
Time bar (total: 11.2s)
| 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% | 50% | 0.1% | 0% | 50% | 0% | 2 |
| 50% | 25% | 25% | 0.1% | 0% | 50% | 0% | 3 |
| 50% | 25% | 25% | 0.1% | 0% | 50% | 0% | 4 |
| 50% | 25% | 25% | 0.1% | 0% | 50% | 0% | 5 |
| 50% | 25% | 25% | 0.1% | 0% | 50% | 0% | 6 |
| 51.6% | 25% | 23.4% | 0.1% | 0% | 51.5% | 0% | 7 |
| 52.5% | 25% | 22.6% | 0.1% | 0% | 52.3% | 0% | 8 |
| 53.8% | 25% | 21.5% | 0.1% | 0% | 53.5% | 0% | 9 |
| 54.5% | 25% | 20.9% | 0.1% | 0% | 54% | 0% | 10 |
| 55.3% | 25% | 20.2% | 0.1% | 0% | 54.7% | 0% | 11 |
| 55.7% | 25% | 19.9% | 0.1% | 0% | 55.1% | 0% | 12 |
Compiled 18 to 15 computations (16.7% saved)
| 1.2s | 8 256× | 0 | valid |
| 753.0ms | 3 555× | 1 | invalid |
| 324.0ms | 1 891× | 1 | exit |
| 142.0ms | 469× | 2 | invalid |
| 46.0ms | 229× | 0 | exit |
| 40.0ms | 491× | 0 | invalid |
ival-div: 553.0ms (28.7% of total)ival-pow: 525.0ms (27.3% of total)ival-mult: 356.0ms (18.5% of total)ival-sqrt: 161.0ms (8.4% of total)adjust: 113.0ms (5.9% of total)ival-sub: 106.0ms (5.5% of total)ival-pi: 71.0ms (3.7% of total)exact: 21.0ms (1.1% of total)ival-true: 12.0ms (0.6% of total)ival-assert: 6.0ms (0.3% of total)| 1× | egg-herbie |
| 232× | associate-*r* |
| 160× | sub-neg |
| 160× | associate-*l* |
| 138× | distribute-lft-neg-in |
| 118× | distribute-lft-in |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 88 |
| 1 | 82 | 74 |
| 2 | 193 | 74 |
| 3 | 383 | 74 |
| 4 | 607 | 74 |
| 5 | 878 | 74 |
| 6 | 1047 | 74 |
| 7 | 1230 | 74 |
| 8 | 1285 | 74 |
| 9 | 1309 | 74 |
| 10 | 1327 | 74 |
| 11 | 1331 | 74 |
| 12 | 1331 | 74 |
| 0 | 13 | 16 |
| 0 | 22 | 16 |
| 1 | 37 | 14 |
| 2 | 54 | 14 |
| 3 | 75 | 14 |
| 4 | 93 | 14 |
| 5 | 108 | 14 |
| 6 | 129 | 14 |
| 7 | 156 | 14 |
| 8 | 165 | 14 |
| 9 | 168 | 14 |
| 0 | 168 | 13 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 4 | 78 | (1.6021947219585171e-226 9.527612262717642e-193) | 0 | - | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
| 0 | 0 | - | 0 | - | k |
| 0 | 0 | - | 0 | - | n |
| 0 | 0 | - | 0 | - | (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 0 | 0 | - | 0 | - | (sqrt.f64 k) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| 0 | 0 | - | 0 | - | (-.f64 #s(literal 1 binary64) k) |
| 0 | 0 | - | 0 | - | (*.f64 #s(literal 2 binary64) (PI.f64)) |
| 0 | 0 | - | 0 | - | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 0 | 0 | - | 0 | - | (PI.f64) |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
pow.f64 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | sensitivity | 82 | 37 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 4 | 0 |
| - | 78 | 174 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 4 | 0 | 0 |
| - | 78 | 37 | 137 |
| number | freq |
|---|---|
| 0 | 174 |
| 1 | 82 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 102.0ms | 512× | 0 | valid |
Compiled 148 to 56 computations (62.2% saved)
ival-mult: 43.0ms (57.3% of total)ival-pow: 15.0ms (20% of total)ival-div: 7.0ms (9.3% of total)ival-sqrt: 4.0ms (5.3% of total)ival-sub: 3.0ms (4% of total)ival-pi: 2.0ms (2.7% of total)exact: 1.0ms (1.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.5% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 18 to 13 computations (27.8% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sqrt.f64 k) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| ✓ | cost-diff | 320 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 512 | (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
| 64× | lower-*.f32 |
| 58× | lower-*.f64 |
| 48× | lower-+.f64 |
| 48× | lower-+.f32 |
| 36× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 54 |
| 0 | 22 | 54 |
| 1 | 37 | 52 |
| 2 | 54 | 52 |
| 3 | 75 | 52 |
| 4 | 93 | 52 |
| 5 | 108 | 52 |
| 6 | 129 | 52 |
| 7 | 156 | 52 |
| 8 | 165 | 52 |
| 9 | 168 | 52 |
| 0 | 168 | 49 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.7% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.7% | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| ✓ | accuracy | 99.6% | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 29.0ms | 256× | 0 | valid |
Compiled 56 to 15 computations (73.2% saved)
ival-pow: 7.0ms (35.4% of total)ival-mult: 4.0ms (20.2% of total)ival-div: 3.0ms (15.2% of total)ival-sqrt: 3.0ms (15.2% of total)ival-pi: 1.0ms (5.1% of total)ival-sub: 1.0ms (5.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))> |
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))> |
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k))> |
#<alt (sqrt.f64 k)> |
#<alt (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)> |
#<alt (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))> |
| Outputs |
|---|
#<alt 1/2> |
#<alt (+ 1/2 (* -1/2 k))> |
#<alt (+ 1/2 (* -1/2 k))> |
#<alt (+ 1/2 (* -1/2 k))> |
#<alt (* -1/2 k)> |
#<alt (* k (- (* 1/2 (/ 1 k)) 1/2))> |
#<alt (* k (- (* 1/2 (/ 1 k)) 1/2))> |
#<alt (* k (- (* 1/2 (/ 1 k)) 1/2))> |
#<alt (* -1/2 k)> |
#<alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))> |
#<alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))> |
#<alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))> |
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))> |
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))> |
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))> |
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))> |
24 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 60.0ms | n | @ | -inf | (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 35.0ms | n | @ | 0 | (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 7.0ms | n | @ | inf | (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 1.0ms | k | @ | -inf | (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 1.0ms | k | @ | 0 | (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 1× | batch-egg-rewrite |
| 4 378× | lower-*.f32 |
| 4 372× | lower-*.f64 |
| 3 286× | lower-pow.f32 |
| 3 284× | lower-pow.f64 |
| 2 442× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 43 |
| 0 | 22 | 43 |
| 1 | 89 | 40 |
| 2 | 497 | 38 |
| 3 | 4474 | 38 |
| 0 | 8599 | 37 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
| Outputs |
|---|
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (neg.f64 k))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(+.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) |
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) |
(+.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 k)) #s(literal 1/2 binary64)) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))) |
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))) |
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(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64)))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (neg.f64 k))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (fma.f64 k k (+.f64 #s(literal 1 binary64) k)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (neg.f64 (/.f64 (*.f64 k (*.f64 k k)) (fma.f64 k k (+.f64 #s(literal 1 binary64) k)))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (neg.f64 (/.f64 (*.f64 k k) (+.f64 #s(literal 1 binary64) k))))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 1/2 binary64) (neg.f64 k))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (neg.f64 k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (PI.f64))) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) n)))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) n))) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (PI.f64)))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 (PI.f64) n))) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 n))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 n)) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
| 1× | egg-herbie |
| 9 974× | lower-fma.f64 |
| 9 974× | lower-fma.f32 |
| 5 988× | lower-*.f64 |
| 5 988× | lower-*.f32 |
| 1 688× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 128 | 1174 |
| 1 | 345 | 1155 |
| 2 | 1011 | 1065 |
| 3 | 3348 | 1038 |
| 4 | 5547 | 966 |
| 0 | 8354 | 945 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
1/2 |
(+ 1/2 (* -1/2 k)) |
(+ 1/2 (* -1/2 k)) |
(+ 1/2 (* -1/2 k)) |
(* -1/2 k) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(* -1/2 k) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
| Outputs |
|---|
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/2 k)) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(+ 1/2 (* -1/2 k)) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(+ 1/2 (* -1/2 k)) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(* -1/2 k) |
(*.f64 #s(literal -1/2 binary64) k) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(* -1/2 k) |
