Toniolo and Linder, Equation (3b), real
Time bar (total: 11.7s)
| 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)
| 1.2s | 8 256× | 0 | valid |
ival-sin: 566.0ms (57.6% of total)ival-pow2: 160.0ms (16.3% of total)ival-sqrt: 74.0ms (7.5% of total)ival-add: 64.0ms (6.5% of total)ival-div: 54.0ms (5.5% of total)ival-mult: 54.0ms (5.5% of total)ival-true: 6.0ms (0.6% of total)ival-assert: 3.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 16 | 0 | - | 1 | (9.119131181611084e-156 1.8068536729062975e-198 -4.098296145755141e-126) | (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 | 15 | 0 |
| ↳ | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) | underflow | 64 | |
| ↳ | (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) | underflow | 61 | |
| ↳ | (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) | underflow | 15 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 15 | 1 |
| - | 0 | 240 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 15 | 0 | 1 |
| - | 0 | 0 | 240 |
| number | freq |
|---|---|
| 0 | 241 |
| 1 | 15 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 183.0ms | 512× | 0 | valid |
Compiled 218 to 56 computations (74.3% saved)
ival-pow2: 62.0ms (42% of total)ival-sin: 58.0ms (39.3% of total)ival-add: 17.0ms (11.5% of total)ival-div: 3.0ms (2% of total)ival-mult: 3.0ms (2% of total)ival-sqrt: 3.0ms (2% of total)ival-assert: 0.0ms (0% of total)ival-true: 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 | 831 | 147 |
| 5 | 1949 | 147 |
| 6 | 2504 | 147 |
| 7 | 2781 | 147 |
| 8 | 2893 | 147 |
| 9 | 2943 | 147 |
| 10 | 2958 | 147 |
| 11 | 2958 | 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 |
|---|---|---|
| ▶ | 94.0% | (*.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)) |
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 | 0.13119125976844204 | (/.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 | 0.244472509768442 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) | |
| accuracy | 0.28744125976844204 | (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) | |
| accuracy | 3.641586186967307 | (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
| 45.0ms | 256× | 0 | valid |
Compiled 134 to 28 computations (79.1% saved)
ival-sin: 24.0ms (68.3% of total)ival-pow2: 5.0ms (14.2% of total)ival-mult: 2.0ms (5.7% of total)ival-sqrt: 2.0ms (5.7% of total)ival-div: 1.0ms (2.8% of total)ival-add: 1.0ms (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 |
|---|
(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 | |
|---|---|---|---|---|
| 30.0ms | 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)) |
| 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)) |
| 3.0ms | 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 | 3847 | 1261 |
| 3 | 7794 | 1261 |
| 0 | 8097 | 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 | 338 | 49 |
| 3 | 2902 | 49 |
| 0 | 8284 | 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 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 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 (pow.f64 (hypot.f64 (sin.f64 ky) (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 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 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 (-.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 (/.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (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 #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 (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 (pow.f64 (hypot.f64 (sin.f64 ky) (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 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (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 (pow.f64 (hypot.f64 (sin.f64 ky) (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 (pow.f64 (hypot.f64 (sin.f64 ky) (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 (pow.f64 (hypot.f64 (sin.f64 ky) (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 (-.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 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky))) |
(*.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 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 ky))) |
(*.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 1/4 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 1/8 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 1/2 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 1/2 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 1/4 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 1/8 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 1/2 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 1/2 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 9 221 to 1 717 computations (81.4% saved)
19 alts after pruning (19 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 346 | 19 | 365 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 347 | 19 | 366 |
| Status | Accuracy | Program |
|---|---|---|
| 95.9% | (/.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))) | |
| 99.1% | (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))) | |
| 39.7% | (*.f64 (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) | |
| 99.6% | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) | |
| ▶ | 99.7% | (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) |
| ▶ | 77.1% | (*.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)) |
| 93.9% | (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) #s(literal 2 binary64))))) (sin.f64 th)) | |
| 43.1% | (*.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)) | |
| ▶ | 57.1% | (*.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)) |
| 39.8% | (*.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 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th)) | |
| 31.2% | (*.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)) | |
| 32.9% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) | |
| 99.6% | (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) | |
| ▶ | 95.7% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
| 25.8% | (*.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)) | |
| 25.7% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (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)))) (sin.f64 th)) | |
| 30.1% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) | |
| ▶ | 33.2% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
Compiled 750 to 586 computations (21.9% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sin.f64 ky) | |
| cost-diff | 0 | (neg.f64 (sin.f64 ky)) | |
| cost-diff | 0 | (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) | |
| cost-diff | 448 | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) | |
| 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 (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 | (sin.f64 ky) | |
| cost-diff | 0 | (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 329 |
| 0 | 78 | 321 |
| 1 | 111 | 316 |
| 2 | 181 | 316 |
| 3 | 360 | 306 |
| 4 | 623 | 306 |
| 5 | 1323 | 306 |
| 6 | 2389 | 306 |
| 7 | 3729 | 306 |
| 8 | 4239 | 306 |
| 9 | 4459 | 306 |
| 10 | 4557 | 306 |
| 11 | 4594 | 306 |
| 12 | 4610 | 306 |
| 13 | 4660 | 306 |
| 14 | 4688 | 306 |
| 15 | 4766 | 306 |
| 16 | 5135 | 306 |
| 17 | 5135 | 306 |
| 0 | 5135 | 300 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(sin.f64 ky) |
ky |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(sin.f64 kx) |
kx |
(sin.f64 th) |
th |
#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 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) |
(neg.f64 (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(sin.f64 th) |
th |
(/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
#s(literal -1 binary64) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(sin.f64 kx) |
kx |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(sin.f64 ky) |
ky |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(sin.f64 kx) |
kx |
(sin.f64 th) |
th |
#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 th) (sin.f64 ky)) (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 #s(literal 1/2 binary64) (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)))) |
(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 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) |
(neg.f64 (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(sin.f64 th) |
th |
(/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
#s(literal -1 binary64) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(sin.f64 kx) |
kx |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0625 | (hypot.f64 (sin.f64 ky) (sin.f64 kx)) | |
| accuracy | 0.16796875 | (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) | |
| accuracy | 0.203125 | (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) | |
| accuracy | 2.721527494376109 | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) | |
| accuracy | 0.13119125976844204 | (/.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 | 3.63146253860364 | (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 | 13.493725756781584 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) | |
| accuracy | 17.174609684164565 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) | |
| accuracy | 0.13119125976844204 | (/.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 | 0.28744125976844204 | (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) | |
| accuracy | 3.641586186967307 | (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) | |
| accuracy | 28.937276803550855 | #s(approx (pow (sin kx) 2) (*.f64 kx kx)) | |
| accuracy | 0.0 | (sin.f64 th) | |
| accuracy | 42.74778530861426 | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) | |
| accuracy | 0.0 | (sin.f64 kx) | |
| accuracy | 0.0625 | (hypot.f64 (sin.f64 ky) (sin.f64 kx)) | |
| accuracy | 0.1171875 | (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) | |
| accuracy | 0.13119125976844204 | (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
| 200.0ms | 106× | 2 | valid |
| 129.0ms | 82× | 1 | valid |
| 27.0ms | 68× | 0 | valid |
Compiled 684 to 84 computations (87.7% saved)
ival-sin: 72.0ms (30.4% of total)ival-mult: 65.0ms (27.5% of total)ival-cos: 37.0ms (15.6% of total)adjust: 17.0ms (7.2% of total)ival-div: 13.0ms (5.5% of total)ival-pow2: 7.0ms (3% of total)ival-hypot: 6.0ms (2.5% of total)ival-sqrt: 6.0ms (2.5% of total)ival-sub: 5.0ms (2.1% of total)ival-add: 4.0ms (1.7% of total)ival-neg: 2.0ms (0.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (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)) |
(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))))) |
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(/.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 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) |
(neg.f64 (sin.f64 ky)) |
(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)))))) |
(/.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 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 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) (* (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)))))) |
(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)))))) |
(* 1/2 (* (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 (- 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)))))))))) |
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)))))))))))) |
(* 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)))))))))) |
(/ -1 (sin ky)) |
(- (* 1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* -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 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
(* (* (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))))) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(* 1/2 (sqrt (+ (* 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))))))))) |
(sin kx) |
(pow (sin kx) 2) |
(- 1 (cos (* 2 kx))) |
(sqrt (+ (* 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))))))))) |
(* -1 (sqrt (/ 1 (+ (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)))) |
(/ 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)))) |
(+ (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)))))) |
(* 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 (- 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))))))))))))))) |
(* -1 (* ky (sin th))) |
(* ky (+ (* -1 (sin th)) (* 1/6 (* (pow ky 2) (sin th))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* -1/120 (* (pow ky 2) (sin th))) (* 1/6 (sin th)))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* 1/6 (sin th)) (* (pow ky 2) (+ (* -1/120 (sin th)) (* 1/5040 (* (pow ky 2) (sin th))))))))) |
(* -1 ky) |
(* ky (- (* 1/6 (pow ky 2)) 1)) |
(* ky (- (* (pow ky 2) (+ 1/6 (* -1/120 (pow ky 2)))) 1)) |
(* ky (- (* (pow ky 2) (+ 1/6 (* (pow ky 2) (- (* 1/5040 (pow ky 2)) 1/120)))) 1)) |
(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)))))))))))) |
(* 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))))))))))))))) |
(/ -1 (sin kx)) |
(- (* 1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/2 (* (pow ky 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)))))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(* -1 (* (sin ky) (sin th))) |
(* -1 (sin ky)) |
(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))) |
(* th (+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sin ky))) (* 1/6 (sin ky)))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* 1/6 (sin ky)) (* (pow th 2) (+ (* -1/120 (sin ky)) (* 1/5040 (* (pow th 2) (sin ky))))))))) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 47.0ms | kx | @ | -inf | ((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (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 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)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (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)) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (neg (sin ky)) (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)))))) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) |
| 46.0ms | ky | @ | inf | ((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (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 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)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (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)) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (neg (sin ky)) (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)))))) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) |
| 9.0ms | ky | @ | 0 | ((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (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 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)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (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)) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (neg (sin ky)) (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)))))) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) |
| 9.0ms | kx | @ | 0 | ((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (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 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)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (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)) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (neg (sin ky)) (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)))))) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) |
| 6.0ms | kx | @ | inf | ((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (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 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)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (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)) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (neg (sin ky)) (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)))))) (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 859 | 5539 |
| 1 | 2883 | 5092 |
| 2 | 7352 | 5082 |
| 0 | 8017 | 4859 |
| 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) (* (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)))))) |
(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)))))) |
(* 1/2 (* (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 (- 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)))))))))) |
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)))))))))))) |
(* 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)))))))))) |
(/ -1 (sin ky)) |
(- (* 1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* -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 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
(* (* (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))))) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(* 1/2 (sqrt (+ (* 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))))))))) |
(sin kx) |
(pow (sin kx) 2) |
(- 1 (cos (* 2 kx))) |
(sqrt (+ (* 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))))))))) |
(* -1 (sqrt (/ 1 (+ (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)))) |
(/ 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)))) |
(+ (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)))))) |
(* 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 (- 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))))))))))))))) |
(* -1 (* ky (sin th))) |
(* ky (+ (* -1 (sin th)) (* 1/6 (* (pow ky 2) (sin th))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* -1/120 (* (pow ky 2) (sin th))) (* 1/6 (sin th)))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* 1/6 (sin th)) (* (pow ky 2) (+ (* -1/120 (sin th)) (* 1/5040 (* (pow ky 2) (sin th))))))))) |
(* -1 ky) |
(* ky (- (* 1/6 (pow ky 2)) 1)) |
(* ky (- (* (pow ky 2) (+ 1/6 (* -1/120 (pow ky 2)))) 1)) |
(* ky (- (* (pow ky 2) (+ 1/6 (* (pow ky 2) (- (* 1/5040 (pow ky 2)) 1/120)))) 1)) |
(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)))))))))))) |
(* 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))))))))))))))) |
(/ -1 (sin kx)) |
(- (* 1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/2 (* (pow ky 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)))))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(* -1 (* (sin ky) (sin th))) |
(* -1 (sin ky)) |
(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))) |
(* th (+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sin ky))) (* 1/6 (sin ky)))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* 1/6 (sin ky)) (* (pow th 2) (+ (* -1/120 (sin ky)) (* 1/5040 (* (pow th 2) (sin ky))))))))) |
| 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)))))))))))) |
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1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))) |
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(+ 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)))))) |
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(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)) |
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(* 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) (+ (* -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)))))))))))) |
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(* 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))) |
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(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))) |
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(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3))))) |
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(* 4 (pow kx 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 kx kx)) |
(* (pow kx 2) (+ 4 (* -4/3 (pow kx 2)))) |
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(* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3)))) |
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(* (pow kx 2) (+ 4 (* (pow kx 2) (- (* (pow kx 2) (+ 8/45 (* -4/315 (pow kx 2)))) 4/3)))) |
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(* 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)))))))) |
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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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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)))) |
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(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6)))) |
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(pow kx 2) |
(*.f64 kx kx) |
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) |
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(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) |
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(* 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)))) |
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(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3)))) |
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(* (sqrt 2) (sqrt (- 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))) |
(+ (* 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 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* (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)))))))))) |
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(+ (* (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)))))))))))) |
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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)))))))))) |
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(/ -1 (sin ky)) |
(/.f64 #s(literal -1 binary64) (sin.f64 ky)) |
(- (* 1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (*.f64 kx kx) (/.f64 #s(literal -1 binary64) (sin.f64 ky))) |
(- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
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(- (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* -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 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
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(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
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(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(* 1/2 (sqrt (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))) |
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(+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))) |
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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 (* (* (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)))))))) |
(sin kx) |
(sin.f64 kx) |
(pow (sin kx) 2) |
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(- 1 (cos (* 2 kx))) |
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(sqrt (+ (* 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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(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
