuracy | Segments | Branch |
|---|---|---|
| 91.4% | 5 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 84.6% | 3 | (sin.f64 kx) |
| 83.8% | 3 | (sin.f64 ky) |
| 83.9% | 2 | kx |
| 83.9% | 2 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 83.7% | 2 | ky |
Compiled 23 to 31 computations (-34.8% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1/2 binary64)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
1 calls:
| 52.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 91.4% | 5 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 13 to 11 computations (15.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1/2 binary64)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
1 calls:
| 31.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 91.4% | 5 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 13 to 11 computations (15.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
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(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
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(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) |
1 calls:
| 51.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 90.8% | 5 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 13 to 11 computations (15.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1/2 binary64)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
8 calls:
| 67.0ms | kx |
| 38.0ms | (sin.f64 kx) |
| 37.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 36.0ms | ky |
| 35.0ms | th |
| Accuracy | Segments | Branch |
|---|---|---|
| 76.1% | 5 | (sin.f64 ky) |
| 69.5% | 4 | (sin.f64 kx) |
| 76.0% | 4 | ky |
| 69.1% | 3 | kx |
| 68.7% | 3 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 73.3% | 4 | (sin.f64 th) |
| 71.2% | 2 | th |
| 86.7% | 5 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 26 to 38 computations (-46.2% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1/2 binary64)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
1 calls:
| 23.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 86.4% | 5 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 13 to 11 computations (15.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
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#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) (sin.f64 ky)) |
(*.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
3 calls:
| 51.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 36.0ms | ky |
| 24.0ms | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 71.7% | 3 | ky |
| 59.7% | 5 | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 78.5% | 6 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 30 to 27 computations (10% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1/2 binary64)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
5 calls:
| 62.0ms | (sin.f64 ky) |
| 60.0ms | ky |
| 19.0ms | th |
| 19.0ms | (sin.f64 th) |
| 18.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 53.6% | 4 | (sin.f64 th) |
| 65.7% | 3 | ky |
| 52.0% | 2 | th |
| 65.9% | 4 | (sin.f64 ky) |
| 71.0% | 4 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 19 to 25 computations (-31.6% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1/2 binary64)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
1 calls:
| 41.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 71.0% | 4 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 13 to 11 computations (15.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1/2 binary64)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
| Outputs |
|---|
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
6 calls:
| 20.0ms | ky |
| 20.0ms | (sin.f64 ky) |
| 18.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 17.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 17.0ms | kx |
| Accuracy | Segments | Branch |
|---|---|---|
| 57.4% | 4 | (sin.f64 ky) |
| 51.2% | 3 | ky |
| 58.4% | 3 | (sin.f64 kx) |
| 58.8% | 3 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 58.8% | 3 | kx |
| 62.9% | 4 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 23 to 31 computations (-34.8% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 #s(approx (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 (fma.f64 (*.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1/2 binary64)))) (sin.f64 th)) |
| Outputs |
|---|
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
1 calls:
| 17.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 62.2% | 4 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 13 to 11 computations (15.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
| Outputs |
|---|
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
1 calls:
| 15.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 62.2% | 4 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 13 to 11 computations (15.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) (sin.f64 th)) |
#s(approx (* (/ (sin th) (* (sqrt (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))))) 1/2)) (sin ky)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 th) ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 #s(approx (* 2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sin.f64 ky))) |
| Outputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) |
6 calls:
| 39.0ms | (sin.f64 kx) |
| 31.0ms | (sin.f64 ky) |
| 14.0ms | kx |
| 13.0ms | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 12.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 49.4% | 3 | (sin.f64 ky) |
| 45.3% | 4 | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 54.8% | 3 | (sin.f64 kx) |
| 55.1% | 3 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 55.1% | 3 | kx |
| 54.0% | 3 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 38 to 41 computations (-7.9% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
| Outputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
2 calls:
| 14.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 12.0ms | kx |
| Accuracy | Segments | Branch |
|---|---|---|
| 55.1% | 3 | kx |
| 55.1% | 3 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
Compiled 5 to 9 computations (-80% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) #s(approx (* (sqrt (- 1 (cos (* 2 kx)))) (sqrt 2)) (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) |
| Outputs |
|---|
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
5 calls:
| 19.0ms | (sin.f64 kx) |
| 13.0ms | kx |
| 12.0ms | th |
| 11.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 11.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 37.0% | 3 | th |
| 51.6% | 2 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 46.3% | 3 | (sin.f64 kx) |
| 43.8% | 2 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 43.8% | 2 | kx |
Compiled 21 to 27 computations (-28.6% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
| Outputs |
|---|
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
1 calls:
| 10.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 51.6% | 2 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 13 to 11 computations (15.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 ky #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) kx) kx (sqrt.f64 #s(literal 1/2 binary64))) kx))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 2 binary64))) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
| Outputs |
|---|
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
4 calls:
| 43.0ms | ky |
| 10.0ms | (sin.f64 ky) |
| 10.0ms | (sin.f64 th) |
| 9.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 43.0% | 2 | (sin.f64 ky) |
| 43.2% | 2 | ky |
| 35.6% | 5 | (sin.f64 th) |
| 45.3% | 2 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 18 to 22 computations (-22.2% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) #s(approx (/ (+ (* (/ 1/12 (sqrt 1/2)) (* kx kx)) (sqrt 1/2)) kx) (*.f64 (/.f64 kx (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/12 binary64)))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 7/360 binary64) (*.f64 #s(literal 1/6 binary64) ky)) (*.f64 kx kx) (*.f64 (*.f64 #s(literal 1/2 binary64) ky) #s(literal 2 binary64))) kx))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64))))))) (sin.f64 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 #s(approx (sqrt (- 1 (cos (* 2 kx)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) kx)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (*.f64 (sqrt.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (*.f64 kx kx) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) (sin.f64 th)) |
| Outputs |
|---|
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
1 calls:
| 12.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 45.2% | 2 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 13 to 11 computations (15.4% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)))))) |
| Outputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
8 calls:
| 7.0ms | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 7.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 5.0ms | (sin.f64 ky) |
| 5.0ms | (sin.f64 kx) |
| 5.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 30.4% | 2 | th |
| 35.0% | 3 | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 31.4% | 2 | (sin.f64 ky) |
| 31.6% | 2 | ky |
| 31.8% | 2 | kx |
| 31.8% | 2 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 32.0% | 3 | (sin.f64 kx) |
| 36.5% | 3 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 40 to 47 computations (-17.5% saved)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
| Outputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
9 calls:
| 6.0ms | (sin.f64 kx) |
| 4.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 3.0ms | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 3.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 3.0ms | (sin.f64 ky) |
| Accuracy | Segments | Branch |
|---|---|---|
| 18.7% | 2 | th |
| 22.2% | 3 | (sin.f64 kx) |
| 18.9% | 2 | (sin.f64 th) |
| 20.5% | 2 | (sin.f64 ky) |
| 20.9% | 2 | ky |
| 22.0% | 2 | kx |
| 22.0% | 2 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 24.2% | 2 | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 25.2% | 3 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
Compiled 42 to 51 computations (-21.4% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
| Outputs |
|---|
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
9 calls:
| 3.0ms | (sin.f64 th) |
| 1.0ms | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
| 1.0ms | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 1.0ms | (sin.f64 ky) |
| 1.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 16.6% | 1 | th |
| 16.6% | 1 | (sin.f64 th) |
| 16.6% | 1 | (sin.f64 ky) |
| 16.6% | 1 | (sin.f64 kx) |
| 16.6% | 1 | ky |
| 16.6% | 1 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 16.6% | 1 | kx |
| 16.6% | 1 | (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| 16.6% | 1 | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) |
Compiled 42 to 51 computations (-21.4% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 25.0ms | 9.17814233924677e-7 | 0.1837049704521445 |
| 19.0ms | 144× | 0 | valid |
Compiled 415 to 360 computations (13.3% saved)
ival-sin: 9.0ms (61.1% of total)ival-pow2: 3.0ms (20.4% of total)ival-div: 1.0ms (6.8% of total)ival-add: 1.0ms (6.8% of total)ival-mult: 1.0ms (6.8% of total)ival-sqrt: 1.0ms (6.8% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 4.0ms | 9.17814233924677e-7 | 0.1837049704521445 |
| 2.0ms | 16× | 0 | valid |
Compiled 415 to 351 computations (15.4% saved)