(*.f64 #s(literal -1/2 binary64) k) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 (PI.f64) (*.f64 k n))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 (PI.f64) (*.f64 k n))))) #s(literal 1/8 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (fma.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 (PI.f64) (*.f64 k n))))) #s(literal -1/48 binary64)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))) #s(literal 1/8 binary64)))) (*.f64 k k))) k) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt k) |
(sqrt.f64 k) |
(sqrt k) |
(sqrt.f64 k) |
(sqrt k) |
(sqrt.f64 k) |
(sqrt k) |
(sqrt.f64 k) |
(sqrt k) |
(sqrt.f64 k) |
(sqrt k) |
(sqrt.f64 k) |
(sqrt k) |
(sqrt.f64 k) |
(sqrt k) |
(sqrt.f64 k) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(sqrt.f64 k) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(sqrt.f64 k) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(sqrt.f64 k) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(sqrt.f64 k) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (fma.f64 (*.f64 k #s(literal 1/8 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 k (*.f64 (*.f64 k (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (fma.f64 (*.f64 k #s(literal -1/48 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
Compiled 11 242 to 1 530 computations (86.4% saved)
12 alts after pruning (12 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 503 | 12 | 515 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 504 | 12 | 516 |
| Status | Accuracy | Program |
|---|---|---|
| 51.0% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| 99.3% | (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))) | |
| ▶ | 99.4% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) |
| 50.4% | (*.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) | |
| 50.8% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64))) | |
| 99.5% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) | |
| ▶ | 51.1% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) |
| ▶ | 51.6% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))) |
| 99.3% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) | |
| 51.5% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) | |
| ▶ | 39.5% | (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
| ▶ | 99.6% | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
Compiled 412 to 308 computations (25.2% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sqrt.f64 k) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) |
| ✓ | cost-diff | 128 | (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) |
| ✓ | cost-diff | 0 | (sqrt.f64 k) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| ✓ | cost-diff | 320 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) |
| ✓ | cost-diff | 0 | (sqrt.f64 k) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| ✓ | cost-diff | 320 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 5824 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 n (PI.f64)) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 n (PI.f64)) k) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) k) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
| 124× | lower-*.f32 |
| 96× | lower-*.f64 |
| 60× | lower-fma.f32 |
| 58× | lower-fma.f64 |
| 48× | *-commutative |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 35 | 230 |
| 0 | 64 | 228 |
| 1 | 98 | 224 |
| 2 | 130 | 224 |
| 3 | 155 | 224 |
| 4 | 173 | 224 |
| 5 | 195 | 224 |
| 6 | 225 | 224 |
| 7 | 250 | 224 |
| 8 | 256 | 224 |
| 0 | 256 | 220 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (*.f64 n (PI.f64)) k) |
(*.f64 n (PI.f64)) |
n |
(PI.f64) |
k |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
#s(literal 1/2 binary64) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
(*.f64 #s(literal -1/2 binary64) k) |
#s(literal -1/2 binary64) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) |
#s(literal 1 binary64) |
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
#s(literal 2 binary64) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
(-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))) |
#s(literal -1/2 binary64) |
(*.f64 k #s(literal -1/2 binary64)) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (*.f64 n (PI.f64)) k) |
(*.f64 n (PI.f64)) |
n |
(PI.f64) |
k |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
#s(literal 1/2 binary64) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
(*.f64 #s(literal -1/2 binary64) k) |
(*.f64 k #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) |
#s(literal 1 binary64) |
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
#s(literal 2 binary64) |
(*.f64 (PI.f64) n) |
(*.f64 n (PI.f64)) |
(PI.f64) |
n |
(-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))) |
(fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(*.f64 k #s(literal -1/2 binary64)) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.7% | (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
| ✓ | accuracy | 99.7% | (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
| ✓ | accuracy | 99.7% | (*.f64 (PI.f64) n) |
| ✓ | accuracy | 75.8% | (PI.f64) |
| ✓ | accuracy | 100.0% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| ✓ | accuracy | 75.8% | (PI.f64) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| ✓ | accuracy | 99.6% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 75.8% | (PI.f64) |
| ✓ | accuracy | 99.7% | (*.f64 n (PI.f64)) |
| ✓ | accuracy | 99.4% | (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 87.7% | (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
| ✓ | accuracy | 75.8% | (PI.f64) |
| ✓ | accuracy | 99.7% | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.7% | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.7% | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
| ✓ | accuracy | 75.8% | (PI.f64) |
| 59.0ms | 192× | 0 | valid |
| 19.0ms | 63× | 0 | exit |
| 0.0ms | 1× | 0 | invalid |
Compiled 232 to 37 computations (84.1% saved)
ival-mult: 20.0ms (37.4% of total)ival-pow: 13.0ms (24.3% of total)ival-div: 8.0ms (15% of total)ival-sqrt: 8.0ms (15% of total)ival-pi: 1.0ms (1.9% of total)ival-add: 1.0ms (1.9% of total)ival-sub: 1.0ms (1.9% of total)exact: 1.0ms (1.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))> |
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))> |
#<alt (/.f64 #s(literal 1 binary64) k)> |
#<alt (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))> |
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))> |
#<alt (/.f64 (*.f64 n (PI.f64)) k)> |
#<alt (*.f64 n (PI.f64))> |
#<alt (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))> |
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)))> |
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k))> |
#<alt (sqrt.f64 k)> |
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))> |
#<alt (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))> |
#<alt (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))> |
#<alt (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))> |
#<alt (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))> |
#<alt (PI.f64)> |
#<alt (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))> |
#<alt (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)> |
#<alt (*.f64 (PI.f64) n)> |
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))> |
| Outputs |
|---|
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))> |
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))> |
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))> |
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (/ (* n (PI)) k)> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))> |
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))> |
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))> |
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ 1 k))> |
#<alt (/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k)> |
#<alt (/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k)> |
#<alt (/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k)> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))> |
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))> |
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))> |
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))> |
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (* k (log (* 2 (* n (PI)))))))> |
#<alt (+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))))))> |
#<alt (+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))> |
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))> |
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))> |
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))> |
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))> |