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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)))) |
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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))))))))))))) (/ (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)))) |
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(/ 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 ky) (*.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)) (/.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 (*.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) |
(+ (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)))))) |
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(* 1/2 (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx)))))) |
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(+ (* 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)))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 4 (pow ky 2))) |
(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))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* -4/3 (pow ky 2))))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -4/3 binary64) #s(literal 4 binary64)) (*.f64 ky ky))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* (pow ky 2) (- (* 8/45 (pow ky 2)) 4/3))))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal 8/45 binary64) #s(literal -4/3 binary64)) (*.f64 ky ky) #s(literal 4 binary64)) (*.f64 ky 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 (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 (-.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))))))))))))))) |
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(* -1 (* ky (sin th))) |
(*.f64 (neg.f64 ky) (sin.f64 th)) |
(* ky (+ (* -1 (sin th)) (* 1/6 (* (pow ky 2) (sin th))))) |
(*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* -1/120 (* (pow ky 2) (sin th))) (* 1/6 (sin th)))))) |
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(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* 1/6 (sin th)) (* (pow ky 2) (+ (* -1/120 (sin th)) (* 1/5040 (* (pow ky 2) (sin th))))))))) |
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(* -1 ky) |
(neg.f64 ky) |
(* ky (- (* 1/6 (pow ky 2)) 1)) |
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky) |
(* ky (- (* (pow ky 2) (+ 1/6 (* -1/120 (pow ky 2)))) 1)) |
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(* ky (- (* (pow ky 2) (+ 1/6 (* (pow ky 2) (- (* 1/5040 (pow ky 2)) 1/120)))) 1)) |
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(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)))) |
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(* (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)))) |
(* 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))))))))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (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))))) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/120 binary64) (fma.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 (*.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 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))))))))))))))) |
(*.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 (/.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)))) #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))))) (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)))) (sqrt.f64 #s(literal 1/2 binary64))))) (fma.f64 (/.f64 #s(literal -1/240 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 -1/5040 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) (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 1/2 binary64))) #s(literal 1/120 binary64) (fma.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 (*.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 ky ky) (*.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))))))) #s(literal 2 binary64))) (*.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) |
(/ -1 (sin kx)) |
(/.f64 #s(literal -1 binary64) (sin.f64 kx)) |
(- (* 1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx))) |
(fma.f64 (*.f64 ky (/.f64 ky (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 ky ky)) (*.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 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(- (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/2 (* (pow ky 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)))))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 ky ky)) (*.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 kx)) (*.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 ky ky) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(* -1 (* (sin ky) (sin th))) |
(*.f64 (neg.f64 (sin.f64 th)) (sin.f64 ky)) |
(* -1 (sin ky)) |
(neg.f64 (sin.f64 ky)) |
(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))) |
(*.f64 (neg.f64 th) (sin.f64 ky)) |
(* th (+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky))))) |
(*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sin ky))) (* 1/6 (sin ky)))))) |
(*.f64 (fma.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/120 binary64) (*.f64 th th) #s(literal 1/6 binary64))) (*.f64 th th) (neg.f64 (sin.f64 ky))) th) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* 1/6 (sin ky)) (* (pow th 2) (+ (* -1/120 (sin ky)) (* 1/5040 (* (pow th 2) (sin ky))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/5040 binary64) (*.f64 th th) #s(literal -1/120 binary64))) (*.f64 th th) (*.f64 #s(literal 1/6 binary64) (sin.f64 ky))) (*.f64 th th) (neg.f64 (sin.f64 ky))) th) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 261 |
| 0 | 78 | 211 |
| 1 | 253 | 209 |
| 2 | 1571 | 209 |
| 0 | 8832 | 209 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) |
(/.f64 (sin.f64 ky) (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)) |
(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))))) |
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(/.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 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) |
(neg.f64 (sin.f64 ky)) |
(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)))))) |
(/.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 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 th) #s(literal 1 binary64)) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (*.f64 (sin.f64 th) #s(literal -1 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 (sin.f64 ky) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (*.f64 (sin.f64 th) #s(literal -1 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 (sin.f64 ky) #s(literal -1/2 binary64))) |
(*.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 (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 (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 (sin.f64 ky) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)) |
(*.f64 (/.f64 (*.f64 (neg.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 #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 (neg.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 (sin.f64 th) #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 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 (neg.f64 (sin.f64 ky)) #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 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 (sin.f64 th) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (sin.f64 ky) (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 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 (/.f64 #s(literal -1 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 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(literal -1/2 binary64))) |
(*.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 #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 (neg.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 (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) (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))) (/.f64 (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 (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 (neg.f64 (sin.f64 th)) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (sin.f64 ky) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (*.f64 (sin.f64 th) (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)))))))) #s(literal -2 binary64)) |
(*.f64 (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(literal 1 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (*.f64 (sin.f64 th) (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 (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 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.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 (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 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(literal 1/2 binary64))) |
(*.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 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sin.f64 th) #s(literal -1 binary64))) |
(*.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 (neg.f64 (sin.f64 ky)) (*.f64 (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 (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 (sin.f64 th) (sin.f64 ky)) (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 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)) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(literal 1 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) |
(*.f64 #s(literal -1 binary64) (/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)))) |
(*.f64 #s(literal -1 binary64) (*.f64 (sin.f64 ky) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (neg.f64 (sin.f64 ky)) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 #s(literal 1 binary64) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) |
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (neg.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 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th))) |
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (neg.f64 (sin.f64 ky)) (*.f64 (sin.f64 th) #s(literal -1 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (/.f64 (*.f64 (sin.f64 th) (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 -1/2 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(literal 1 binary64))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (*.f64 (sin.f64 th) #s(literal -1 binary64))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th))) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64))) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (/.f64 (*.f64 (sin.f64 th) (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 1/2 binary64)) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.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 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(literal 1 binary64)) (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 (neg.f64 (sin.f64 th)) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (*.f64 (sin.f64 th) #s(literal -1 binary64)))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (*.f64 (sin.f64 th) #s(literal -1 binary64))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (neg.f64 (sin.f64 ky)) (*.f64 (sin.f64 th) #s(literal -1 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))) |
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (neg.f64 (sin.f64 ky)) (*.f64 (sin.f64 th) #s(literal -1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky)))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
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(*.f64 (/.f64 (sqrt.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 (sqrt.f64 (sin.f64 ky)) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 ky) (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 #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 1/4 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 #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) (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 (sin.f64 ky) #s(literal 1 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (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 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 -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.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))))))) #s(literal 2 binary64)) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 ky)) |
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 #s(literal 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 (sin.f64 ky) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (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)) |
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 0 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal 3 binary64)) (pow.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 0 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 #s(literal 0 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (fma.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (*.f64 (/.f64 #s(literal 0 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 ky) #s(literal 2 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 (*.f64 (sin.f64 ky) #s(literal 1 binary64))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (neg.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)))))))) #s(literal -1/2 binary64)) |
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))) (*.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) |
(/.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))))))) |
(/.f64 (*.f64 (sin.f64 ky) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (neg.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))))))) #s(literal 1/2 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(/.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(exp.f64 (-.f64 (log.f64 (sin.f64 ky)) (*.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)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal -1 binary64)) |
(*.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(pow.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)) |
(/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(neg.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(literal -1 binary64))) |
Compiled 28 302 to 3 701 computations (86.9% saved)
37 alts after pruning (36 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 756 | 32 | 788 |
| Fresh | 10 | 4 | 14 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 0 | 0 |
| Total | 770 | 37 | 807 |
| Status | Accuracy | Program |
|---|---|---|
| 57.1% | (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))) (sin.f64 ky))) | |
| 95.5% | (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky)))) | |
| 77.0% | (*.f64 (/.f64 (*.f64 (sin.f64 th) (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)) | |
| 77.1% | (*.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)) |
| ▶ | 52.8% | (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
| 62.7% | (*.f64 (/.f64 (sin.f64 ky) (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 th)) | |
| 76.8% | (*.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)) | |
| 86.1% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (/.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))) #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)) | |
| 42.1% | (*.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))) | |
| 35.7% | (*.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)) | |
| 35.7% | (*.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)) | |
| 34.0% | (*.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))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 47.9% | (*.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)) | |
| 29.1% | (*.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)) | |
| 35.6% | (*.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)) | |
| 29.2% | (*.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)) | |
| 32.9% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) | |
| 39.2% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) | |
| ▶ | 31.4% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
| 43.6% | (*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) | |
| 57.0% | (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))))) | |
| 35.7% | (*.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)) (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)) | |
| 24.6% | (*.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))))))) (sin.f64 th)) | |
| 77.0% | (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.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))))))))) (sin.f64 th)) | |
| 25.8% | (*.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)) | |
| 30.1% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) | |
| 25.7% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (neg.f64 ky) (*.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)) (/.f64 ky (sin.f64 kx)))) (sin.f64 th)) | |
| 49.3% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) | |
| 35.4% | #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))))))) | |
| 24.5% | #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))))))) | |
| 76.9% | #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))))))))) | |
| ▶ | 42.3% | #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))))))))) |
| ✓ | 33.2% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
| 19.4% | #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))) | |
| 19.5% | #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))) | |
| ▶ | 19.4% | #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 2 213 to 1 663 computations (24.9% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (hypot.f64 (sin.f64 ky) (sin.f64 kx)) | |
| cost-diff | 0 | (sin.f64 ky) | |
| cost-diff | 0 | (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #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(literal 2 binary64) (*.f64 (sin.f64 ky) th)) | |
| cost-diff | 0 | (*.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)))))))) | |
| cost-diff | 0 | #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))))))))) | |
| cost-diff | 192 | (-.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))))) | |
| cost-diff | 0 | (sin.f64 ky) | |
| cost-diff | 0 | (neg.f64 (sin.f64 ky)) | |
| cost-diff | 0 | (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) | |
| cost-diff | 0 | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 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 | 66 | 382 |
| 0 | 103 | 377 |
| 1 | 160 | 375 |
| 2 | 274 | 369 |
| 3 | 549 | 357 |
| 4 | 968 | 357 |
| 5 | 1450 | 357 |
| 6 | 2047 | 357 |
| 7 | 2354 | 357 |
| 8 | 2521 | 357 |
| 9 | 2548 | 357 |
| 10 | 2551 | 357 |
| 11 | 2551 | 357 |
| 12 | 2601 | 357 |
| 13 | 2601 | 357 |
| 0 | 2601 | 350 |
| 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 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) |
(neg.f64 (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(sin.f64 th) |
th |
#s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(/.f64 #s(literal -1 binary64) (sin.f64 kx)) |
#s(literal -1 binary64) |
(sin.f64 kx) |
kx |
#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 #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(literal 2 binary64) (*.f64 (sin.f64 ky) th)) |
#s(literal 2 binary64) |
(*.f64 (sin.f64 ky) th) |
(sin.f64 ky) |
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(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(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(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)))) |
(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) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(sin.f64 ky) |
ky |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(sin.f64 kx) |
kx |
#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) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)) |
(/.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 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) |
(*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) |
(neg.f64 (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(sin.f64 th) |
th |
#s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(/.f64 #s(literal -1 binary64) (sin.f64 kx)) |
#s(literal -1 binary64) |
(sin.f64 kx) |
kx |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)))) |
(*.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 (sqrt.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) |
(*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (sin.f64 ky) th) |
(sin.f64 ky) |
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))))))) |
(sqrt.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(/.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(literal -1/2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
#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 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
#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 (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) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 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) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #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 ky) (sin.f64 kx))) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(sin.f64 ky) |
ky |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(sin.f64 kx) |
kx |
#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) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.09375 | (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) | |
| accuracy | 0.1171875 | (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| accuracy | 0.13119125976844204 | (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) | |
| accuracy | 30.151368900103094 | #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) | |
| accuracy | 3.9029827696287565 | (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))))))) | |
| accuracy | 11.033817788445095 | (-.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))))) | |
| accuracy | 13.493725756781584 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) | |
| accuracy | 29.908261654955574 | #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))))))))) | |
| accuracy | 0.08203125 | (/.f64 #s(literal -1 binary64) (sin.f64 kx)) | |
| accuracy | 0.203125 | (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) | |
| accuracy | 2.721527494376109 | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| accuracy | 45.38357521017723 | #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) | |
| accuracy | 0.05078125 | (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) | |
| accuracy | 0.09375 | (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) | |
| accuracy | 30.151368900103094 | #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) | |
| accuracy | 42.74778530861426 | #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 | 0.0 | (sin.f64 kx) | |
| accuracy | 0.0625 | (hypot.f64 (sin.f64 ky) (sin.f64 kx)) | |
