
Time bar (total: 15.7s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 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% | 50% | 1.6% | 7 |
| 52.5% | 25% | 22.6% | 0.1% | 0% | 50% | 2.3% | 8 |
| 53.8% | 25% | 21.5% | 0.1% | 0% | 50% | 3.5% | 9 |
| 54.5% | 25% | 20.9% | 0.1% | 0% | 50% | 4.1% | 10 |
| 55.3% | 25% | 20.2% | 0.1% | 0% | 50% | 4.8% | 11 |
| 55.7% | 25% | 19.9% | 0.1% | 0% | 50% | 5.1% | 12 |
Compiled 19 to 14 computations (26.3% saved)
ival-pow: 76.0ms (60.2% of total)ival-mult: 17.0ms (13.5% of total)ival-div: 14.0ms (11.1% of total)ival-sqrt: 8.0ms (6.3% of total)ival-pi: 5.0ms (4% of total)ival-sub: 5.0ms (4% of total)const: 1.0ms (0.8% of total)backward-pass: 0.0ms (0% of total)| 2.0s | 3919× | 5 | exit |
| 1.1s | 8256× | 0 | valid |
| 572.0ms | 1976× | 1 | invalid |
| 70.0ms | 507× | 0 | invalid |
| 38.0ms | 242× | 0 | unsamplable |
ival-pow: 763.0ms (30.2% of total)ival-mult: 477.0ms (18.9% of total)ival-div: 375.0ms (14.9% of total)backward-pass: 369.0ms (14.6% of total)ival-sqrt: 206.0ms (8.2% of total)ival-sub: 169.0ms (6.7% of total)ival-pi: 126.0ms (5% of total)const: 39.0ms (1.5% of total)| 2× | egg-herbie |
| 1106× | fnmadd-define |
| 930× | fma-define |
| 846× | fmsub-define |
| 760× | fnmsub-define |
| 680× | sum3-define |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 33 | 92 |
| 1 | 93 | 88 |
| 2 | 208 | 88 |
| 3 | 414 | 83 |
| 4 | 742 | 82 |
| 5 | 1486 | 82 |
| 6 | 2091 | 82 |
| 7 | 2661 | 82 |
| 8 | 3559 | 82 |
| 9 | 3711 | 82 |
| 10 | 3770 | 82 |
| 11 | 3814 | 82 |
| 12 | 3822 | 82 |
| 0 | 13 | 14 |
| 1 | 30 | 14 |
| 2 | 47 | 14 |
| 3 | 69 | 14 |
| 4 | 90 | 13 |
| 5 | 113 | 13 |
| 6 | 149 | 13 |
| 7 | 188 | 13 |
| 8 | 214 | 13 |
| 9 | 228 | 13 |
| 10 | 229 | 13 |
| 0 | 229 | 13 |
| 1× | iter limit |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| Outputs |
|---|
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
| Inputs |
|---|
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))) |
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))) |
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))) |
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))) |
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2))) |
| Outputs |
|---|
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
(* (rsqrt k) (pow (* 2 (* (PI) n)) (fnmsub k 1/2 -1/2))) |
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))) |
(* (rsqrt (neg k)) (pow (* 2 (* (PI) n)) (fnmsub k -1/2 -1/2))) |
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))) |
(* (rsqrt k) (pow (* (PI) (* n -2)) (fnmsub k 1/2 -1/2))) |
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))) |
(fnmsub (rsqrt (neg k)) (pow (* 2 (* (PI) n)) (fnmsub k -1/2 -1/2)) 0) |
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))) |
(* (pow (* (PI) (* n -2)) (fnmsub k 1/2 -1/2)) (neg (rsqrt k))) |
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2))) |
(* (rsqrt n) (pow (* k (* 2 (PI))) (fnmsub n 1/2 -1/2))) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 3 | 223 | (2.5985308456311224e-47 1.0994244550744063e-294) | 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 | - | (*.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) |
| 0 | 0 | - | 0 | - | (*.f64 #s(literal 2 binary64) (PI.f64)) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| 0 | 0 | - | 0 | - | (-.f64 #s(literal 1 binary64) k) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | (sqrt.f64 k) |
| 0 | 0 | - | 0 | - | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | n |