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))> |
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))> |
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))> |
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))> |
#<alt -1/2> |
#<alt (- (* 1/2 k) 1/2)> |
#<alt (- (* 1/2 k) 1/2)> |
#<alt (- (* 1/2 k) 1/2)> |
#<alt (* 1/2 k)> |
#<alt (* k (- 1/2 (* 1/2 (/ 1 k))))> |
#<alt (* k (- 1/2 (* 1/2 (/ 1 k))))> |
#<alt (* k (- 1/2 (* 1/2 (/ 1 k))))> |
#<alt (* 1/2 k)> |
#<alt (* -1 (* k (- (* 1/2 (/ 1 k)) 1/2)))> |
#<alt (* -1 (* k (- (* 1/2 (/ 1 k)) 1/2)))> |
#<alt (* -1 (* k (- (* 1/2 (/ 1 k)) 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)> |
#<alt (/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)> |
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (+ (* k (+ (* 1/8 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))> |
#<alt (* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))> |
#<alt (* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))> |
#<alt (* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))> |
#<alt (+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))> |
#<alt (+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
96 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | n | @ | 0 | (* (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ (* -1/2 k) 1/2))) |
| 2.0ms | k | @ | 0 | (/ 1 (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2))))) |
| 1.0ms | n | @ | -inf | (/ 1 (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2))))) |
| 1.0ms | k | @ | -inf | (/ 1 (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2))))) |
| 1.0ms | n | @ | inf | (/ 1 (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2))))) |
| 1× | batch-egg-rewrite |
| 6 372× | lower-*.f32 |
| 6 344× | lower-*.f64 |
| 2 982× | lower-fma.f32 |
| 2 980× | lower-fma.f64 |
| 2 720× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 35 | 163 |
| 0 | 64 | 156 |
| 1 | 232 | 148 |
| 2 | 1140 | 146 |
| 0 | 8701 | 144 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (*.f64 n (PI.f64)) k) |
(*.f64 n (PI.f64)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)) |
(-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) |
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(PI.f64) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 (PI.f64) n) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) #s(literal -1 binary64))) |
(exp.f64 (fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
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(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 k #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 n (*.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 n (*.f64 k #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 (*.f64 n (PI.f64)) (*.f64 k #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 (*.f64 n (PI.f64)) (*.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 1 binary64))) |
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) (*.f64 k #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (pow.f64 (PI.f64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (pow.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (pow.f64 n (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) (pow.f64 n (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 k #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))) |
| 1× | egg-herbie |
| 8 642× | lower-fma.f64 |
| 8 642× | lower-fma.f32 |
| 6 898× | lower-*.f64 |
| 6 898× | lower-*.f32 |
| 3 102× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 312 | 4640 |
| 1 | 966 | 4458 |
| 2 | 3269 | 4306 |
| 3 | 6582 | 4090 |
| 0 | 8117 | 3944 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(/ (* n (PI)) k) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(sqrt (/ 1 k)) |
(/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
1 |
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2)))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
-1/2 |
(- (* 1/2 k) 1/2) |
(- (* 1/2 k) 1/2) |
(- (* 1/2 k) 1/2) |
(* 1/2 k) |
(* k (- 1/2 (* 1/2 (/ 1 k)))) |
(* k (- 1/2 (* 1/2 (/ 1 k)))) |
(* k (- 1/2 (* 1/2 (/ 1 k)))) |
(* 1/2 k) |
(* -1 (* k (- (* 1/2 (/ 1 k)) 1/2))) |
(* -1 (* k (- (* 1/2 (/ 1 k)) 1/2))) |
(* -1 (* k (- (* 1/2 (/ 1 k)) 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/8 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))) |
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2)))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt k) (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k)))))) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 k (fma.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
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(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
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(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) |
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) |
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 k (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal 1/48 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (*.f64 k (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/8 binary64)))) (*.f64 k k) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (neg.f64 k) #s(literal -1/2 binary64))) |
Compiled 40 068 to 4 634 computations (88.4% saved)
18 alts after pruning (17 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2 084 | 17 | 2 101 |
| Fresh | 7 | 0 | 7 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 0 | 0 |
| Total | 2 095 | 18 | 2 113 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.6% | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
| 75.4% | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) | |
| 51.1% | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) | |
| 51.6% | (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) | |
| ▶ | 40.5% | (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
| 99.4% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) | |
| ▶ | 99.4% | (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))) |
| 40.4% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) | |
| 76.0% | (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))) | |
| 51.5% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) | |
| 5.3% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) | |
| ✓ | 39.5% | (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
| 51.6% | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) | |
| ▶ | 39.4% | (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
| 51.6% | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| 51.6% | (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) | |
| 39.6% | (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) | |
| ▶ | 5.3% | (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
Compiled 459 to 359 computations (21.8% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))) |
| ✓ | cost-diff | 0 | (/.f64 k (*.f64 n (PI.f64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
| ✓ | cost-diff | 0 | (PI.f64) |
| ✓ | cost-diff | 0 | (*.f64 (PI.f64) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) k) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
| ✓ | cost-diff | 0 | (*.f64 (PI.f64) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
| 40× | lower-*.f32 |
| 30× | lower-*.f64 |
| 28× | lower-/.f32 |
| 16× | *-commutative |
| 16× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 28 | 167 |
| 0 | 52 | 167 |
| 1 | 68 | 167 |
| 2 | 78 | 167 |
| 3 | 79 | 167 |
| 0 | 79 | 167 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
k |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
(sqrt.f64 k) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 n k)) |
(/.f64 n k) |
n |
k |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) |
(/.f64 k (*.f64 n (PI.f64))) |
k |
(*.f64 n (PI.f64)) |
n |
(PI.f64) |
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))) |
#s(literal 1 binary64) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) |
k |
#s(literal 1/2 binary64) |
#s(literal -1/2 binary64) |
(sqrt.f64 k) |
| Outputs |
|---|
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
k |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
(sqrt.f64 k) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 n k)) |
(/.f64 n k) |
n |
k |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) |
(/.f64 k (*.f64 n (PI.f64))) |
k |
(*.f64 n (PI.f64)) |
n |
(PI.f64) |
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) |
#s(literal 1 binary64) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) |
k |
#s(literal 1/2 binary64) |
#s(literal -1/2 binary64) |