| accuracy | 0.28515625 | (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) | |
| accuracy | 0.29296875 | (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
| 193.0ms | 64× | 2 | valid |
| 95.0ms | 143× | 0 | valid |
| 55.0ms | 48× | 1 | valid |
| 3.0ms | 1× | 3 | valid |
Compiled 767 to 125 computations (83.7% saved)
ival-cos: 115.0ms (39.2% of total)ival-mult: 64.0ms (21.8% of total)ival-sin: 20.0ms (6.8% of total)ival-sub: 19.0ms (6.5% of total)ival-div: 17.0ms (5.8% of total)adjust: 14.0ms (4.8% of total)ival-add: 14.0ms (4.8% of total)ival-sqrt: 11.0ms (3.7% of total)ival-pow2: 6.0ms (2% of total)ival-hypot: 6.0ms (2% of total)const: 5.0ms (1.7% of total)ival-neg: 2.0ms (0.7% of total)exact: 1.0ms (0.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 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 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) |
(neg.f64 (sin.f64 ky)) |
(sin.f64 ky) |
(-.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 (+ (* (- 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 #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(literal 2 binary64) (*.f64 (sin.f64 ky) th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(sin.f64 kx) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
#s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(/.f64 #s(literal -1 binary64) (sin.f64 kx)) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) 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))))))) |
| 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)))))) |
(- 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 (* (* (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 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -2 (* (* (pow kx 2) (* th (* (sin ky) (sqrt 1/2)))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (pow kx 2) (* th (* (sin ky) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (* (pow kx 2) (* th (* (sin ky) (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 ky)))))) (* (* th (* (sin ky) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky)))))))))) |
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)))))) |
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)))) |
(/ -1 (sin ky)) |
(- (* 1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* -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 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
(/ -1 kx) |
(/ (- (* -1/6 (pow kx 2)) 1) kx) |
(/ (- (* (pow kx 2) (- (* -7/360 (pow kx 2)) 1/6)) 1) kx) |
(/ (- (* (pow kx 2) (- (* (pow kx 2) (- (* -31/15120 (pow kx 2)) 7/360)) 1/6)) 1) kx) |
(* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) |
(+ (* -1 (* (* (pow kx 2) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky))))))))) |
(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 ky)))))) (* 1/2 (* (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky))))))))))) |
(* (* (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 (+ (cos (* 2 kx)) (cos (* 2 ky)))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) |
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(sin kx) |
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(/ -1 (sin kx)) |
(* (sqrt 1/2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (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 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)))))) |
(* -1 (* ky (sin th))) |
(* ky (+ (* -1 (sin th)) (* 1/6 (* (pow ky 2) (sin th))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* -1/120 (* (pow ky 2) (sin th))) (* 1/6 (sin th)))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* 1/6 (sin th)) (* (pow ky 2) (+ (* -1/120 (sin th)) (* 1/5040 (* (pow ky 2) (sin th))))))))) |
(* -1 ky) |
(* ky (- (* 1/6 (pow ky 2)) 1)) |
(* ky (- (* (pow ky 2) (+ 1/6 (* -1/120 (pow ky 2)))) 1)) |
(* ky (- (* (pow ky 2) (+ 1/6 (* (pow ky 2) (- (* 1/5040 (pow ky 2)) 1/120)))) 1)) |
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 (cos (* 2 kx))) |
(- (+ 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 (* (* 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))))))))))))))) |
(* 2 (* (* ky (* th (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* th (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (* th (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (* th (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* th (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx))))))))))))))) |
(* 2 (* ky th)) |
(* ky (+ (* -1/3 (* (pow ky 2) th)) (* 2 th))) |
(* ky (+ (* 2 th) (* (pow ky 2) (+ (* -1/3 th) (* 1/60 (* (pow ky 2) th)))))) |
(* ky (+ (* 2 th) (* (pow ky 2) (+ (* -1/3 th) (* (pow ky 2) (+ (* -1/2520 (* (pow ky 2) th)) (* 1/60 th))))))) |
(/ 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)))) |
(- (* 1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/2 (* (pow ky 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)))))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin 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 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) |
(+ (* -1 (* (* (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* (pow ky 2) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx))))))))) |
(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 kx)))))) (* 1/2 (* (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx))))))))))) |
(* -1 (* (sin ky) (sin th))) |
(* -1 (sin ky)) |
(* 2 (* th (sin 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) |
(* -1 (* th (sin ky))) |
(* th (+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sin ky))) (* 1/6 (sin ky)))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* 1/6 (sin ky)) (* (pow th 2) (+ (* -1/120 (sin ky)) (* 1/5040 (* (pow th 2) (sin ky))))))))) |
(* 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 | |
|---|---|---|---|---|
| 32.0ms | 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) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (neg (sin ky)) (sin ky) (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (* 2 (* (sin ky) th)) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin kx) (* (+ (* (* th th) -1/6) 1) th) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/ -1 (sin kx)) (- 1 (cos (* 2 ky))) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) |
| 22.0ms | 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) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (neg (sin ky)) (sin ky) (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (* 2 (* (sin ky) th)) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin kx) (* (+ (* (* th th) -1/6) 1) th) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/ -1 (sin kx)) (- 1 (cos (* 2 ky))) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) |
| 9.0ms | 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) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (neg (sin ky)) (sin ky) (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (* 2 (* (sin ky) th)) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin kx) (* (+ (* (* th th) -1/6) 1) th) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/ -1 (sin kx)) (- 1 (cos (* 2 ky))) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) |
| 9.0ms | 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 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) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (neg (sin ky)) (sin ky) (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (* 2 (* (sin ky) th)) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin kx) (* (+ (* (* th th) -1/6) 1) th) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/ -1 (sin kx)) (- 1 (cos (* 2 ky))) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) |
| 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 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) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (neg (sin ky)) (sin ky) (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (* 2 (* (sin ky) th)) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin kx) (* (+ (* (* th th) -1/6) 1) th) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/ -1 (sin kx)) (- 1 (cos (* 2 ky))) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 887 | 5707 |
| 1 | 2977 | 5422 |
| 2 | 7641 | 5420 |
| 0 | 8036 | 5202 |
| 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)))))) |
(- 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 (* (* (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 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* -2 (* (* (pow kx 2) (* th (* (sin ky) (sqrt 1/2)))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (pow kx 2) (* th (* (sin ky) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky)))))))) |
(+ (* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (* (pow kx 2) (* th (* (sin ky) (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 ky)))))) (* (* th (* (sin ky) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky)))))))))) |
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)))))) |
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)))) |
(/ -1 (sin ky)) |
(- (* 1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* -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 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
(/ -1 kx) |
(/ (- (* -1/6 (pow kx 2)) 1) kx) |
(/ (- (* (pow kx 2) (- (* -7/360 (pow kx 2)) 1/6)) 1) kx) |
(/ (- (* (pow kx 2) (- (* (pow kx 2) (- (* -31/15120 (pow kx 2)) 7/360)) 1/6)) 1) kx) |
(* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) |
(+ (* -1 (* (* (pow kx 2) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky))))))))) |
(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 ky)))))) (* 1/2 (* (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky))))))))))) |
(* (* (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 (+ (cos (* 2 kx)) (cos (* 2 ky)))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) |
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(sin kx) |
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(/ -1 (sin kx)) |
(* (sqrt 1/2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (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 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)))))) |
(* -1 (* ky (sin th))) |
(* ky (+ (* -1 (sin th)) (* 1/6 (* (pow ky 2) (sin th))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* -1/120 (* (pow ky 2) (sin th))) (* 1/6 (sin th)))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* 1/6 (sin th)) (* (pow ky 2) (+ (* -1/120 (sin th)) (* 1/5040 (* (pow ky 2) (sin th))))))))) |
(* -1 ky) |
(* ky (- (* 1/6 (pow ky 2)) 1)) |
(* ky (- (* (pow ky 2) (+ 1/6 (* -1/120 (pow ky 2)))) 1)) |
(* ky (- (* (pow ky 2) (+ 1/6 (* (pow ky 2) (- (* 1/5040 (pow ky 2)) 1/120)))) 1)) |
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 (cos (* 2 kx))) |
(- (+ 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 (* (* 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))))))))))))))) |
(* 2 (* (* ky (* th (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(* ky (+ (* 2 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(* ky (+ (* 2 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* th (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))) |
(* ky (+ (* 2 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (* th (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (* th (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* th (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx))))))))))))))) |
(* 2 (* ky th)) |
(* ky (+ (* -1/3 (* (pow ky 2) th)) (* 2 th))) |
(* ky (+ (* 2 th) (* (pow ky 2) (+ (* -1/3 th) (* 1/60 (* (pow ky 2) th)))))) |
(* ky (+ (* 2 th) (* (pow ky 2) (+ (* -1/3 th) (* (pow ky 2) (+ (* -1/2520 (* (pow ky 2) th)) (* 1/60 th))))))) |
(/ 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)))) |
(- (* 1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/2 (* (pow ky 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)))))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin 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 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) |
(+ (* -1 (* (* (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* (pow ky 2) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx))))))))) |
(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 kx)))))) (* 1/2 (* (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx))))))))))) |
(* -1 (* (sin ky) (sin th))) |
(* -1 (sin ky)) |
(* 2 (* th (sin 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) |
(* -1 (* th (sin ky))) |
(* th (+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sin ky))) (* 1/6 (sin ky)))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* 1/6 (sin ky)) (* (pow th 2) (+ (* -1/120 (sin ky)) (* 1/5040 (* (pow th 2) (sin ky))))))))) |
(* 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) (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 (*.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 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))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (*.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 (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)) (sin.f64 ky)))) (*.f64 kx kx) (/.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))) |
(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 (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 (* (* (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)))))))) |
(fma.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (*.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))))) (*.f64 (/.f64 (*.f64 (neg.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)))) (-.f64 (*.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)))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sin.f64 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)))) (-.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 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64)))))) (*.f64 kx kx) (*.f64 (/.f64 (*.f64 (neg.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 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) ky)))))) |
(+ (* -2 (* (* (pow kx 2) (* th (* (sin ky) (sqrt 1/2)))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))) |
(fma.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 (*.f64 kx kx) th) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 ky)))) (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 ky) th) (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) ky))))))) |
(+ (* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (pow kx 2) (* th (* (sin ky) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky)))))))) |
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(+ (* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1 (* (* (pow kx 2) (* th (* (sin ky) (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 ky)))))) (* (* th (* (sin ky) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky)))))))))) |
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1 |
#s(literal 1 binary64) |
(+ 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)))))) |
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(+ 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)))))) |
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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)))) |
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(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6)))) |
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(/ -1 (sin ky)) |
(/.f64 #s(literal -1 binary64) (sin.f64 ky)) |
(- (* 1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky))) |
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(- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
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(- (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* -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 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
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(/ -1 kx) |
(/.f64 #s(literal -1 binary64) kx) |
(/ (- (* -1/6 (pow kx 2)) 1) kx) |
(/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx) |
(/ (- (* (pow kx 2) (- (* -7/360 (pow kx 2)) 1/6)) 1) kx) |
(/.f64 (fma.f64 (fma.f64 #s(literal -7/360 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (*.f64 kx kx) #s(literal -1 binary64)) kx) |
(/ (- (* (pow kx 2) (- (* (pow kx 2) (- (* -31/15120 (pow kx 2)) 7/360)) 1/6)) 1) kx) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -31/15120 binary64) (*.f64 kx kx) #s(literal -7/360 binary64)) (*.f64 kx kx) #s(literal -1/6 binary64)) (*.f64 kx kx) #s(literal -1 binary64)) kx) |
(* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) |
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(+ (* -1 (* (* (pow kx 2) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
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(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 ky))))))))) |
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(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 ky)))))) (* 1/2 (* (* (sqrt 1/2) (- (+ (* 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 (- 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 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 kx kx)) (-.f64 (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (/.f64 #s(literal 4/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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) (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 #s(literal 1/2 binary64) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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) (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 (neg.f64 (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
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(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
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(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))) |
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
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(* 2 (* (* th (* (sin ky) (sqrt 1/2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) |
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(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
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(sin kx) |
(sin.f64 kx) |
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
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(/ -1 (sin kx)) |
(/.f64 #s(literal -1 binary64) (sin.f64 kx)) |
(* (sqrt 1/2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) |
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(/ (* ky (sin th)) (sin kx)) |
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 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))))))))))))) (/ (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)))) |
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(/ (sin th) (sin kx)) |
(/.f64 (sin.f64 th) (sin.f64 kx)) |
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(+ (* (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))) |
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(+ (* (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))) |
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(+ (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)))))) |
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(+ (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)))))) |
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(* -1 (* ky (sin th))) |
(*.f64 (neg.f64 ky) (sin.f64 th)) |
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(*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* -1/120 (* (pow ky 2) (sin th))) (* 1/6 (sin th)))))) |
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(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* 1/6 (sin th)) (* (pow ky 2) (+ (* -1/120 (sin th)) (* 1/5040 (* (pow ky 2) (sin th))))))))) |
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(* -1 ky) |
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(* ky (- (* (pow ky 2) (+ 1/6 (* (pow ky 2) (- (* 1/5040 (pow ky 2)) 1/120)))) 1)) |
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ky |
(* ky (+ 1 (* -1/6 (pow ky 2)))) |
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(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6)))) |
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(- 1 (cos (* 2 kx))) |
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(- (+ 1 (* 2 (pow ky 2))) (cos (* 2 kx))) |
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(- (+ 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 (* (* 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))))))))))))))) |
(*.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 (-.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)))) #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 (-.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 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) (*.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))))) #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) |
(* 2 (* (* ky (* th (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(* ky (+ (* 2 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (pow ky 2) (+ (* -1 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th)) (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)) 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)) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) ky) |
(* ky (+ (* 2 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* 1/120 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* th (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx)))))))))) (* 2 (+ (* -1 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* 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 (sqrt.f64 #s(literal 1/2 binary64)) th) (-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/2 binary64) (fma.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th)) (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)) 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 (neg.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th)) (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)) 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)) th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) ky) |