ival-sin: 1.0ms (64% of total)ival-div: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)ival-add: 0.0ms (0% of total)ival-mult: 0.0ms (0% of total)ival-sqrt: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-pow2: 0.0ms (0% of total)| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9942470468070546 | 0.999999999792623 |
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | -0.25935602080755743 | -0.2075215595273257 |
| 0.0ms | -0.9753916093139281 | -0.9707913329755891 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9942470468070546 | 0.999999999792623 |
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | -0.25935602080755743 | -0.2075215595273257 |
| 0.0ms | -0.9753916093139281 | -0.9707913329755891 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9942470468070546 | 0.999999999792623 |
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | -0.25935602080755743 | -0.2075215595273257 |
| 0.0ms | -0.9753916093139281 | -0.9707913329755891 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9942470468070546 | 0.999999999792623 |
| 0.0ms | 2.0442175659886983e-7 | 0.0017551811387782651 |
| 0.0ms | -0.2075215595273257 | 7.062894827265358e-305 |
| 0.0ms | -0.9753916093139281 | -0.9707913329755891 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.999999999792623 | 0.9999999999881585 |
| 0.0ms | 2.0442175659886983e-7 | 0.0017551811387782651 |
| 0.0ms | -0.2075215595273257 | 7.062894827265358e-305 |
| 0.0ms | -0.9753916093139281 | -0.9707913329755891 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9942470468070546 | 0.999999999792623 |
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | -0.2075215595273257 | 7.062894827265358e-305 |
| 0.0ms | -0.9753916093139281 | -0.9707913329755891 |
Compiled 19 to 19 computations (0% saved)
| 5× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9942470468070546 | 0.999999999792623 |
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | 6.64287818448709e-107 | 9.572511223064547e-106 |
| 0.0ms | -0.25935602080755743 | -0.2075215595273257 |
| 0.0ms | -0.9753916093139281 | -0.9707913329755891 |
Compiled 19 to 19 computations (0% saved)
| 3× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | 6.64287818448709e-107 | 9.572511223064547e-106 |
| 0.0ms | -0.7130459078636668 | -0.7062561081005618 |
Compiled 19 to 19 computations (0% saved)
| 3× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | 6.64287818448709e-107 | 9.572511223064547e-106 |
| 0.0ms | -0.7130459078636668 | -0.7062561081005618 |
Compiled 19 to 19 computations (0% saved)
| 3× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | 6.64287818448709e-107 | 9.572511223064547e-106 |
| 0.0ms | -0.999999999996641 | -0.9921364661897758 |
Compiled 19 to 19 computations (0% saved)
| 3× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | 6.64287818448709e-107 | 9.572511223064547e-106 |
| 0.0ms | -0.2075215595273257 | 7.062894827265358e-305 |
Compiled 19 to 19 computations (0% saved)
| 3× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | 6.64287818448709e-107 | 9.572511223064547e-106 |
| 0.0ms | -0.2075215595273257 | 7.062894827265358e-305 |
Compiled 19 to 19 computations (0% saved)
| 2× | binary-search |
| 1× | narrow-enough |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 22.0ms | 1.5670702033112442e-6 | 0.0008705265834285086 |
| 22.0ms | 4.0192768014650596e-147 | 3.790173253332737e-145 |
| 34.0ms | 240× | 0 | valid |
Compiled 856 to 687 computations (19.7% saved)
ival-sin: 12.0ms (52.3% of total)ival-pow2: 4.0ms (17.4% of total)ival-div: 2.0ms (8.7% of total)ival-sqrt: 2.0ms (8.7% of total)ival-add: 1.0ms (4.4% of total)ival-mult: 1.0ms (4.4% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 2× | binary-search |
| 1× | narrow-enough |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 9.0ms | 1.5670702033112442e-6 | 0.0008705265834285086 |
| 1.0ms | 4.0192768014650596e-147 | 3.790173253332737e-145 |
| 6.0ms | 32× | 0 | valid |
Compiled 880 to 703 computations (20.1% saved)
ival-sin: 2.0ms (64.3% of total)ival-pow2: 1.0ms (32.1% of total)ival-div: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)ival-add: 0.0ms (0% of total)ival-mult: 0.0ms (0% of total)ival-sqrt: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
Compiled 19 to 19 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
Compiled 19 to 19 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
Compiled 19 to 19 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
Compiled 19 to 19 computations (0% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0017551811387782651 | 0.0022979798249754407 |
| 0.0ms | 1.0685311318583048e-96 | 1.5424177977438381e-93 |
Compiled 19 to 19 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 2.7570480288e-313 | 8.746704017895e-312 |
Compiled 19 to 19 computations (0% saved)
| 1× | egg-herbie |
Useful iterations: 6 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 312 | 3257 |
| 1 | 382 | 3257 |
| 2 | 491 | 3257 |
| 3 | 732 | 3199 |
| 4 | 1121 | 3199 |
| 5 | 1737 | 3199 |
| 6 | 2661 | 3196 |
| 7 | 3031 | 3196 |
| 8 | 3549 | 3196 |
| 9 | 4743 | 3196 |
| 10 | 5122 | 3196 |
| 11 | 5151 | 3196 |
| 12 | 5508 | 3196 |
| 13 | 5653 | 3196 |
| 14 | 6168 | 3196 |
| 15 | 6833 | 3196 |
| 16 | 7469 | 3196 |
| 17 | 7589 | 3196 |
| 18 | 7679 | 3196 |
| 19 | 7679 | 3196 |
| 20 | 7685 | 3196 |
| 21 | 7685 | 3196 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(if (<=.f64 ky #s(literal 7148113328562451/4611686018427387904 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64))) (sin.f64 ky))) |
(if (<=.f64 ky #s(literal 208967022709991/144115188075855872 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 (sin.f64 th) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/18014398509481984 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 944473296573929/2361183241434822606848 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