(sqrt.f64 k) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.7% | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
| ✓ | accuracy | 99.7% | (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)) |
| ✓ | accuracy | 99.7% | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
| ✓ | accuracy | 75.8% | (PI.f64) |
| ✓ | accuracy | 99.7% | (*.f64 n (PI.f64)) |
| ✓ | accuracy | 99.5% | (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
| ✓ | accuracy | 88.8% | (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) |
| ✓ | accuracy | 75.8% | (PI.f64) |
| ✓ | accuracy | 99.5% | (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
| ✓ | accuracy | 98.8% | (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
| ✓ | accuracy | 87.7% | (sqrt.f64 (/.f64 n k)) |
| ✓ | accuracy | 75.8% | (PI.f64) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) k) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
| ✓ | accuracy | 99.7% | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
| ✓ | accuracy | 99.7% | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.7% | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
| ✓ | accuracy | 75.8% | (PI.f64) |
| 117.0ms | 192× | 0 | valid |
| 43.0ms | 63× | 0 | exit |
| 0.0ms | 1× | 0 | invalid |
Compiled 169 to 32 computations (81.1% saved)
ival-sqrt: 40.0ms (54.6% of total)ival-mult: 10.0ms (13.7% of total)ival-pow: 10.0ms (13.7% of total)ival-div: 9.0ms (12.3% of total)ival-add: 2.0ms (2.7% of total)ival-pi: 1.0ms (1.4% of total)exact: 1.0ms (1.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))> |
#<alt (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))> |
#<alt (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))> |
#<alt (*.f64 (PI.f64) #s(literal 2 binary64))> |
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))> |
#<alt (/.f64 #s(literal 1 binary64) k)> |
#<alt (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))> |
#<alt (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))> |
#<alt (PI.f64)> |
#<alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))> |
#<alt (sqrt.f64 #s(literal 2 binary64))> |
#<alt (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))> |
#<alt (/.f64 k (*.f64 n (PI.f64)))> |
#<alt (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))> |
#<alt (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))> |
#<alt (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))> |
#<alt (sqrt.f64 (/.f64 n k))> |
#<alt (*.f64 n (PI.f64))> |
| Outputs |
|---|
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (* 2 (* n (PI)))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (sqrt (/ k (* n (PI))))> |
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (/ k (* n (PI)))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)> |
#<alt (/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)> |
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (+ (* k (+ (* 1/8 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))> |
#<alt (* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))> |
#<alt (* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))> |
#<alt (* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))> |
#<alt (* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))> |
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))> |
#<alt (+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))> |
#<alt (+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))> |
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (sqrt (/ n k))> |
#<alt (* (sqrt (/ n k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ n k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ n k)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ n k)) (pow (sqrt -1) 2))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
72 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 21.0ms | k | @ | -inf | (* (sqrt (* (PI) 2)) (sqrt (/ n k))) |
| 2.0ms | n | @ | 0 | (/ 1 (* (pow (* n (* (PI) 2)) (+ (* k 1/2) -1/2)) (sqrt k))) |
| 1.0ms | n | @ | -inf | (/ 1 (* (pow (* n (* (PI) 2)) (+ (* k 1/2) -1/2)) (sqrt k))) |
| 1.0ms | n | @ | inf | (/ 1 (* (pow (* n (* (PI) 2)) (+ (* k 1/2) -1/2)) (sqrt k))) |
| 1.0ms | k | @ | -inf | (/ (pow (* n (* (PI) 2)) (+ (* k -1/2) 1/2)) (sqrt k)) |
| 1× | batch-egg-rewrite |
| 6 476× | lower-*.f32 |
| 6 466× | lower-*.f64 |
| 3 312× | lower-/.f32 |
| 3 300× | lower-/.f64 |
| 2 630× | lower-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 28 | 119 |
| 0 | 52 | 115 |
| 1 | 187 | 114 |
| 2 | 1080 | 114 |
| 0 | 8635 | 114 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(PI.f64) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 #s(literal 2 binary64)) |
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) |
(/.f64 k (*.f64 n (PI.f64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(sqrt.f64 (/.f64 n k)) |
(*.f64 n (PI.f64)) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) #s(literal -1 binary64))) |
(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
(exp.f64 (fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))) |
(exp.f64 (-.f64 (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
(exp.f64 (-.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (log.f64 k) #s(literal 1/2 binary64)))) |
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k)))) |
(neg.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k)))) |
(neg.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))) #s(literal 1 binary64))) |
(neg.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) |
(/.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) |
(/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))) |
(/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) |
(/.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 k))) |
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) |
(/.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64)))) (*.f64 (neg.f64 (sqrt.f64 k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))) |
(/.f64 (neg.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) |
(/.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))) |
(/.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 (neg.f64 k)))) |
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (sqrt.f64 (neg.f64 k)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (neg.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (sqrt.f64 (neg.f64 k)) (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 (neg.f64 k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (neg.f64 k)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (neg.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) |
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 (*.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) #s(literal -1 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (neg.f64 k)))) |
(/.f64 (*.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (*.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 (neg.f64 k)))) |
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64)))) |
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) |
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(PI.f64) |
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(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64))) |
(fabs.f64 (PI.f64)) |
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(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))) |
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(*.f64 (*.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 n #s(literal -1/2 binary64))) (pow.f64 n (*.f64 k #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 n (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n #s(literal -1/2 binary64))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 n (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) (pow.f64 n (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (pow.f64 n (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) (pow.f64 n (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 n k)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 n k)) |
(neg.f64 (/.f64 (sqrt.f64 n) (neg.f64 (sqrt.f64 k)))) |
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) #s(literal 1 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 k n)))) |
(/.f64 (sqrt.f64 n) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (neg.f64 n)) (sqrt.f64 (neg.f64 k))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 k (neg.f64 n)))) |
(/.f64 (neg.f64 (sqrt.f64 n)) (neg.f64 (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 n #s(literal -1 binary64))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 n))) (neg.f64 (sqrt.f64 (neg.f64 k)))) |
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 n))) (sqrt.f64 k)) |