(* ky (+ (* 2 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (+ (* -1 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))) (* (pow ky 2) (+ (* 2 (* (pow ky 2) (+ (* -1/2 (* (* th (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (* th (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (* 2 (+ (* 1/120 (* (* th (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* th (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* th (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx))))))))))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) (-.f64 (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (/.f64 #s(literal 4/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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) (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)))))) (*.f64 #s(literal -1/12 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) (-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))))))) (fma.f64 (*.f64 #s(literal -1/120 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th)) (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)) 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 (sqrt.f64 #s(literal 1/2 binary64)) th) (-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/2 binary64) (fma.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th)) (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)) 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 (neg.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th)) (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)) 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) |
(* 2 (* ky th)) |
(*.f64 (*.f64 ky th) #s(literal 2 binary64)) |
(* ky (+ (* -1/3 (* (pow ky 2) th)) (* 2 th))) |
(*.f64 (*.f64 th (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 2 binary64))) ky) |
(* ky (+ (* 2 th) (* (pow ky 2) (+ (* -1/3 th) (* 1/60 (* (pow ky 2) th)))))) |
(*.f64 (fma.f64 (*.f64 th (fma.f64 #s(literal 1/60 binary64) (*.f64 ky ky) #s(literal -1/3 binary64))) (*.f64 ky ky) (*.f64 #s(literal 2 binary64) th)) ky) |
(* ky (+ (* 2 th) (* (pow ky 2) (+ (* -1/3 th) (* (pow ky 2) (+ (* -1/2520 (* (pow ky 2) th)) (* 1/60 th))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 th (fma.f64 #s(literal -1/2520 binary64) (*.f64 ky ky) #s(literal 1/60 binary64))) (*.f64 ky ky) (*.f64 #s(literal -1/3 binary64) th)) (*.f64 ky ky) (*.f64 #s(literal 2 binary64) th)) 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)))) |
(*.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))) |
(- (* 1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx))) |
(fma.f64 (*.f64 ky (/.f64 ky (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 ky ky)) (*.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 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(- (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/2 (* (pow ky 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)))))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(fma.f64 (fma.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 (*.f64 #s(literal 1/2 binary64) (*.f64 ky ky)) (*.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 kx)))) (*.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 #s(literal -1 binary64) (sin.f64 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 #s(literal -2/315 binary64) (*.f64 ky ky) #s(literal 4/45 binary64)) (*.f64 ky ky) #s(literal -2/3 binary64)) (*.f64 ky ky) #s(literal 2 binary64)) (*.f64 ky ky)) |
(* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) |
(*.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))) |
(+ (* -1 (* (* (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
(fma.f64 (neg.f64 (*.f64 (*.f64 ky 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) kx))) #s(literal 3 binary64)))) (*.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)))) |
(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* (pow ky 2) (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx))))))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 ky ky) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (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) (*.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)))) |
(+ (* (sqrt 1/2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 1/2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (* (sqrt 1/2) (+ (* -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 (- 1 (cos (* 2 kx)))))) (* 1/2 (* (* (sqrt 1/2) (- (+ (* 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 (- 1 (cos (* 2 kx))))))))))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (-.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 1/2 binary64))) (-.f64 (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (/.f64 #s(literal 4/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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) (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)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))) (/.f64 #s(literal 2/3 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) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))))) (*.f64 ky ky) (*.f64 (neg.f64 (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) (*.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)))) |
(* -1 (* (sin ky) (sin th))) |
(*.f64 (neg.f64 (sin.f64 th)) (sin.f64 ky)) |
(* -1 (sin ky)) |
(neg.f64 (sin.f64 ky)) |
(* 2 (* th (sin ky))) |
(*.f64 (*.f64 (sin.f64 ky) th) #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))))) (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) |
(* -1 (* th (sin ky))) |
(*.f64 (neg.f64 th) (sin.f64 ky)) |
(* th (+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky))))) |
(*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sin ky))) (* 1/6 (sin ky)))))) |
(*.f64 (fma.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/120 binary64) (*.f64 th th) #s(literal 1/6 binary64))) (*.f64 th th) (neg.f64 (sin.f64 ky))) th) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* 1/6 (sin ky)) (* (pow th 2) (+ (* -1/120 (sin ky)) (* 1/5040 (* (pow th 2) (sin ky))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/5040 binary64) (*.f64 th th) #s(literal -1/120 binary64))) (*.f64 th th) (*.f64 #s(literal 1/6 binary64) (sin.f64 ky))) (*.f64 th th) (neg.f64 (sin.f64 ky))) th) |
(* 2 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (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 2 binary64) (sin.f64 ky) (*.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 th th) (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)) |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th)) |
(* -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: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 66 | 272 |
| 0 | 103 | 267 |
| 1 | 349 | 265 |
| 2 | 2208 | 252 |
| 0 | 9198 | 252 |
| 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 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) |
(neg.f64 (sin.f64 ky)) |
(sin.f64 ky) |
(-.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 (+ (* (- 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 #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(literal 2 binary64) (*.f64 (sin.f64 ky) th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) |
(sin.f64 kx) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) |
#s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(/.f64 #s(literal -1 binary64) (sin.f64 kx)) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) 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))))))) |
| Outputs |
|---|
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #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 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #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) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) #s(literal 2 binary64)) |
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (*.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) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (/.f64 (sin.f64 th) #s(literal 1/2 binary64))) |
(*.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))) (sin.f64 th)) |
(*.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 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 1/2 binary64)) |
(/.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 #s(literal 1 binary64) (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (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 (sin.f64 ky) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (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 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) (sin.f64 th)))) |
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (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))) |
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (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)) (sin.f64 th)) |
(*.f64 (neg.f64 (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (sin.f64 th) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) #s(literal -1 binary64)) |
(/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (neg.f64 (sin.f64 th))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(neg.f64 (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(neg.f64 (/.f64 (sin.f64 th) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) #s(literal -1 binary64))) |
(sin.f64 th) |
(*.f64 (pow.f64 (pow.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) |
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) |
(*.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)) (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 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sqrt.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 binary64)))) |
(*.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 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 binary64)) #s(literal 1/2 binary64))) |
(*.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 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal -1 binary64)))) |
(*.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (sqrt.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 binary64)))) |
(*.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (pow.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 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 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(pow.f64 (exp.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)) |
(pow.f64 (*.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (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)))) #s(literal 1/4 binary64)) |
(pow.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)) #s(literal 2 binary64)) |
(pow.f64 (/.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #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 1/2 binary64)) |
(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #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))))) (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) |
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(/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
(*.f64 (*.f64 #s(literal 2 binary64) th) (sin.f64 ky)) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) th) |
(*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) |
(*.f64 (sin.f64 ky) (*.f64 th #s(literal 2 binary64))) |
(*.f64 th (*.f64 #s(literal 2 binary64) (sin.f64 ky))) |
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(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)))) |
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(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(neg.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) |
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(*.f64 (sqrt.f64 (sin.f64 kx)) (sqrt.f64 (sin.f64 kx))) |
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(sin.f64 kx) |
(exp.f64 (log.f64 (sin.f64 kx))) |
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(/.f64 (*.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64)) #s(literal -1 binary64)) th) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) |
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(/.f64 (*.f64 th (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) |
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(fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th (*.f64 #s(literal 1 binary64) th)) |
(fma.f64 #s(literal 1 binary64) th (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) |
(fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) (*.f64 th #s(literal 1 binary64))) |
(fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)))) |
(+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th) (*.f64 #s(literal 1 binary64) th)) |
(+.f64 (*.f64 #s(literal 1 binary64) th) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) |
(+.f64 (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))) (*.f64 th #s(literal 1 binary64))) |
(+.f64 (*.f64 th #s(literal 1 binary64)) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)))) |
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(/.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) (/.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 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 1 binary64)) #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(fma.f64 #s(literal -1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64)) |
(fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(-.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 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) |
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (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))))) (sqrt.f64 (-.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (-.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 1 binary64)))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (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)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (-.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 1 binary64)))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(*.f64 (pow.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal -1/4 binary64))) |
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal -1/2 binary64))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(pow.f64 (exp.f64 (-.f64 (log.f64 #s(literal 1/2 binary64)) (log1p.f64 (fma.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)) |
(pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64))) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 1/2 binary64)) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(/.f64 (sqrt.f64 #s(literal -1/2 binary64)) (sqrt.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) |
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) |
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) |
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) |
(exp.f64 (*.f64 (-.f64 (log.f64 #s(literal 1/2 binary64)) (log1p.f64 (fma.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))) |
Compiled 42 987 to 3 929 computations (90.9% saved)
60 alts after pruning (56 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 777 | 35 | 812 |
| Fresh | 10 | 21 | 31 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 1 | 1 |
| Total | 789 | 60 | 849 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.6% | (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
| 52.8% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) | |
| 95.5% | (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky)))) | |
| 77.1% | (*.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)) |
| 62.6% | (*.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)) | |
| ▶ | 33.2% | (*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
| ✓ | 52.8% | (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
| 36.7% | (*.f64 (/.f64 (sin.f64 ky) (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)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 25.2% | (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 76.8% | (*.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)) | |
| ▶ | 35.7% | (*.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)) |
| 35.7% | (*.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)) | |
| 47.9% | (*.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)) | |
| 29.1% | (*.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)) | |
| 35.6% | (*.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)) | |
| 29.2% | (*.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)) | |
| 32.9% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) | |
| 29.1% | (*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 39.2% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) | |
| 27.1% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) | |
| 17.3% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) | |
| 21.5% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) | |
| 17.7% | (*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 32.8% | (*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) | |
| 32.8% | (*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) | |
| 43.6% | (*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) | |
| 28.6% | (*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 32.9% | (*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) | |
| 35.7% | (*.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)) (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)) | |
| 24.6% | (*.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))))))) (sin.f64 th)) | |
| 30.1% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) | |
| 17.4% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 28.0% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| ▶ | 17.7% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
| 49.3% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) | |
| 17.9% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 42.2% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) | |
| 42.3% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) th)) | |
| 35.4% | #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))))))) | |
| 24.5% | #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))))))) | |
| 76.9% | #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))))))))) | |
| ✓ | 42.3% | #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))))))))) |
| 14.5% | #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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) | |
| 15.4% | #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) #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)))))))) | |
| 26.7% | #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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 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)))))))) | |
| 42.1% | #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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) | |
| 20.3% | #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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) | |
| 16.1% | #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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) | |
| 42.1% | #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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) | |
| 13.6% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) | |
| 20.3% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) ky)))))))) | |
| ✓ | 33.2% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
| 19.4% | #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))) | |
| 19.5% | #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))) | |
| 19.4% | #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))) | |
| 19.4% | #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))) | |
| 10.2% | #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))) | |
| ▶ | 12.0% | #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))) |
| 12.0% | #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 4 186 to 3 022 computations (27.8% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sin.f64 ky) | |
| cost-diff | 0 | (*.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)) | |
| cost-diff | 128 | (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))) | |
| cost-diff | 384 | (/.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))) | |
| cost-diff | 0 | #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) | |
| cost-diff | 0 | (sin.f64 th) | |
| cost-diff | 0 | (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) | |
| cost-diff | 0 | (sin.f64 ky) | |
| cost-diff | 0 | (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) | |
| cost-diff | 0 | #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) | |
| cost-diff | 0 | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 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 | (hypot.f64 (sin.f64 kx) (sin.f64 ky)) | |
| cost-diff | 0 | (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) | |
| cost-diff | 0 | (sin.f64 ky) | |
| cost-diff | 384 | (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 70 | 519 |
| 0 | 107 | 479 |
| 1 | 161 | 469 |
| 2 | 253 | 469 |
| 3 | 440 | 459 |
| 4 | 708 | 456 |
| 5 | 1107 | 456 |
| 6 | 1803 | 456 |
| 7 | 2607 | 456 |
| 8 | 3003 | 456 |
| 9 | 3464 | 456 |
| 10 | 3956 | 456 |
| 11 | 4432 | 456 |
| 12 | 5474 | 456 |
| 13 | 5955 | 456 |
| 14 | 6239 | 456 |
| 15 | 6311 | 456 |
| 16 | 6432 | 456 |
| 17 | 6466 | 456 |
| 18 | 6503 | 456 |
| 19 | 6664 | 456 |
| 20 | 7094 | 456 |
| 21 | 7470 | 456 |
| 22 | 7482 | 456 |
| 0 | 8338 | 441 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(sin.f64 ky) |
ky |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(sin.f64 kx) |
kx |
(sin.f64 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 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 (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
#s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) |
(*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th) |
(*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) |
(sin.f64 ky) |
ky |
(fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) |
#s(literal 1/6 binary64) |
(*.f64 th th) |
th |
#s(literal -1 binary64) |
#s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(/.f64 #s(literal -1 binary64) (sin.f64 kx)) |
(sin.f64 kx) |
kx |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) |
(sin.f64 th) |
th |
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(*.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)) |
(/.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 ky) |
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)) |
(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(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)))) |
(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))) |
(-.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 |
(*.f64 (*.f64 ky ky) #s(literal 4 binary64)) |
(*.f64 ky ky) |
#s(literal 4 binary64) |
(sin.f64 th) |
th |
| Outputs |
|---|
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th)) |
(sin.f64 ky) |
ky |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(sin.f64 kx) |
kx |
(sin.f64 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 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 (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th) (neg.f64 (sin.f64 ky))))) |
#s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) |
#s(approx (* (neg (sin ky)) (sin th)) (*.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th) (neg.f64 (sin.f64 ky)))) |