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(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/18014398509481984 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))))) |
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(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 2404907604760405/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))) |
(if (<=.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #s(literal 50600563327/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th)))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
| Outputs |
|---|
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(if (<=.f64 ky #s(literal 7148113328562451/4611686018427387904 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 (/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) (cos.f64 (+.f64 ky ky))))) #s(literal 1/2 binary64))) (sin.f64 ky))) |
(if (<=.f64 ky #s(literal 208967022709991/144115188075855872 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 (sin.f64 th) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)))) (sin.f64 ky)))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (pow.f64 #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))) #s(literal -1 binary64)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (pow.f64 #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))) #s(literal -1 binary64)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (pow.f64 #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))) #s(literal -1 binary64)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8782019273372467/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/18014398509481984 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 944473296573929/2361183241434822606848 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th)))) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))))) |
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(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/18014398509481984 binary64)) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8263199609878107/82631996098781074868989413504096379978550585370535152410581099409300723904538918228148651304964410605948901503127919788032 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/18014398509481984 binary64)) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) (sin.f64 ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8263199609878107/82631996098781074868989413504096379978550585370535152410581099409300723904538918228148651304964410605948901503127919788032 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))))) |
(if (<=.f64 kx #s(literal 3779087587416285/899782758908639276562107701537196371773939423660383326620151114522367516134297574063808137220778171429984182126704179024641653211098859937801703036173032771026944 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (if (<=.f64 kx #s(literal 5312662293228351/73786976294838206464 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th)))) |
(if (<=.f64 kx #s(literal 3779087587416285/899782758908639276562107701537196371773939423660383326620151114522367516134297574063808137220778171429984182126704179024641653211098859937801703036173032771026944 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (if (<=.f64 kx #s(literal 5312662293228351/73786976294838206464 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1 binary64))))) (sin.f64 th)))) |
(if (<=.f64 kx #s(literal 3779087587416285/899782758908639276562107701537196371773939423660383326620151114522367516134297574063808137220778171429984182126704179024641653211098859937801703036173032771026944 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (if (<=.f64 kx #s(literal 6050532056176733/73786976294838206464 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))) |
(if (<=.f64 kx #s(literal 3779087587416285/899782758908639276562107701537196371773939423660383326620151114522367516134297574063808137220778171429984182126704179024641653211098859937801703036173032771026944 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (if (<=.f64 kx #s(literal 6050532056176733/73786976294838206464 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal -1 binary64))))))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) (sqrt.f64 (pow.f64 #s(approx (- 1 (cos (* 2 kx))) (*.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (*.f64 kx kx) #s(literal -2/3 binary64)) (*.f64 kx kx) #s(literal 2 binary64)) (*.f64 kx kx))) #s(literal -1 binary64))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) #s(approx (* (* 2 (* (sqrt 1/2) ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) ky) kx) #s(literal 2 binary64)))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 2404907604760405/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) ky)) #s(approx (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))) |
(if (<=.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #s(literal 50600563327/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th)))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) th))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 77 | 539 |
| 0 | 119 | 523 |
| 1 | 395 | 519 |
| 2 | 2356 | 519 |
| 0 | 8602 | 504 |
| 0 | 870 | 5422 |
| 1 | 2872 | 5030 |
| 2 | 7448 | 5022 |
| 0 | 8027 | 4738 |
| 0 | 904 | 6412 |
| 1 | 3057 | 5778 |
| 0 | 8008 | 5566 |
| 0 | 850 | 5570 |
| 1 | 2797 | 4961 |
| 2 | 7300 | 4801 |
| 0 | 8025 | 4572 |
| 0 | 13 | 49 |
| 0 | 22 | 49 |
| 1 | 62 | 49 |
| 2 | 344 | 49 |
| 3 | 2978 | 49 |
| 0 | 8260 | 34 |
| 0 | 317 | 1402 |
| 1 | 1011 | 1353 |
| 2 | 3865 | 1261 |
| 3 | 7812 | 1261 |
| 0 | 8115 | 1188 |
| 0 | 59 | 386 |
| 0 | 93 | 376 |
| 1 | 310 | 357 |
| 2 | 1880 | 331 |
| 0 | 8739 | 317 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 5 977 to 2 161 computations (63.8% saved)
(negabs ky)
(negabs th)
(abs kx)
Compiled 6 738 to 702 computations (89.6% saved)
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