(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) |
(/.f64 (*.f64 (sqrt.f64 n) #s(literal 1 binary64)) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 n) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (/.f64 (neg.f64 (sqrt.f64 n)) #s(literal -1 binary64)) (sqrt.f64 k)) |
(pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) |
(pow.f64 (sqrt.f64 (/.f64 k n)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (/.f64 k n) #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (/.f64 n k) (/.f64 n k)) #s(literal 1/4 binary64)) |
(pow.f64 (exp.f64 (log.f64 (/.f64 n k))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 n k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (neg.f64 n)) (pow.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (neg.f64 n)) (sqrt.f64 (/.f64 #s(literal -1 binary64) k))) |
(*.f64 (sqrt.f64 (neg.f64 n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k)))) |
(*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) |
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/4 binary64)) (pow.f64 (/.f64 k n) #s(literal -1/4 binary64))) |
(*.f64 (*.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) |
(*.f64 (*.f64 (sqrt.f64 n) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(-.f64 #s(literal 0 binary64) (*.f64 n (neg.f64 (PI.f64)))) |
(neg.f64 (*.f64 n (neg.f64 (PI.f64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) |
(/.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64)) |
(/.f64 (*.f64 n (neg.f64 (PI.f64))) #s(literal -1 binary64)) |
(*.f64 n (PI.f64)) |
(*.f64 n (neg.f64 (neg.f64 (PI.f64)))) |
(*.f64 (PI.f64) n) |
(*.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) |
(*.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (*.f64 n (neg.f64 (PI.f64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) n)) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n)) |
(*.f64 (neg.f64 n) (neg.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) n))) |
(*.f64 (neg.f64 (PI.f64)) (neg.f64 n)) |
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 (neg.f64 (neg.f64 (PI.f64))) n) |
(*.f64 (*.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64)))) |
(*.f64 (*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) |
| 1× | egg-herbie |
| 11 814× | lower-fma.f64 |
| 11 814× | lower-fma.f32 |
| 6 186× | lower-*.f64 |
| 6 186× | lower-*.f32 |
| 2 402× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 249 | 3666 |
| 1 | 760 | 3532 |
| 2 | 2567 | 3216 |
| 3 | 5118 | 3175 |
| 0 | 8496 | 3045 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(* 2 (* n (PI))) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(sqrt (/ k (* n (PI)))) |
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) |
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) |
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) |
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(/ k (* n (PI))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/8 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))) |
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))) |
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2)))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(sqrt (/ n k)) |
(* (sqrt (/ n k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ n k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ n k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ n k)) (pow (sqrt -1) 2)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
| Outputs |
|---|
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 k (fma.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
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(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) |
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (fma.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) |
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(fma.f64 k (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) k)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (fma.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (fma.f64 (*.f64 #s(literal 1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/8 binary64)))) (*.f64 k k) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (fma.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 n k)) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 n k)) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 n k)) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt (/ n k)) |
(sqrt.f64 (/.f64 n k)) |
(* (sqrt (/ n k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 n k))) |
(* (sqrt (/ n k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 n k))) |
(* (sqrt (/ n k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 n k))) |
(* (sqrt (/ n k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 n k))) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
Compiled 31 946 to 3 934 computations (87.7% saved)
23 alts after pruning (17 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 783 | 11 | 1 794 |
| Fresh | 6 | 6 | 12 |
| Picked | 0 | 5 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 789 | 23 | 1 812 |
| Status | Accuracy | Program |
|---|---|---|
| 5.3% | (pow.f64 k #s(literal -1/2 binary64)) | |
| ✓ | 99.6% | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
| 75.4% | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) | |
| 51.1% | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) | |
| ▶ | 51.5% | (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| 51.6% | (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) | |
| ✓ | 40.5% | (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
| ▶ | 99.4% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
| ✓ | 99.4% | (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))) |
| 40.4% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))) | |
| ▶ | 5.3% | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| 76.0% | (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))) | |
| 51.6% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) | |
| 51.4% | (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (PI.f64))) (sqrt.f64 n)) | |
| ✓ | 39.5% | (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
| 51.6% | (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64)))) | |
| 5.3% | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) | |
| ✓ | 39.4% | (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
| ▶ | 14.0% | (sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
| 39.6% | (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) | |
| ▶ | 5.3% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
| ✓ | 5.3% | (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
| 13.5% | (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))) |
Compiled 483 to 364 computations (24.6% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 k k) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (*.f64 n (PI.f64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| ✓ | cost-diff | 0 | (sqrt.f64 k) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
| ✓ | cost-diff | 1600 | (*.f64 (sqrt.f64 k) (sqrt.f64 k)) |
| ✓ | cost-diff | 0 | (sqrt.f64 k) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 k) |
| ✓ | cost-diff | 0 | (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 704 | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
| 118× | lower-*.f32 |
| 106× | lower-*.f64 |
| 38× | *-commutative |
| 32× | lower-/.f32 |
| 26× | associate-*l* |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 139 |
| 0 | 47 | 127 |
| 1 | 62 | 127 |
| 2 | 83 | 125 |
| 3 | 93 | 125 |
| 4 | 106 | 125 |
| 5 | 106 | 125 |
| 6 | 119 | 125 |
| 7 | 136 | 125 |
| 8 | 143 | 125 |
| 9 | 148 | 125 |
| 0 | 148 | 125 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
#s(literal 1 binary64) |
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) |
#s(literal 1 binary64) |
(*.f64 (sqrt.f64 k) (sqrt.f64 k)) |
(sqrt.f64 k) |
k |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(*.f64 n (PI.f64)) |
n |
(PI.f64) |
(sqrt.f64 k) |
k |
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
(pow.f64 (*.f64 k k) #s(literal -1/2 binary64)) |
(*.f64 k k) |
k |
#s(literal -1/2 binary64) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
(*.f64 (sqrt.f64 k) (sqrt.f64 k)) |
k |
(sqrt.f64 k) |
k |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(*.f64 n (PI.f64)) |
n |
(PI.f64) |
(sqrt.f64 k) |
k |
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
(pow.f64 (*.f64 k k) #s(literal -1/2 binary64)) |
(*.f64 k k) |
k |
#s(literal -1/2 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 k k) |
| ✓ | accuracy | 99.9% | (sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
| ✓ | accuracy | 78.4% | (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)) |