(*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th) |
(*.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th) (neg.f64 (sin.f64 ky))) |
(*.f64 (sin.f64 ky) (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)) (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64)) |
#s(literal 1/6 binary64) |
(*.f64 th th) |
th |
#s(literal -1 binary64) |
#s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(/.f64 #s(literal -1 binary64) (sin.f64 kx)) |
(sin.f64 kx) |
kx |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) |
(sin.f64 th) |
th |
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) |
(sin.f64 ky) |
ky |
(*.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)) |
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sin.f64 th)) (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (*.f64 #s(literal 4 binary64) ky) ky #s(literal 2 binary64)))))) |
(/.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))) |
(/.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (*.f64 #s(literal 4 binary64) ky) ky #s(literal 2 binary64)))))) |
(sin.f64 ky) |
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)) |
(/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (*.f64 #s(literal 4 binary64) ky) ky #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(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))))) |
(sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (*.f64 #s(literal 4 binary64) ky) ky #s(literal 2 binary64))))) |
#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(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (fma.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (*.f64 #s(literal 4 binary64) ky) ky #s(literal 2 binary64)))) |
(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))) |
(fma.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (*.f64 #s(literal 4 binary64) ky) ky #s(literal 2 binary64))) |
(-.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 |
(*.f64 (*.f64 ky ky) #s(literal 4 binary64)) |
(*.f64 #s(literal 4 binary64) (*.f64 ky ky)) |
(*.f64 ky ky) |
#s(literal 4 binary64) |
(sin.f64 th) |
th |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.13119125976844204 | (/.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))) | |
| accuracy | 3.63146253860364 | (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))))) | |
| accuracy | 17.174609684164565 | (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) | |
| accuracy | 33.21483629840722 | #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)))) | |
| accuracy | 0.0 | (sin.f64 ky) | |
| accuracy | 0.28515625 | (*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) | |
| accuracy | 0.29296875 | (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) | |
| accuracy | 43.04601520600584 | #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) | |
| accuracy | 2.721527494376109 | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| accuracy | 3.328638538214663 | (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) | |
| accuracy | 30.1173906646843 | #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) | |
| accuracy | 45.38357521017723 | #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) | |
| accuracy | 0.19921875 | (*.f64 (*.f64 th th) #s(literal -1/6 binary64)) | |
| accuracy | 30.151368900103094 | #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)) | |
| accuracy | 32.69075597898339 | #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) | |
| accuracy | 42.74778530861426 | #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 | 0.0 | (sin.f64 kx) | |
| accuracy | 0.0625 | (hypot.f64 (sin.f64 kx) (sin.f64 ky)) | |
| accuracy | 0.23828125 | (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) | |
| accuracy | 0.26171875 | (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
| 391.0ms | 72× | 1 | valid |
| 140.0ms | 60× | 2 | valid |
| 102.0ms | 124× | 0 | valid |
Compiled 905 to 130 computations (85.6% saved)
ival-hypot: 279.0ms (48.7% of total)ival-cos: 82.0ms (14.3% of total)ival-mult: 64.0ms (11.2% of total)ival-sin: 52.0ms (9.1% of total)adjust: 32.0ms (5.6% of total)const: 19.0ms (3.3% of total)ival-div: 18.0ms (3.1% of total)ival-add: 8.0ms (1.4% of total)ival-pow2: 6.0ms (1% of total)ival-sqrt: 5.0ms (0.9% of total)ival-sub: 4.0ms (0.7% of total)ival-neg: 2.0ms (0.3% of total)exact: 1.0ms (0.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(sin.f64 ky) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) |
(hypot.f64 (sin.f64 kx) (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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
#s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) |
(*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) |
(sin.f64 th) |
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) |
(/.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))) |
(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))) |
(*.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)) |
(sin.f64 kx) |
(*.f64 (*.f64 th th) #s(literal -1/6 binary64)) |
#s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
#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)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(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))))) |
| 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 ky) (sin th)) |
(+ (* 1/2 (/ (pow kx 2) (* (sin ky) (sin th)))) (/ (sin ky) (sin th))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (* (sin ky) (sin th)))) (* 1/2 (/ 1 (* (sin ky) (sin th)))))) (/ (sin ky) (sin th))) |
(+ (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (* (sin ky) (sin th)))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (* (sin ky) (sin th)))))) (* 1/2 (/ 1 (* (sin ky) (sin th)))))) (/ (sin ky) (sin th))) |
(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 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))) |
(* 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)))))))))) |
(* 4 (pow ky 2)) |
(+ (* 4 (pow kx 2)) (* 4 (pow ky 2))) |
(+ (* 4 (pow ky 2)) (* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))) |
(+ (* 4 (pow ky 2)) (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (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)))))))))) |
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)))) |
(/ -1 (sin ky)) |
(- (* 1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* -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 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin 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 (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 th)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(* (sin th) (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)))) (* 4 (pow ky 2))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(sin kx) |
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))) |
(- 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)))) |
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)))) |
(/ (sin kx) (sin th)) |
(+ (* 1/2 (/ (pow ky 2) (* (sin kx) (sin th)))) (/ (sin kx) (sin th))) |
(+ (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (* (sin kx) (sin th)))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) |
(+ (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (* (sin kx) (sin th)))))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) |
(+ (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)))))) |
(* -1 (* ky (sin th))) |
(* ky (+ (* -1 (sin th)) (* 1/6 (* (pow ky 2) (sin th))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* -1/120 (* (pow ky 2) (sin th))) (* 1/6 (sin th)))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* 1/6 (sin th)) (* (pow ky 2) (+ (* -1/120 (sin th)) (* 1/5040 (* (pow ky 2) (sin th))))))))) |
(* ky (- (* 1/6 (pow th 2)) 1)) |
(* ky (- (+ (* -1/6 (* (pow ky 2) (- (* 1/6 (pow th 2)) 1))) (* 1/6 (pow th 2))) 1)) |
(* ky (- (+ (* 1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (- (* 1/6 (pow th 2)) 1)) (* 1/120 (* (pow ky 2) (- (* 1/6 (pow th 2)) 1)))))) 1)) |
(* ky (- (+ (* 1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (- (* 1/6 (pow th 2)) 1)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (- (* 1/6 (pow th 2)) 1))) (* 1/120 (- (* 1/6 (pow th 2)) 1))))))) 1)) |
(/ (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))) |
(* 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)))) |
(* 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))))))))))))))) |
(/ -1 (sin kx)) |
(- (* 1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/2 (* (pow ky 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)))))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(+ (* 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))))) |
(* (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)))))))))))) |
(* -1 (* (sin ky) (sin th))) |
(* (sin ky) (- (* 1/6 (pow th 2)) 1)) |
(* (pow ky 2) (+ 4 (* 2 (/ (- 1 (cos (* 2 kx))) (pow 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)))))))))))) |
(* (/ 1 th) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/ (+ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* 1/6 (* (pow th 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) th) |
(/ (+ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (pow th 2) (+ (* 7/360 (* (pow th 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/6 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) th) |
(/ (+ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (pow th 2) (+ (* 1/6 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 31/15120 (* (pow th 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 7/360 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) th) |
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 (* -1/6 (pow th 2))) |
(* -1 (* th (sin ky))) |
(* th (+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sin ky))) (* 1/6 (sin ky)))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* 1/6 (sin ky)) (* (pow th 2) (+ (* -1/120 (sin ky)) (* 1/5040 (* (pow th 2) (sin ky))))))))) |
(* -1 (sin ky)) |
(+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky)))) |
(* 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))))))))))) |
(* 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)) |
(* 1/6 (* (pow th 2) (sin ky))) |
(* (pow th 2) (+ (* -1 (/ (sin ky) (pow th 2))) (* 1/6 (sin ky)))) |
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2))))) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 21.0ms | ky | @ | inf | ((/ (sin ky) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th))) (sin ky) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ (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) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (* (sin ky) (+ (* 1/6 (* th th)) -1)) (* (/ (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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin kx) (* (* th th) -1/6) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))))) |
| 10.0ms | th | @ | inf | ((/ (sin ky) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th))) (sin ky) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ (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) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (* (sin ky) (+ (* 1/6 (* th th)) -1)) (* (/ (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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin kx) (* (* th th) -1/6) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))))) |
| 6.0ms | ky | @ | 0 | ((/ (sin ky) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th))) (sin ky) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ (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) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (* (sin ky) (+ (* 1/6 (* th th)) -1)) (* (/ (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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin kx) (* (* th th) -1/6) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))))) |
| 6.0ms | th | @ | -inf | ((/ (sin ky) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th))) (sin ky) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ (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) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (* (sin ky) (+ (* 1/6 (* th th)) -1)) (* (/ (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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin kx) (* (* th th) -1/6) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))))) |
| 5.0ms | ky | @ | -inf | ((/ (sin ky) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th))) (sin ky) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ (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) (* (* (neg (sin ky)) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (neg (sin ky)) (sin th)) (* (sin ky) (+ (* 1/6 (* th th)) -1)) (* (/ (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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (sin kx) (* (* th th) -1/6) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))) (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 873 | 5642 |
| 1 | 2892 | 5185 |
| 2 | 7398 | 5177 |
| 0 | 8019 | 4904 |
| 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 ky) (sin th)) |
(+ (* 1/2 (/ (pow kx 2) (* (sin ky) (sin th)))) (/ (sin ky) (sin th))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (* (sin ky) (sin th)))) (* 1/2 (/ 1 (* (sin ky) (sin th)))))) (/ (sin ky) (sin th))) |
(+ (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (* (sin ky) (sin th)))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (* (sin ky) (sin th)))))) (* 1/2 (/ 1 (* (sin ky) (sin th)))))) (/ (sin ky) (sin th))) |
(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 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))) |
(* 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)))))))))) |
(* 4 (pow ky 2)) |
(+ (* 4 (pow kx 2)) (* 4 (pow ky 2))) |
(+ (* 4 (pow ky 2)) (* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))) |
(+ (* 4 (pow ky 2)) (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (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)))))))))) |
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)))) |
(/ -1 (sin ky)) |
(- (* 1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
(- (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* -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 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin 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 (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 th)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(* (sin th) (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)))) (* 4 (pow ky 2))) |
(* 2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))))))) |
(sin kx) |
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* 2 (- 1 (cos (* 2 ky))))) |
(- 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)))) |
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)))) |
(/ (sin kx) (sin th)) |
(+ (* 1/2 (/ (pow ky 2) (* (sin kx) (sin th)))) (/ (sin kx) (sin th))) |
(+ (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (* (sin kx) (sin th)))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) |
(+ (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (* (sin kx) (sin th)))))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) |
(+ (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)))))) |
(* -1 (* ky (sin th))) |
(* ky (+ (* -1 (sin th)) (* 1/6 (* (pow ky 2) (sin th))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* -1/120 (* (pow ky 2) (sin th))) (* 1/6 (sin th)))))) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* 1/6 (sin th)) (* (pow ky 2) (+ (* -1/120 (sin th)) (* 1/5040 (* (pow ky 2) (sin th))))))))) |
(* ky (- (* 1/6 (pow th 2)) 1)) |
(* ky (- (+ (* -1/6 (* (pow ky 2) (- (* 1/6 (pow th 2)) 1))) (* 1/6 (pow th 2))) 1)) |
(* ky (- (+ (* 1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (- (* 1/6 (pow th 2)) 1)) (* 1/120 (* (pow ky 2) (- (* 1/6 (pow th 2)) 1)))))) 1)) |
(* ky (- (+ (* 1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (- (* 1/6 (pow th 2)) 1)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (- (* 1/6 (pow th 2)) 1))) (* 1/120 (- (* 1/6 (pow th 2)) 1))))))) 1)) |
(/ (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))) |
(* 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)))) |
(* 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))))))))))))))) |
(/ -1 (sin kx)) |
(- (* 1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(- (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/2 (* (pow ky 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)))))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(+ (* 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))))) |
(* (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)))))))))))) |
(* -1 (* (sin ky) (sin th))) |
(* (sin ky) (- (* 1/6 (pow th 2)) 1)) |
(* (pow ky 2) (+ 4 (* 2 (/ (- 1 (cos (* 2 kx))) (pow 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)))))))))))) |
(* (/ 1 th) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/ (+ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* 1/6 (* (pow th 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) th) |
(/ (+ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (pow th 2) (+ (* 7/360 (* (pow th 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/6 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) th) |
(/ (+ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (pow th 2) (+ (* 1/6 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 31/15120 (* (pow th 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 7/360 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) th) |
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 (* -1/6 (pow th 2))) |
(* -1 (* th (sin ky))) |
(* th (+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sin ky))) (* 1/6 (sin ky)))))) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* 1/6 (sin ky)) (* (pow th 2) (+ (* -1/120 (sin ky)) (* 1/5040 (* (pow th 2) (sin ky))))))))) |
(* -1 (sin ky)) |
(+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky)))) |
(* 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))))))))))) |
(* 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)) |
(* 1/6 (* (pow th 2) (sin ky))) |
(* (pow th 2) (+ (* -1 (/ (sin ky) (pow th 2))) (* 1/6 (sin ky)))) |
(* -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) (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 (*.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 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 ky) (sin th)) |
(/.f64 (sin.f64 ky) (sin.f64 th)) |
(+ (* 1/2 (/ (pow kx 2) (* (sin ky) (sin th)))) (/ (sin ky) (sin th))) |
(fma.f64 (/.f64 (*.f64 kx kx) (sin.f64 th)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (/.f64 (sin.f64 ky) (sin.f64 th))) |
(+ (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (* (sin ky) (sin th)))) (* 1/2 (/ 1 (* (sin ky) (sin th)))))) (/ (sin ky) (sin th))) |
(fma.f64 (fma.f64 (/.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 kx)) (sin.f64 th)) (/.f64 #s(literal -1/2 binary64) (sin.f64 ky)) (/.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 th)) (sin.f64 ky))) (*.f64 kx kx) (/.f64 (sin.f64 ky) (sin.f64 th))) |
(+ (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (* (sin ky) (sin th)))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (* (sin ky) (sin th)))))) (* 1/2 (/ 1 (* (sin ky) (sin th)))))) (/ (sin ky) (sin th))) |
(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 (/.f64 kx (sin.f64 th)) (/.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)) (*.f64 (sin.f64 th) (sin.f64 ky)))) (*.f64 kx kx) (/.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 th)) (sin.f64 ky))) (*.f64 kx kx) (/.f64 (sin.f64 ky) (sin.f64 th))) |
(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)) |
(/ (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))) |
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(* 2 (* (* (sin ky) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
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(* 4 (pow ky 2)) |
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(* 2 (* (* (sin ky) (* (sin th) (sqrt 1/2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) |
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kx |
(* kx (+ 1 (* -1/6 (pow kx 2)))) |
(*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx) |
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6)))) |
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(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6)))) |
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(/ -1 (sin ky)) |
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(- (* 1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky))) |
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(- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
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(- (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* -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 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky))) |
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(* 2 (- 1 (cos (* 2 ky)))) |
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(+ (* 2 (- 1 (cos (* 2 ky)))) (* 4 (pow kx 2))) |
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(+ (* 2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))) |
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(+ (* 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 (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)))))))))))) |
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(* (* (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 th)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) |
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
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(* 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)))) (* 4 (pow 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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(sin kx) |
(sin.f64 kx) |
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) |
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(+ (* 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)))))) |
(- 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)))) |
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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)))) |
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(/ (sin kx) (sin th)) |
(/.f64 (sin.f64 kx) (sin.f64 th)) |
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(fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 th)) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (/.f64 (sin.f64 kx) (sin.f64 th))) |
(+ (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (* (sin kx) (sin th)))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) |
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(+ (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (* (sin kx) (sin th)))))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) |
(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 (/.f64 ky (sin.f64 th)) (/.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)) (*.f64 (sin.f64 th) (sin.f64 kx)))) (*.f64 ky ky) (/.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 th)) (sin.f64 kx))) (*.f64 ky ky) (/.f64 (sin.f64 kx) (sin.f64 th))) |
(+ (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)) |
(* -1 (* ky (sin th))) |
(*.f64 (neg.f64 ky) (sin.f64 th)) |
(* ky (+ (* -1 (sin th)) (* 1/6 (* (pow ky 2) (sin th))))) |
(*.f64 (*.f64 (sin.f64 th) (fma.f64 #s(literal 1/6 binary64) (*.f64 ky ky) #s(literal -1 binary64))) ky) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* -1/120 (* (pow ky 2) (sin th))) (* 1/6 (sin th)))))) |
(*.f64 (fma.f64 (*.f64 (sin.f64 th) (fma.f64 #s(literal -1/120 binary64) (*.f64 ky ky) #s(literal 1/6 binary64))) (*.f64 ky ky) (neg.f64 (sin.f64 th))) ky) |
(* ky (+ (* -1 (sin th)) (* (pow ky 2) (+ (* 1/6 (sin th)) (* (pow ky 2) (+ (* -1/120 (sin th)) (* 1/5040 (* (pow ky 2) (sin th))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 th) (fma.f64 #s(literal 1/5040 binary64) (*.f64 ky ky) #s(literal -1/120 binary64))) (*.f64 ky ky) (*.f64 #s(literal 1/6 binary64) (sin.f64 th))) (*.f64 ky ky) (neg.f64 (sin.f64 th))) ky) |
(* ky (- (* 1/6 (pow th 2)) 1)) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky) |
(* ky (- (+ (* -1/6 (* (pow ky 2) (- (* 1/6 (pow th 2)) 1))) (* 1/6 (pow th 2))) 1)) |
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(* ky (- (+ (* 1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (- (* 1/6 (pow th 2)) 1)) (* 1/120 (* (pow ky 2) (- (* 1/6 (pow th 2)) 1)))))) 1)) |
(*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 ky ky) #s(literal -1/6 binary64))) (*.f64 ky ky) (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky) |
(* ky (- (+ (* 1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (- (* 1/6 (pow th 2)) 1)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (- (* 1/6 (pow th 2)) 1))) (* 1/120 (- (* 1/6 (pow th 2)) 1))))))) 1)) |
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(/ (sin th) (sin kx)) |
(/.f64 (sin.f64 th) (sin.f64 kx)) |
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(+ (* (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))) |
(* 2 (* (* ky (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) |
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(* 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))))))))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (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))))) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/120 binary64) (fma.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 (*.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 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 (- 1 (cos (* 2 kx)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)) |
(* 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))))))))))))) |
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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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(/ -1 (sin kx)) |
(/.f64 #s(literal -1 binary64) (sin.f64 kx)) |
(- (* 1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (*.f64 ky ky) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 ky ky)) (*.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 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
(- (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/2 (* (pow ky 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)))))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx))) |
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(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* -4/3 (pow ky 2))))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 ky ky) #s(literal 4 binary64)) (*.f64 ky ky))) |
(+ (* 2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 4 (* (pow ky 2) (- (* 8/45 (pow ky 2)) 4/3))))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal 8/45 binary64) (*.f64 ky ky) #s(literal -4/3 binary64)) (*.f64 ky ky) #s(literal 4 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 #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)))))))))))) |
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(* -1 (* (sin ky) (sin th))) |
(*.f64 (neg.f64 (sin.f64 th)) (sin.f64 ky)) |
(* (sin ky) (- (* 1/6 (pow th 2)) 1)) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 ky)) |
(* (pow ky 2) (+ 4 (* 2 (/ (- 1 (cos (* 2 kx))) (pow ky 2))))) |
(*.f64 (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (*.f64 ky ky)) #s(literal 2 binary64) #s(literal 4 binary64)) (*.f64 ky 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)))))))))) |
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(* 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 th) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th) |
(/ (+ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* 1/6 (* (pow th 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) th) |
(/.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th) |
(/ (+ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (pow th 2) (+ (* 7/360 (* (pow th 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/6 (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 th) #s(literal 1/6 binary64))) (*.f64 th th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th) |
(/ (+ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (pow th 2) (+ (* 1/6 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 31/15120 (* (pow th 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 7/360 (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 th) #s(literal 7/360 binary64))) (*.f64 th th) (*.f64 #s(literal 1/6 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 th th) (hypot.f64 (sin.f64 kx) (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) |
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)) |
(* -1 (* th (sin ky))) |
(*.f64 (neg.f64 th) (sin.f64 ky)) |
(* th (+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky))))) |
(*.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 ky)) th) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sin ky))) (* 1/6 (sin ky)))))) |
(*.f64 (fma.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/120 binary64) (*.f64 th th) #s(literal 1/6 binary64))) (*.f64 th th) (neg.f64 (sin.f64 ky))) th) |
(* th (+ (* -1 (sin ky)) (* (pow th 2) (+ (* 1/6 (sin ky)) (* (pow th 2) (+ (* -1/120 (sin ky)) (* 1/5040 (* (pow th 2) (sin ky))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/5040 binary64) (*.f64 th th) #s(literal -1/120 binary64))) (*.f64 th th) (*.f64 #s(literal 1/6 binary64) (sin.f64 ky))) (*.f64 th th) (neg.f64 (sin.f64 ky))) th) |
(* -1 (sin ky)) |
(neg.f64 (sin.f64 ky)) |
(+ (* -1 (sin ky)) (* 1/6 (* (pow th 2) (sin ky)))) |
(*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 ky)) |
(* 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) |
(* 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 (/.f64 #s(literal 1 binary64) th) th) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 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 2) (sin ky))) |
(*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky)) |
(* (pow th 2) (+ (* -1 (/ (sin ky) (pow th 2))) (* 1/6 (sin ky)))) |
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 ky) (/.f64 (neg.f64 (sin.f64 ky)) (*.f64 th th))) (*.f64 th th)) |
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2))))) |
(*.f64 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 (/.f64 #s(literal 1 binary64) th) th))) (pow.f64 th #s(literal 3 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 70 | 413 |
| 0 | 107 | 373 |
| 1 | 352 | 365 |
| 2 | 2103 | 365 |
| 0 | 9175 | 361 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(sin.f64 ky) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) |
(hypot.f64 (sin.f64 kx) (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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
#s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) |
(*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
(/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) |
(sin.f64 th) |
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) |
(/.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))) |
(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))) |
(*.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)) |
(sin.f64 kx) |
(*.f64 (*.f64 th th) #s(literal -1/6 binary64)) |
#s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
#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)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(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))))) |
| Outputs |
|---|
(*.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 (sin.f64 ky) (pow.f64 (sin.f64 th) #s(literal -1 binary64))) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) |
(*.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 (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 (sqrt.f64 (sin.f64 ky)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))) |
(*.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 (*.f64 (sin.f64 th) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (sin.f64 ky) (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 (sqrt.f64 (sin.f64 ky)) (pow.f64 (sin.f64 th) #s(literal -1 binary64))) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (neg.f64 (sin.f64 th)) #s(literal -1 binary64)))) |
(*.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) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (/.f64 (sin.f64 ky) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))) |
(*.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) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (sin.f64 th)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (sin.f64 ky) (neg.f64 (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) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (neg.f64 (sin.f64 th))) |
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (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 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (sin.f64 th) #s(literal -1 binary64)) (sin.f64 ky)) #s(literal -1 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))) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)) |
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sin.f64 ky) (neg.f64 (pow.f64 (sin.f64 th) #s(literal -1 binary64))))) |
(*.f64 #s(literal -1 binary64) (/.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))) |
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))) |
(*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))) |
(*.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))) (/.f64 #s(literal -1 binary64) (neg.f64 (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 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(pow.f64 (/.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky)) #s(literal -1 binary64)) |
(/.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 (*.f64 (sin.f64 ky) #s(literal 1 binary64))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th)))) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th)))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th))) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64))) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) |
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th)))) (*.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th))) (sin.f64 ky))) (*.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th))))) |
(/.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 th) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (*.f64 (sin.f64 ky) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(/.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(/.f64 (neg.f64 (sin.f64 th)) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky)) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky)))) |
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (neg.f64 (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (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 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))) |
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (pow.f64 (sin.f64 th) #s(literal -1 binary64))) (/.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) (/.f64 (neg.f64 (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (sin.f64 ky)) (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 2 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (sin.f64 ky) #s(literal 1 binary64)) |
(sin.f64 ky) |
(exp.f64 (log.f64 (sin.f64 ky))) |
(*.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (sin.f64 th) #s(literal -1 binary64))) |
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(*.f64 (pow.f64 (sin.f64 th) #s(literal -1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) |
(*.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (sin.f64 th)) #s(literal -1 binary64))) |
(*.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (neg.f64 (sin.f64 th)) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (pow.f64 (sin.f64 th) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) #s(literal 1 binary64)) |
(/.f64 (neg.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 1 binary64))) (neg.f64 (sin.f64 th))) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (neg.f64 (neg.f64 (neg.f64 (sin.f64 th))))) |
(/.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 1 binary64)) (sin.f64 th)) |
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (neg.f64 (neg.f64 (sin.f64 th)))) |
(/.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (sin.f64 th))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) |
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) |
(neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(literal -1 binary64))) |
(*.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)) (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 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sqrt.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 binary64)))) |
(*.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 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 binary64)) #s(literal 1/2 binary64))) |
(*.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 (hypot.f64 (pow.f64 (sin.f64 ky) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))) #s(literal -1 binary64)))) |
(*.f64 (hypot.f64 (pow.f64 (sin.f64 ky) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (sqrt.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 kx) (sin.f64 ky)) #s(literal 2 binary64))) #s(literal -1 binary64)))) |
(*.f64 (hypot.f64 (pow.f64 (sin.f64 ky) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (pow.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (hypot.f64 (pow.f64 (sin.f64 ky) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 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 kx) (sin.f64 ky)) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(pow.f64 (exp.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)) |
(pow.f64 (*.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (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)))) #s(literal 1/4 binary64)) |
(pow.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)) #s(literal 2 binary64)) |
(pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) |
(/.f64 (neg.f64 (hypot.f64 (pow.f64 (sin.f64 ky) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64)))))) |
(/.f64 (neg.f64 (hypot.f64 (pow.f64 (sin.f64 ky) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (neg.f64 (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 kx) (sin.f64 ky)) #s(literal 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 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.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 kx) (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)))))) #s(literal 2 binary64)) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) |
(/.f64 (hypot.f64 (pow.f64 (sin.f64 ky) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))))) |
(/.f64 (hypot.f64 (pow.f64 (sin.f64 ky) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 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 kx) (sin.f64 ky)) #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.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 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.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 kx) (sin.f64 ky)) #s(literal 2 binary64))) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))) |
(sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) |
(hypot.f64 (neg.f64 (sin.f64 ky)) (sin.f64 kx)) |
(hypot.f64 (sin.f64 kx) (neg.f64 (sin.f64 ky))) |
(hypot.f64 (sin.f64 kx) (sin.f64 ky)) |
(hypot.f64 (sin.f64 ky) (sin.f64 kx)) |
(exp.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))) |
#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) |
(*.f64 th #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64)))) |
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) |
(*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64)))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
#s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 th (sin.f64 ky)) (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)) (sin.f64 ky)) |
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(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) (*.f64 #s(literal 1/2 binary64) (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 #s(literal 4 binary64) (*.f64 ky ky))))))) |
(/.f64 (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (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 #s(literal 4 binary64) (*.f64 ky ky)))))) #s(literal 1/2 binary64)) |
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th)) (*.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 #s(literal 4 binary64) (*.f64 ky ky))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (*.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 #s(literal 4 binary64) (*.f64 ky ky))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (*.f64 #s(literal 1/2 binary64) (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 #s(literal 4 binary64) (*.f64 ky ky))))))) |
(/.f64 (neg.f64 (sin.f64 th)) (neg.f64 (*.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 #s(literal 4 binary64) (*.f64 ky ky))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.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 #s(literal 4 binary64) (*.f64 ky ky))))) (sin.f64 th)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))))) |
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (*.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 #s(literal 4 binary64) (*.f64 ky ky))))) #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.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 #s(literal 4 binary64) (*.f64 ky ky))))) (sin.f64 th)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(/.f64 (sin.f64 th) (*.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 #s(literal 4 binary64) (*.f64 ky ky))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (*.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 #s(literal 4 binary64) (*.f64 ky ky))))) #s(literal -1/2 binary64))) (/.f64 (*.f64 (sin.f64 th) (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 #s(literal 4 binary64) (*.f64 ky ky))))) #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (sin.f64 kx)) (sqrt.f64 (sin.f64 kx))) |
(pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (sin.f64 kx) #s(literal 1 binary64)) |
(sin.f64 kx) |
(exp.f64 (log.f64 (sin.f64 kx))) |
(*.f64 (*.f64 #s(literal -1/6 binary64) th) th) |
(*.f64 (*.f64 #s(literal 1/6 binary64) th) (*.f64 th #s(literal -1 binary64))) |
(*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 th th)) #s(literal -1 binary64)) |
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) |
(*.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 th th) #s(literal -1 binary64))) |
(*.f64 (*.f64 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 (*.f64 th th) #s(literal -1/6 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) |
(*.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 th th) #s(literal 1 binary64))) |
(*.f64 #s(literal -1/6 binary64) (*.f64 th th)) |
(*.f64 th (*.f64 (*.f64 #s(literal -1/6 binary64) th) #s(literal 1 binary64))) |
(*.f64 th (*.f64 #s(literal -1/6 binary64) th)) |
#s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) |
#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 #s(literal 4 binary64) (*.f64 ky ky)))) |
(*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) (pow.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64))) (pow.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)) #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))))) |
(pow.f64 (/.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.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)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(/.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) |
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)))) (neg.f64 (neg.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64))))) (neg.f64 (neg.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))))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (*.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)))) (*.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (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))) (*.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)) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)))) (*.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)) (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)))) |
(/.f64 (neg.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(/.f64 (neg.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (neg.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)))) (neg.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)))) |
(/.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) |
(/.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64))) (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))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.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)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.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)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64))))) |
(fma.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) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) |
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) |
(fma.f64 #s(literal -1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) |
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) |
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (/.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) |