| ✓ | accuracy | 99.8% | (*.f64 n (PI.f64)) |
| ✓ | accuracy | 99.7% | (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| ✓ | accuracy | 99.6% | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
| ✓ | accuracy | 54.2% | (PI.f64) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 k) |
| ✓ | accuracy | 99.9% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
| ✓ | accuracy | 99.7% | (*.f64 (sqrt.f64 k) (sqrt.f64 k)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 k) |
| ✓ | accuracy | 99.8% | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| ✓ | accuracy | 99.8% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
| ✓ | accuracy | 99.7% | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.7% | (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 54.2% | (PI.f64) |
| 30.0ms | 135× | 0 | valid |
| 27.0ms | 120× | 0 | exit |
| 0.0ms | 1× | 0 | invalid |
Compiled 141 to 29 computations (79.4% saved)
ival-mult: 10.0ms (25.2% of total)ival-pow: 10.0ms (25.2% of total)ival-sqrt: 8.0ms (20.1% of total)ival-div: 7.0ms (17.6% of total)ival-add: 3.0ms (7.5% of total)ival-pi: 1.0ms (2.5% of total)exact: 1.0ms (2.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))> |
#<alt (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))> |
#<alt (sqrt.f64 k)> |
#<alt (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))> |
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k))> |
#<alt (*.f64 (sqrt.f64 k) (sqrt.f64 k))> |
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))> |
#<alt (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))> |
#<alt (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))> |
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))> |
#<alt (sqrt.f64 #s(literal 2 binary64))> |
#<alt (sqrt.f64 (*.f64 n (PI.f64)))> |
#<alt (sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))> |
#<alt (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))> |
#<alt (*.f64 k k)> |
#<alt (PI.f64)> |
#<alt (*.f64 n (PI.f64))> |
| Outputs |
|---|
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))> |
#<alt (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))> |
#<alt (+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))))> |
#<alt (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))))> |
#<alt (+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/48 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))))))))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))> |
#<alt (* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (sqrt k)> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt k> |
#<alt k> |
#<alt k> |
#<alt k> |
#<alt k> |
#<alt k> |
#<alt k> |
#<alt k> |
#<alt (* -1 (* k (pow (sqrt -1) 2)))> |
#<alt (* -1 (* k (pow (sqrt -1) 2)))> |
#<alt (* -1 (* k (pow (sqrt -1) 2)))> |
#<alt (* -1 (* k (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ -1 (* k (pow (sqrt -1) 2)))> |
#<alt (/ -1 (* k (pow (sqrt -1) 2)))> |
#<alt (/ -1 (* k (pow (sqrt -1) 2)))> |
#<alt (/ -1 (* k (pow (sqrt -1) 2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* (sqrt (* n (PI))) (sqrt 2))> |
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))> |
#<alt (sqrt (* n (PI)))> |
#<alt (sqrt (* n (PI)))> |
#<alt (sqrt (* n (PI)))> |
#<alt (sqrt (* n (PI)))> |
#<alt (sqrt (* n (PI)))> |
#<alt (sqrt (* n (PI)))> |
#<alt (sqrt (* n (PI)))> |
#<alt (sqrt (* n (PI)))> |
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (sqrt (/ 1 k))> |
#<alt (* (sqrt (/ 1 k)) (sqrt -1))> |
#<alt (* (sqrt (/ 1 k)) (sqrt -1))> |
#<alt (* (sqrt (/ 1 k)) (sqrt -1))> |
#<alt (* (sqrt (/ 1 k)) (sqrt -1))> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ 1 k)> |
#<alt (/ -1 k)> |
#<alt (/ -1 k)> |
#<alt (/ -1 k)> |
#<alt (/ -1 k)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (pow k 2)> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
#<alt (* n (PI))> |
57 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | k | @ | 0 | (/ (sqrt k) (pow (* n (* (PI) 2)) (+ (* k -1/2) 1/2))) |
| 1.0ms | k | @ | -inf | (/ (sqrt k) (pow (* n (* (PI) 2)) (+ (* k -1/2) 1/2))) |
| 1.0ms | n | @ | -inf | (/ (sqrt k) (pow (* n (* (PI) 2)) (+ (* k -1/2) 1/2))) |
| 1.0ms | n | @ | inf | (/ (sqrt k) (pow (* n (* (PI) 2)) (+ (* k -1/2) 1/2))) |
| 1.0ms | k | @ | inf | (/ (sqrt k) (pow (* n (* (PI) 2)) (+ (* k -1/2) 1/2))) |
| 1× | batch-egg-rewrite |
| 5 432× | lower-*.f32 |
| 5 420× | lower-*.f64 |
| 2 964× | lower-fma.f32 |
| 2 962× | lower-fma.f64 |
| 2 680× | lower-/.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 105 |
| 0 | 47 | 87 |
| 1 | 160 | 81 |
| 2 | 799 | 81 |
| 3 | 7326 | 81 |
| 0 | 8850 | 81 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(sqrt.f64 k) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 k) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(sqrt.f64 #s(literal 2 binary64)) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
(pow.f64 (*.f64 k k) #s(literal -1/2 binary64)) |
(*.f64 k k) |
(PI.f64) |
(*.f64 n (PI.f64)) |
| Outputs |
|---|
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))) |
(exp.f64 (fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))) |
(exp.f64 (fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 #s(literal -1/2 binary64) (log.f64 k)))) |
(exp.f64 (fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 k))))) |
(exp.f64 (fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 k)) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
(exp.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 k) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 k)) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
(exp.f64 (-.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (log.f64 k)))) |
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k |
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(-.f64 #s(literal 0 binary64) (neg.f64 k)) |
(sqrt.f64 (*.f64 k k)) |
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(pow.f64 k #s(literal 1 binary64)) |
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(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) #s(literal -1 binary64))) |
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(exp.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 k) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 k)) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))) |
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 #s(literal -1/2 binary64) (log.f64 k)))) |
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 k))))) |
(exp.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (log.f64 k)))) |
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(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
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(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (sqrt.f64 k))) |
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(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) #s(literal 2 binary64))) |
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(exp.f64 (log.f64 (*.f64 k k))) |
(exp.f64 (*.f64 (log.f64 (*.f64 k k)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal 4 binary64))) |
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(sqrt.f64 (*.f64 k (*.f64 k (*.f64 k k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 k k))) |
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(/.f64 (*.f64 k (neg.f64 k)) #s(literal -1 binary64)) |
(/.f64 (*.f64 (neg.f64 k) k) #s(literal -1 binary64)) |
(/.f64 (*.f64 (neg.f64 k) (neg.f64 k)) #s(literal 1 binary64)) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) |
(/.f64 (*.f64 (*.f64 k (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 k)) (*.f64 k (sqrt.f64 k))) #s(literal -1 binary64)) |
(pow.f64 k #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 k) #s(literal 4 binary64)) |
(pow.f64 (*.f64 k k) #s(literal 1 binary64)) |
(pow.f64 (*.f64 k (*.f64 k (*.f64 k k))) #s(literal 1/2 binary64)) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 k)) |
(*.f64 k k) |
(*.f64 (sqrt.f64 k) (*.f64 k (sqrt.f64 k))) |
(*.f64 (sqrt.f64 k) (*.f64 #s(literal 1 binary64) (*.f64 k (sqrt.f64 k)))) |
(*.f64 (*.f64 k k) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (sqrt.f64 k)) (*.f64 (sqrt.f64 (sqrt.f64 k)) (*.f64 k (sqrt.f64 k)))) |
(*.f64 (*.f64 k (sqrt.f64 k)) (sqrt.f64 k)) |
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(*.f64 (*.f64 (*.f64 k (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) |
(PI.f64) |
(log.f64 (exp.f64 (PI.f64))) |
(+.f64 (log.f64 (pow.f64 (E.f64) (/.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (pow.f64 (E.f64) (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))) |
(+.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))))) |
(exp.f64 (log.f64 (PI.f64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64))) |
(fabs.f64 (PI.f64)) |
(sqrt.f64 (*.f64 (PI.f64) (PI.f64))) |
(cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) |
(pow.f64 (PI.f64) #s(literal 1 binary64)) |
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64)) |
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64)) |
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) |
(pow.f64 (E.f64) (log.f64 (PI.f64))) |
(*.f64 #s(literal 1 binary64) (PI.f64)) |
(*.f64 (PI.f64) #s(literal 1 binary64)) |
(*.f64 (PI.f64) (log.f64 (E.f64))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) |
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))))) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (sqrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64))) |
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(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64))))) |
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(*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) |
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64))))) |
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))) |
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(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
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(*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) |
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))))) |
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64))))) |
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(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) |
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(*.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) |
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(*.f64 (PI.f64) n) |
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(*.f64 (*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64)))) |
(*.f64 (*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) |
| 1× | egg-herbie |
| 8 938× | lower-fma.f64 |
| 8 938× | lower-fma.f32 |
| 6 534× | lower-*.f64 |
| 6 534× | lower-*.f32 |
| 1 730× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 184 | 2221 |
| 1 | 553 | 2131 |
| 2 | 1902 | 2105 |
| 3 | 4239 | 2021 |
| 0 | 8286 | 1942 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))) |
(+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/48 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))))))))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(* (sqrt k) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt k) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt k) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt k) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt k) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(sqrt k) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
k |
k |
k |
k |
k |
k |
k |
k |
(* -1 (* k (pow (sqrt -1) 2))) |
(* -1 (* k (pow (sqrt -1) 2))) |
(* -1 (* k (pow (sqrt -1) 2))) |
(* -1 (* k (pow (sqrt -1) 2))) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ -1 (* k (pow (sqrt -1) 2))) |
(/ -1 (* k (pow (sqrt -1) 2))) |
(/ -1 (* k (pow (sqrt -1) 2))) |
(/ -1 (* k (pow (sqrt -1) 2))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(sqrt (* n (PI))) |
(sqrt (* n (PI))) |
(sqrt (* n (PI))) |
(sqrt (* n (PI))) |
(sqrt (* n (PI))) |
(sqrt (* n (PI))) |
(sqrt (* n (PI))) |
(sqrt (* n (PI))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(sqrt (/ 1 k)) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ 1 k) |
(/ -1 k) |
(/ -1 k) |
(/ -1 k) |
(/ -1 k) |
(pow k 2) |
(pow k 2) |
(pow k 2) |
(pow k 2) |
(pow k 2) |
(pow k 2) |
(pow k 2) |
(pow k 2) |
(pow k 2) |
(pow k 2) |
(pow k 2) |
(pow k 2) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (*.f64 k (*.f64 k k))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (*.f64 k (*.f64 k k))))) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 k (fma.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (*.f64 k (*.f64 k k))))) #s(literal -1/48 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
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(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
k |
k |
k |
k |
k |
k |
k |
k |
(* -1 (* k (pow (sqrt -1) 2))) |
k |
(* -1 (* k (pow (sqrt -1) 2))) |
k |
(* -1 (* k (pow (sqrt -1) 2))) |
k |
(* -1 (* k (pow (sqrt -1) 2))) |
k |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ -1 (* k (pow (sqrt -1) 2))) |
(/.f64 #s(literal 1 binary64) k) |
(/ -1 (* k (pow (sqrt -1) 2))) |
(/.f64 #s(literal 1 binary64) k) |
(/ -1 (* k (pow (sqrt -1) 2))) |
(/.f64 #s(literal 1 binary64) k) |
(/ -1 (* k (pow (sqrt -1) 2))) |
(/.f64 #s(literal 1 binary64) k) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(sqrt (* n (PI))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(sqrt (* n (PI))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(sqrt (* n (PI))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(sqrt (* n (PI))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(sqrt (* n (PI))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(sqrt (* n (PI))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(sqrt (* n (PI))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(sqrt (* n (PI))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal -1 binary64))) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal -1 binary64))) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal -1 binary64))) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal -1 binary64))) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
(/ -1 k) |
(/.f64 #s(literal -1 binary64) k) |
(/ -1 k) |
(/.f64 #s(literal -1 binary64) k) |
(/ -1 k) |
(/.f64 #s(literal -1 binary64) k) |
(/ -1 k) |
(/.f64 #s(literal -1 binary64) k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(pow k 2) |
(*.f64 k k) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
Compiled 21 465 to 3 093 computations (85.6% saved)
30 alts after pruning (20 fresh and 10 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 424 | 14 | 1 438 |
| Fresh | 6 | 6 | 12 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 6 | 6 |
| Total | 1 431 | 30 | 1 461 |
| Status | Accuracy | Program |
|---|---|---|
| 19.9% | (pow.f64 (*.f64 k (*.f64 k (*.f64 k k))) #s(literal -1/8 binary64)) | |
| ✓ | 99.6% | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
| 51.1% | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) | |
| 51.4% | (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)) | |
| ✓ | 51.5% | (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| 5.3% | (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) | |
| 51.6% | (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) | |
| ✓ | 40.5% | (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
| 5.3% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))) | |
| ✓ | 99.4% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
| ✓ | 99.4% | (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))) |
| 40.4% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))) | |
| 5.3% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) | |
| ✓ | 5.3% | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| 76.0% | (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) | |
| 51.2% | (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k)))) | |
| 51.4% | (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))) | |
| ✓ | 39.5% | (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
| 51.6% | (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64)))) | |
| 5.3% | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) | |
| ✓ | 39.4% | (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
| 51.5% | (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) | |
| 39.6% | (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) | |
| 5.3% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))) | |
| ✓ | 5.3% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
| ✓ | 5.3% | (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
| 5.3% | (sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))) | |
| 5.3% | (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 k)))) | |
| 39.6% | (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) | |
| 13.9% | (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
Compiled 1 024 to 449 computations (56.2% saved)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (PI.f64))) (sqrt.f64 n)) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
(pow.f64 (*.f64 k (*.f64 k (*.f64 k k))) #s(literal -1/8 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) |
(*.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
4 calls:
| 18.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 18.0ms | k |