(-.f64 (pow.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64)))) |
(-.f64 (pow.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)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) (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)))) |
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) |
(+.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 1 binary64)) |
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) |
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) |
(*.f64 (pow.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 #s(literal 4 binary64) (*.f64 ky ky)))) #s(literal 1/4 binary64)) (pow.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 #s(literal 4 binary64) (*.f64 ky ky)))) #s(literal 1/4 binary64))) |
(pow.f64 (exp.f64 (log.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 #s(literal 4 binary64) (*.f64 ky ky)))))) #s(literal 1/2 binary64)) |
(pow.f64 (*.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 #s(literal 4 binary64) (*.f64 ky ky)))) #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 #s(literal 4 binary64) (*.f64 ky ky))))) #s(literal 1/4 binary64)) |
(pow.f64 (pow.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 #s(literal 4 binary64) (*.f64 ky ky)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.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 #s(literal 4 binary64) (*.f64 ky ky)))) #s(literal 1/2 binary64)) |
(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 #s(literal 4 binary64) (*.f64 ky ky))))) |
(exp.f64 (*.f64 (log.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 #s(literal 4 binary64) (*.f64 ky ky))))) #s(literal 1/2 binary64))) |
Compiled 24 659 to 2 724 computations (89% saved)
74 alts after pruning (67 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 586 | 18 | 604 |
| Fresh | 2 | 49 | 51 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 4 | 4 |
| Total | 590 | 74 | 664 |
| Status | Accuracy | Program |
|---|---|---|
| 48.6% | (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (sin.f64 th))) | |
| 77.1% | (/.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)))))) #s(literal 2 binary64)) (sin.f64 th))) | |
| 53.1% | (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) | |
| 32.9% | (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) | |
| 52.8% | (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) | |
| 95.5% | (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky)))) | |
| 77.1% | (*.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)) |
| 62.6% | (*.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)) | |
| ✓ | 33.2% | (*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky)) |
| ✓ | 52.8% | (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
| 36.7% | (*.f64 (/.f64 (sin.f64 ky) (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)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 25.2% | (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 76.8% | (*.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)) | |
| 35.7% | (*.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)) | |
| 29.2% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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)) | |
| 13.8% | (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 binary64))))) #s(literal 2 binary64))) (sin.f64 th)) | |
| 47.9% | (*.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)) | |
| 29.1% | (*.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)) | |
| 35.6% | (*.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)) | |
| 29.2% | (*.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)) | |
| 32.9% | (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) | |
| 33.6% | (*.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 #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)) | |
| 33.1% | (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (sin.f64 ky)) | |
| 33.1% | (*.f64 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) | |
| 29.1% | (*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 39.2% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) | |
| 27.1% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) | |
| 17.3% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) | |
| 21.5% | (*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) | |
| 17.7% | (*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 32.8% | (*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) | |
| 32.8% | (*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) | |
| 43.6% | (*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) | |
| 28.6% | (*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 32.9% | (*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) | |
| 35.7% | (*.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)) (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)) | |
| 24.6% | (*.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))))))) (sin.f64 th)) | |
| 30.1% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) | |
| 17.4% | (*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) | |
| 28.0% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 25.4% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) | |
| ✓ | 17.7% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
| 14.6% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) | |
| 14.6% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) | |
| 15.5% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 17.9% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 16.0% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 12.3% | (*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) | |
| 42.2% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) | |
| 42.3% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) th)) | |
| 35.4% | #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))))))) | |
| 24.5% | #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))))))) | |
| 76.9% | #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))))))))) | |
| ✓ | 42.3% | #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))))))))) |
| 14.5% | #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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) | |
| 15.4% | #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) #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)))))))) | |
| 26.7% | #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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 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)))))))) | |
| 42.1% | #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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) | |
| 20.3% | #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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) | |
| 16.1% | #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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) | |
| 42.1% | #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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) | |
| 13.6% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) | |
| 20.3% | #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) ky)))))))) | |
| ✓ | 33.2% | #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
| 19.4% | #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))) | |
| 19.5% | #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))) | |
| 19.4% | #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))) | |
| 19.4% | #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))) | |
| 10.2% | #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))) | |
| ✓ | 12.0% | #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))) |
| 12.0% | #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 #s(literal -1/6 binary64) th) th)) th))) | |
| 19.6% | #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))) | |
| 12.0% | #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 6 150 to 2 487 computations (59.6% 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 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 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 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) (/.f64 (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 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (sin.f64 th))) |
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))) (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 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.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))))))))) (sin.f64 th)) |
(*.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 th) (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 (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 (/.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 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 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) |
(*.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 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) |
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))) |
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (neg.f64 ky) (*.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)) (/.f64 ky (sin.f64 kx)))) (sin.f64 th)) |
(*.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 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (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)))) (sin.f64 th)) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (/.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))) #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) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) #s(literal 2 binary64))))) (sin.f64 th)) |
(*.f64 (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) |
9 calls:
| 37.0ms | (sin.f64 kx) |
| 36.0ms | kx |
| 34.0ms | (*.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)) |
| 34.0ms | (sin.f64 th) |
| 33.0ms | 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 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 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 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) (/.f64 (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 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (sin.f64 th))) |
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))) (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 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.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))))))))) (sin.f64 th)) |
(*.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 th) (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 (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 (/.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 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)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(/.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)))))) #s(literal 2 binary64)) (sin.f64 th))) |
9 calls:
| 30.0ms | (sin.f64 ky) |
| 29.0ms | th |
| 29.0ms | (sin.f64 th) |
| 27.0ms | (*.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)) |
| 26.0ms | (sin.f64 kx) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 2 | kx |
| 99.2% | 2 | ky |
| 87.8% | 2 | th |
| 84.9% | 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)) |
| 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))))) |
| 99.2% | 3 | (sin.f64 ky) |
| 99.6% | 2 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 99.6% | 3 | (sin.f64 kx) |
| 87.8% | 3 | (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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 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 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 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) (/.f64 (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 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (sin.f64 th))) |
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))) (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 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.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))))))))) (sin.f64 th)) |
(*.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 th) (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 (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)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.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)) |
2 calls:
| 25.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 24.0ms | kx |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 2 | kx |
| 99.6% | 2 | (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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 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 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 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) (/.f64 (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 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (sin.f64 th))) |
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))) (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 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.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))))))))) (sin.f64 th)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.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))))))))) (sin.f64 th)) |
2 calls:
| 24.0ms | kx |
| 22.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 2 | kx |
| 99.5% | 2 | (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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 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 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 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) (/.f64 (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 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (sin.f64 th))) |
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))) (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))))))))) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (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 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 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 calls:
| 25.0ms | kx |
| 22.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 2 | kx |
| 99.5% | 2 | (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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 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 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 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) (/.f64 (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 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) |
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (sin.f64 th))) |
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx 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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) (sin.f64 th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (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) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 th)) |
8 calls:
| 29.0ms | (sin.f64 kx) |
| 26.0ms | (sin.f64 ky) |
| 25.0ms | kx |
| 25.0ms | (sin.f64 th) |
| 24.0ms | th |
| Accuracy | Segments | Branch |
|---|---|---|
| 78.7% | 3 | (sin.f64 th) |
| 78.7% | 2 | th |
| 88.9% | 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))))) |
| 80.2% | 3 | (sin.f64 ky) |
| 80.1% | 3 | (sin.f64 kx) |
| 80.2% | 2 | ky |
| 80.0% | 2 | kx |
| 80.0% | 2 | (pow.f64 (sin.f64 kx) #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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 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 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 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) (/.f64 (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 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (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) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 th)) |
1 calls:
| 47.0ms | (/.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 |
|---|---|---|
| 88.9% | 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 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 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 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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)) |
| 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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (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) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 th)) |
2 calls:
| 29.0ms | (/.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))))) |
| 21.0ms | (*.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 |
|---|---|---|
| 76.2% | 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)) |
| 87.6% | 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 29 to 24 computations (17.2% 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 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 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 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (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 th)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (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) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 th)) |
1 calls:
| 20.0ms | (/.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 |
|---|---|---|
| 87.6% | 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
| 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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (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)) |
1 calls:
| 22.0ms | (/.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 |
|---|---|---|
| 85.4% | 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
| 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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (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)) |
8 calls:
| 53.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 24.0ms | (sin.f64 ky) |
| 22.0ms | (sin.f64 th) |
| 22.0ms | th |
| 20.0ms | ky |
| Accuracy | Segments | Branch |
|---|---|---|
| 70.8% | 3 | (sin.f64 th) |
| 69.4% | 4 | (sin.f64 kx) |
| 71.1% | 4 | (sin.f64 ky) |
| 72.7% | 3 | th |
| 69.3% | 3 | kx |
| 68.9% | 3 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 70.9% | 3 | ky |
| 81.5% | 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
#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 (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))) 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 (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 (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 ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1 binary64))) (cos.f64 (*.f64 #s(literal 2 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)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (sin.f64 ky)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 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)) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) th))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
1 calls:
| 19.0ms | (/.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 |
|---|---|---|
| 81.5% | 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
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#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
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#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)) |
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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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
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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 (sin.f64 ky) th)) #s(approx (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))))) (*.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))))) (sqrt.f64 #s(literal 1/2 binary64)))))) |
(*.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 (*.f64 (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)) (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)) |
#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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (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)) |
1 calls:
| 21.0ms | (/.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 |
|---|---|---|
| 81.5% | 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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)) |
| 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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
1 calls:
| 22.0ms | (/.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 |
|---|---|---|
| 81.5% | 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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))) |
| 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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
2 calls:
| 16.0ms | (/.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))))) |
| 15.0ms | (*.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 |
|---|---|---|
| 52.1% | 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)) |
| 73.1% | 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 29 to 24 computations (17.2% 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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 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 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
2 calls:
| 18.0ms | th |
| 14.0ms | (/.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 |
|---|---|---|
| 56.4% | 3 | th |
| 74.2% | 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 14 to 14 computations (0% 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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 (/.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) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 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) (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)))) #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) (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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (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:
| 14.0ms | (/.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 |
|---|---|---|
| 71.7% | 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 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th)) |
(*.f64 (*.f64 #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx))) (sin.f64 th)) (neg.f64 (sin.f64 ky))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)) (sin.f64 th))) (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)) |
| Outputs |
|---|
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 kx) (sin.f64 th)))) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