| 17.0ms | n |
| 14.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | k |
| 99.6% | 1 | n |
| 99.6% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 99.6% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 31 to 23 computations (25.8% saved)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (PI.f64))) (sqrt.f64 n)) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
(pow.f64 (*.f64 k (*.f64 k (*.f64 k k))) #s(literal -1/8 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))) |
| Outputs |
|---|
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
4 calls:
| 20.0ms | n |
| 13.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 12.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 12.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | k |
| 99.6% | 1 | n |
| 99.6% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 99.6% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 31 to 23 computations (25.8% saved)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (PI.f64))) (sqrt.f64 n)) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
(pow.f64 (*.f64 k (*.f64 k (*.f64 k k))) #s(literal -1/8 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) |
4 calls:
| 21.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 13.0ms | k |
| 11.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 11.0ms | n |
| Accuracy | Segments | Branch |
|---|---|---|
| 62.6% | 5 | n |
| 97.6% | 3 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 62.6% | 5 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 97.6% | 2 | k |
Compiled 31 to 23 computations (25.8% saved)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (PI.f64))) (sqrt.f64 n)) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
(pow.f64 (*.f64 k (*.f64 k (*.f64 k k))) #s(literal -1/8 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))) |
| Outputs |
|---|
(pow.f64 (*.f64 k (*.f64 k (*.f64 k k))) #s(literal -1/8 binary64)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
2 calls:
| 14.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 11.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 67.5% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 67.4% | 2 | k |
Compiled 21 to 15 computations (28.6% saved)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (PI.f64))) (sqrt.f64 n)) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) |
| Outputs |
|---|
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
2 calls:
| 10.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 10.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 61.1% | 2 | k |
| 61.1% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 21 to 15 computations (28.6% saved)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Outputs |
|---|
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
1 calls:
| 4.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 61.1% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 18 to 13 computations (27.8% saved)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
| Outputs |
|---|
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
2 calls:
| 5.0ms | k |
| 3.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 61.0% | 2 | k |
| 61.1% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 21 to 15 computations (28.6% saved)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
| Outputs |
|---|
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) |
4 calls:
| 3.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 3.0ms | n |
| 3.0ms | k |
| 2.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 41.6% | 2 | n |
| 41.6% | 2 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 49.1% | 2 | k |
| 49.0% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 31 to 23 computations (25.8% saved)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
| Outputs |
|---|
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
4 calls:
| 4.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 3.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 2.0ms | n |
| 2.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 39.6% | 1 | n |
| 39.6% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 39.6% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 39.6% | 1 | k |
Compiled 31 to 23 computations (25.8% saved)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
| Outputs |
|---|
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
4 calls:
| 5.0ms | k |
| 2.0ms | n |
| 2.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 2.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 39.6% | 1 | k |
| 39.6% | 1 | n |
| 39.6% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 39.6% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 31 to 23 computations (25.8% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64)) |
| Outputs |
|---|
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
4 calls:
| 2.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 2.0ms | n |
| 2.0ms | k |
| 2.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 5.3% | 1 | k |
| 5.3% | 1 | n |
| 5.3% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 5.3% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 31 to 23 computations (25.8% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 18.0ms | 0.5491195962576092 | 6270.845583003633 |
| 13.0ms | 128× | 0 | valid |
Compiled 253 to 210 computations (17% saved)
ival-mult: 3.0ms (30.2% of total)ival-pow: 3.0ms (30.2% of total)ival-div: 2.0ms (20.2% of total)ival-sub: 1.0ms (10.1% of total)ival-sqrt: 1.0ms (10.1% of total)ival-pi: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 5.590283864241657e-119 |
Compiled 21 to 18 computations (14.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 5.590283864241657e-119 |
Compiled 21 to 18 computations (14.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 5.590283864241657e-119 |
Compiled 21 to 18 computations (14.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 5.590283864241657e-119 |
Compiled 21 to 18 computations (14.3% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 69.0ms | 0.005915565381942559 | 0.5491195962576092 |
| 65.0ms | 112× | 0 | valid |
Compiled 168 to 137 computations (18.5% saved)
ival-pow: 57.0ms (91.3% of total)ival-mult: 2.0ms (3.2% of total)ival-div: 1.0ms (1.6% of total)ival-sqrt: 1.0ms (1.6% of total)ival-pi: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-sub: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | egg-herbie |
| 28× | *-commutative_binary64 |
| 4× | +-commutative_binary64 |
| 4× | sub-neg_binary64 |
| 2× | 1-exp_binary64 |
| 2× | neg-sub0_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 64 | 240 |
| 1 | 81 | 240 |
| 2 | 85 | 240 |
| 3 | 87 | 240 |
| 4 | 88 | 240 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(if (<=.f64 k #s(literal 1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (pow.f64 (*.f64 k (*.f64 k (*.f64 k k))) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) |
(if (<=.f64 k #s(literal 2206763817411543/4503599627370496 binary64)) (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k))))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(if (<=.f64 k #s(literal 1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (pow.f64 (*.f64 k (*.f64 k (*.f64 k k))) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (pow.f64 (*.f64 k (*.f64 k (*.f64 k k))) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) |
(if (<=.f64 k #s(literal 2206763817411543/4503599627370496 binary64)) (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k))))) |
(sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) |
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
| 11 814× | lower-fma.f64 |
| 11 814× | lower-fma.f32 |
| 9 974× | lower-fma.f64 |
| 9 974× | lower-fma.f32 |
| 8 642× | lower-fma.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 249 | 3666 |
| 1 | 760 | 3532 |
| 2 | 2567 | 3216 |
| 3 | 5118 | 3175 |
| 0 | 8496 | 3045 |
| 0 | 26 | 105 |
| 0 | 47 | 87 |
| 1 | 160 | 81 |
| 2 | 799 | 81 |
| 3 | 7326 | 81 |
| 0 | 8850 | 81 |
| 0 | 28 | 119 |
| 0 | 52 | 115 |
| 1 | 187 | 114 |
| 2 | 1080 | 114 |
| 0 | 8635 | 114 |
| 0 | 35 | 163 |
| 0 | 64 | 156 |
| 1 | 232 | 148 |
| 2 | 1140 | 146 |
| 0 | 8701 | 144 |
| 0 | 312 | 4640 |
| 1 | 966 | 4458 |
| 2 | 3269 | 4306 |
| 3 | 6582 | 4090 |
| 0 | 8117 | 3944 |
| 0 | 128 | 1174 |
| 1 | 345 | 1155 |
| 2 | 1011 | 1065 |
| 3 | 3348 | 1038 |
| 4 | 5547 | 966 |
| 0 | 8354 | 945 |
| 1× | fuel |
| 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× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 803 to 459 computations (42.8% saved)
Compiled 520 to 150 computations (71.2% saved)
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