7 calls:
| 16.0ms | ky |
| 15.0ms | (sin.f64 ky) |
| 15.0ms | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 14.0ms | (/.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))))) |
| 14.0ms | (sin.f64 th) |
| Accuracy | Segments | Branch |
|---|---|---|
| 55.6% | 3 | (sin.f64 kx) |
| 54.1% | 3 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 54.1% | 3 | kx |
| 62.5% | 4 | (sin.f64 ky) |
| 44.3% | 3 | (sin.f64 th) |
| 56.0% | 3 | ky |
| 64.6% | 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 25 to 35 computations (-40% 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.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)) |
| Outputs |
|---|
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (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:
| 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 |
|---|---|---|
| 64.6% | 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 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky)) |
| Outputs |
|---|
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) 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)) |
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) |
1 calls:
| 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))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 64.6% | 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 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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)) (sin th)) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))) |
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.f64 (*.f64 ky ky) #s(literal 4 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) #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(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) #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(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 ky) th) (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) 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 (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)) |
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.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 #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)) |
| Outputs |
|---|
#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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) 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:
| 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))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 64.3% | 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 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (neg.f64 th) (sin.f64 ky))) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 #s(approx (neg (sin ky)) (neg.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 #s(literal -1 binary64) kx)))) |
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (/ -1 (sin kx)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal -1 binary64)) kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (*.f64 (*.f64 th th) #s(literal 1/6 binary64)) (sin.f64 ky))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal -1 binary64))) ky)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 (*.f64 (neg.f64 (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 (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.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 (sin.f64 ky) th)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
| 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)) |
2 calls:
| 10.0ms | (sin.f64 ky) |
| 8.0ms | (/.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 |
|---|---|---|
| 51.3% | 3 | (sin.f64 ky) |
| 56.6% | 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 15 to 15 computations (0% 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 (*.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))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 #s(approx (* (sin ky) (+ (* 1/6 (* th th)) -1)) (*.f64 (fma.f64 (*.f64 th th) #s(literal 1/6 binary64) #s(literal -1 binary64)) ky)) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) (sin.f64 kx)))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx))))) |
#s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) #s(approx (* (* 2 (* (sin ky) th)) (sqrt (/ 1/2 (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky)))))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) |
(*.f64 #s(approx (* (neg (sin ky)) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/6 binary64) (*.f64 th th) #s(literal -1 binary64))) th)) #s(approx (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 #s(literal -1 binary64) #s(approx (sin kx) (*.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))))) |
#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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 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 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 6.0ms | (*.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)) |
| 6.0ms | kx |
| 6.0ms | ky |
| 6.0ms | (sin.f64 kx) |
| Accuracy | Segments | Branch |
|---|---|---|
| 40.5% | 2 | (sin.f64 ky) |
| 42.7% | 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)) |
| 41.5% | 2 | kx |
| 41.5% | 2 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 42.2% | 3 | (sin.f64 kx) |
| 40.6% | 2 | ky |
| 38.0% | 3 | th |
| 46.3% | 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 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 (*.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))) |
#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))))) |
| 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)) (sin.f64 th)) |
2 calls:
| 4.0ms | (sin.f64 th) |
| 4.0ms | (/.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 |
|---|---|---|
| 33.2% | 1 | (sin.f64 th) |
| 41.5% | 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 15 to 15 computations (0% 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 (*.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))) |
| 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:
| 4.0ms | (*.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 | (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 kx) |
| 3.0ms | (sin.f64 ky) |
| Accuracy | Segments | Branch |
|---|---|---|
| 19.6% | 1 | (sin.f64 th) |
| 19.6% | 1 | th |
| 25.1% | 2 | (sin.f64 ky) |
| 24.8% | 2 | ky |
| 26.2% | 3 | (sin.f64 kx) |
| 28.5% | 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)) |
| 26.1% | 2 | kx |
| 26.1% | 2 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 27.9% | 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 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))) |
8 calls:
| 2.0ms | (/.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 | (*.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 | (sin.f64 kx) |
| 1.0ms | th |
| 1.0ms | (sin.f64 ky) |
| Accuracy | Segments | Branch |
|---|---|---|
| 19.6% | 1 | th |
| 19.6% | 1 | (sin.f64 kx) |
| 19.6% | 1 | ky |
| 19.6% | 1 | (sin.f64 ky) |
| 19.6% | 1 | (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) |
| 19.6% | 1 | kx |
| 19.6% | 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))))) |
| 19.6% | 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 40 to 47 computations (-17.5% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.2191126462041584e-15 | 8.3334130169013e-7 |
Compiled 19 to 19 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.2191126462041584e-15 | 8.3334130169013e-7 |
Compiled 19 to 19 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.2191126462041584e-15 | 8.3334130169013e-7 |
Compiled 19 to 19 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.2191126462041584e-15 | 8.3334130169013e-7 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9999995735978008 | 1.0 |
| 0.0ms | 6.676890127215528e-6 | 0.004876665236225074 |
| 0.0ms | -0.03154178293083937 | 1.0764666829265835e-304 |
| 0.0ms | -0.9998202253101762 | -0.9987353857156005 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9999995735978008 | 1.0 |
| 0.0ms | 6.676890127215528e-6 | 0.004876665236225074 |
| 0.0ms | -0.03154178293083937 | 1.0764666829265835e-304 |
| 0.0ms | -0.9998202253101762 | -0.9987353857156005 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9999995735978008 | 1.0 |
| 0.0ms | 6.676890127215528e-6 | 0.004876665236225074 |
| 0.0ms | -0.03154178293083937 | 1.0764666829265835e-304 |
| 0.0ms | -0.9998202253101762 | -0.9987353857156005 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9999995735978008 | 1.0 |
| 0.0ms | 6.676890127215528e-6 | 0.004876665236225074 |
| 0.0ms | -0.03154178293083937 | 1.0764666829265835e-304 |
| 0.0ms | -0.9998202253101762 | -0.9987353857156005 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9999995735978008 | 1.0 |
| 0.0ms | 6.676890127215528e-6 | 0.004876665236225074 |
| 0.0ms | -0.03154178293083937 | 1.0764666829265835e-304 |
| 0.0ms | -0.9998202253101762 | -0.9987353857156005 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9999995735978008 | 1.0 |
| 0.0ms | 6.676890127215528e-6 | 0.004876665236225074 |
| 0.0ms | -0.03154178293083937 | 1.0764666829265835e-304 |
| 0.0ms | -0.9998202253101762 | -0.9987353857156005 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9999995735978008 | 1.0 |
| 0.0ms | 6.676890127215528e-6 | 0.004876665236225074 |
| 0.0ms | -0.03154178293083937 | 1.0764666829265835e-304 |
| 0.0ms | -0.9998202253101762 | -0.9987353857156005 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9999995735978008 | 1.0 |
| 0.0ms | 6.676890127215528e-6 | 0.004876665236225074 |
| 0.0ms | -0.03154178293083937 | 1.0764666829265835e-304 |
| 0.0ms | -0.9998202253101762 | -0.9987353857156005 |
Compiled 19 to 19 computations (0% saved)
| 4× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.9999995735978008 | 1.0 |
| 0.0ms | 6.676890127215528e-6 | 0.004876665236225074 |
| 0.0ms | -0.03154178293083937 | 1.0764666829265835e-304 |
| 0.0ms | -0.9998202253101762 | -0.9987353857156005 |
Compiled 19 to 19 computations (0% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.03562702248538329 | 0.08215631331043383 |
| 0.0ms | -0.1285911937355022 | -0.041263132133594484 |
Compiled 19 to 19 computations (0% saved)
| 3× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.03562702248538329 | 0.08215631331043383 |
| 0.0ms | 3.4499218845258355e-244 | 4.1691989502459995e-242 |
| 0.0ms | -0.9999999999999993 | -0.9998202253101762 |
Compiled 19 to 19 computations (0% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.03562702248538329 | 0.08215631331043383 |
| 0.0ms | -0.9999999999999993 | -0.9998202253101762 |
Compiled 19 to 19 computations (0% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.03562702248538329 | 0.08215631331043383 |
| 0.0ms | -0.5213896269909511 | -0.508405520691846 |
Compiled 19 to 19 computations (0% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.03562702248538329 | 0.08215631331043383 |
| 0.0ms | -0.5213896269909511 | -0.508405520691846 |
Compiled 19 to 19 computations (0% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.03562702248538329 | 0.08215631331043383 |
| 0.0ms | -0.5213896269909511 | -0.508405520691846 |
Compiled 19 to 19 computations (0% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.004876665236225074 | 0.03562702248538329 |
| 0.0ms | -0.03154178293083937 | 1.0764666829265835e-304 |
Compiled 19 to 19 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.004876665236225074 | 0.03562702248538329 |
Compiled 19 to 19 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.004876665236225074 | 0.03562702248538329 |
Compiled 19 to 19 computations (0% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 14.0ms | 6.372055099116783e-97 | 6.347257432033778e-90 |
| 8.0ms | 144× | 0 | valid |
Compiled 505 to 397 computations (21.4% saved)
ival-sin: 4.0ms (83.8% of total)ival-mult: 1.0ms (21% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 3.23269734234064e-310 | 4.9748795481725607e-303 |
Compiled 19 to 19 computations (0% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 272 | 3214 |
| 1 | 342 | 3214 |
| 2 | 379 | 3214 |
| 3 | 414 | 3214 |
| 4 | 485 | 3214 |
| 5 | 532 | 3214 |
| 6 | 573 | 3214 |
| 7 | 620 | 3214 |
| 8 | 665 | 3214 |
| 9 | 671 | 3214 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) |
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2535301200456459/1267650600228229401496703205376 binary64)) (*.f64 (/.f64 (sin.f64 ky) (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 th)) (/.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)))))) #s(literal 2 binary64)) (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 -8998192055486251/9007199254740992 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 -5764607523034235/288230376151711744 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 5902958103587057/590295810358705651712 binary64)) (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 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 9007195414051421/9007199254740992 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)))))) |
(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 -8998192055486251/9007199254740992 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 -5764607523034235/288230376151711744 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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) (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 5902958103587057/590295810358705651712 binary64)) (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (sin.f64 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 9007195414051421/9007199254740992 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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) #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 -3602879701896397/36028797018963968 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 3602879701896397/72057594037927936 binary64)) (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (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 -4503149267407759/4503599627370496 binary64)) (*.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)) (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 7687697232696013/15375394465392026070980930960402958051966483647589383243116337952281869440244186537876296086692518667977838631290276787444086150484586994200087471936798525767761360737466168478385414860572969804431318564695864578364068534363514095860253929241066696020120829952 binary64)) (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx))))) #s(approx (+ (* (- 1 (cos (* 2 kx))) 2) (* (* ky ky) 4)) (*.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)) (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 3602879701896397/72057594037927936 binary64)) (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (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 -4503149267407759/4503599627370496 binary64)) (*.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)) (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 3602879701896397/72057594037927936 binary64)) (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (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 -1170935903116329/2251799813685248 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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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 3602879701896397/72057594037927936 binary64)) (/.f64 (sin.f64 ky) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin th)) (/.f64 (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 -1170935903116329/2251799813685248 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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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 3602879701896397/72057594037927936 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (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 -1170935903116329/2251799813685248 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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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 3602879701896397/72057594037927936 binary64)) (*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 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 -5764607523034235/288230376151711744 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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 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 (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 8485944879163265/2293498615990071511610820895302086940796564989168281123737588839386922876088484808070018553110125686554624 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)) (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 101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) |
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) |
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2535301200456459/1267650600228229401496703205376 binary64)) (*.f64 (/.f64 (sin.f64 ky) (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 th)) (/.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)))))) #s(literal 2 binary64)) (sin.f64 th)))) |
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2535301200456459/1267650600228229401496703205376 binary64)) (*.f64 (/.f64 (sin.f64 ky) (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 th)) (/.f64 (sin.f64 ky) (/.f64 (/.f64 (sqrt.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 th)))) |
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2535301200456459/1267650600228229401496703205376 binary64)) (*.f64 (/.f64 (sin.f64 ky) (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 th)) (*.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))) |
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2535301200456459/1267650600228229401496703205376 binary64)) (*.f64 (/.f64 (sin.f64 ky) (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 th)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sin.f64 ky)) (sqrt.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1 binary64))) #s(literal 2 binary64)))) (sin.f64 th))) |
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2535301200456459/1267650600228229401496703205376 binary64)) (*.f64 (/.f64 (sin.f64 ky) (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 th)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.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))))))))) (sin.f64 th))) |
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2535301200456459/1267650600228229401496703205376 binary64)) (*.f64 (/.f64 (sin.f64 ky) (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 th)) (*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 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(literal 2 binary64) (sin.f64 ky)))) (sin.f64 th))) |
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(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -1170935903116329/2251799813685248 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (*.f64 (*.f64 th (sin.f64 ky)) #s(literal 2 binary64)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (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 -1170935903116329/2251799813685248 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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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 3602879701896397/72057594037927936 binary64)) (*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 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 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -1170935903116329/2251799813685248 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (*.f64 (*.f64 th (sin.f64 ky)) #s(literal 2 binary64)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) (*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 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 -5764607523034235/288230376151711744 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) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.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 5764607523034235/1152921504606846976 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 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -5764607523034235/288230376151711744 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (* (- 1 (cos (* ky 2))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 2)) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (- (cos (* 2 kx)) (- 1 (cos (* 2 ky))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (*.f64 (*.f64 th (sin.f64 ky)) #s(literal 2 binary64)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 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 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 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 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 5764607523034235/1152921504606846976 binary64)) (*.f64 #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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx)))) #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 8485944879163265/2293498615990071511610820895302086940796564989168281123737588839386922876088484808070018553110125686554624 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)) (sin.f64 th))) |
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 8485944879163265/2293498615990071511610820895302086940796564989168281123737588839386922876088484808070018553110125686554624 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)) (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 101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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)))) |
(if (<=.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)) #s(literal 101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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 | 70 | 413 |
| 0 | 107 | 373 |
| 1 | 352 | 365 |
| 2 | 2103 | 365 |
| 0 | 9175 | 361 |
| 0 | 13 | 49 |
| 0 | 22 | 49 |
| 1 | 62 | 49 |
| 2 | 338 | 49 |
| 3 | 2902 | 49 |
| 0 | 8284 | 34 |
| 0 | 873 | 5642 |
| 1 | 2892 | 5185 |
| 2 | 7398 | 5177 |
| 0 | 8019 | 4904 |
| 0 | 859 | 5539 |
| 1 | 2883 | 5092 |
| 2 | 7352 | 5082 |
| 0 | 8017 | 4859 |
| 0 | 66 | 272 |
| 0 | 103 | 267 |
| 1 | 349 | 265 |
| 2 | 2208 | 252 |
| 0 | 9198 | 252 |
| 0 | 317 | 1402 |
| 1 | 1011 | 1353 |
| 2 | 3847 | 1261 |
| 3 | 7794 | 1261 |
| 0 | 8097 | 1188 |
| 0 | 887 | 5707 |
| 1 | 2977 | 5422 |
| 2 | 7641 | 5420 |
| 0 | 8036 | 5202 |
| 0 | 45 | 261 |
| 0 | 78 | 211 |
| 1 | 253 | 209 |
| 2 | 1571 | 209 |
| 0 | 8832 | 209 |
| 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× | 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× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 6 372 to 2 236 computations (64.9% saved)
(negabs ky)
(negabs th)
(abs kx)
Compiled 6 592 to 678 computations (89.7% saved)
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