| 0 | 0 | - | 0 | - | k |
| 113.0ms | 512× | 0 | valid |
Compiled 132 to 41 computations (68.9% saved)
ival-pow: 15.0ms (30.5% of total)ival-mult: 11.0ms (22.3% of total)ival-div: 10.0ms (20.3% of total)ival-sqrt: 7.0ms (14.2% of total)ival-sub: 3.0ms (6.1% of total)ival-pi: 2.0ms (4.1% of total)const: 1.0ms (2% of total)backward-pass: 0.0ms (0% of total)Compiled 16 to 12 computations (25% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.5% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
| ▶ | 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 34 to 25 computations (26.5% saved)
| 1× | egg-herbie |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 (PI.f64) n) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) |
| ✓ | cost-diff | 0 | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 k) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| ✓ | cost-diff | 128 | (*.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)))) |
| 64× | sum3-define |
| 64× | *-lowering-*.f32 |
| 64× | *-lowering-*.f64 |
| 48× | +-lowering-+.f64 |
| 48× | +-lowering-+.f32 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 20 | 98 |
| 1 | 38 | 98 |
| 2 | 58 | 98 |
| 3 | 78 | 98 |
| 4 | 100 | 92 |
| 5 | 129 | 92 |
| 6 | 170 | 92 |
| 7 | 202 | 92 |
| 8 | 231 | 92 |
| 9 | 235 | 92 |
| 0 | 235 | 92 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
(/ 1 (sqrt k)) |
1 |
(sqrt k) |
k |
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) |
(* (* 2 (PI)) n) |
(* 2 (PI)) |
2 |
(PI) |
n |
(/ (- 1 k) 2) |
(- 1 k) |
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k)) |
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) |
(* 2 (* (PI) n)) |
2 |
(* (PI) n) |
(PI) |
n |
(- 1/2 (/ k 2)) |
1/2 |
(/ k 2) |
k |
(sqrt k) |
| Outputs |
|---|
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/ 1 (sqrt k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
1 |
#s(literal 1 binary64) |
(sqrt k) |
(sqrt.f64 k) |
k |
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) |
(* (* 2 (PI)) n) |
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
(* 2 (PI)) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
2 |
#s(literal 2 binary64) |
(PI) |
(PI.f64) |
n |
(/ (- 1 k) 2) |
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))) |
(- 1 k) |
(-.f64 #s(literal 1 binary64) k) |
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k)) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) |
(* 2 (* (PI) n)) |
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
2 |
#s(literal 2 binary64) |
(* (PI) n) |
(*.f64 (PI.f64) n) |
(PI) |
(PI.f64) |
n |
(- 1/2 (/ k 2)) |
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(/ k 2) |
(/.f64 k #s(literal 2 binary64)) |
k |
(sqrt k) |
(sqrt.f64 k) |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (PI.f64) |
| ✓ | accuracy | 99.8% | (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.7% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
| ✓ | accuracy | 99.7% | (*.f64 (PI.f64) n) |
| ✓ | accuracy | 99.8% | (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% | (*.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% | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| 93.0ms | 256× | 0 | valid |
Compiled 105 to 21 computations (80% saved)
ival-pow: 15.0ms (33.4% of total)ival-div: 10.0ms (22.3% of total)ival-mult: 8.0ms (17.8% of total)ival-sqrt: 7.0ms (15.6% of total)ival-sub: 3.0ms (6.7% of total)ival-pi: 1.0ms (2.2% of total)const: 1.0ms (2.2% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))> |
#<alt (/ 1 (sqrt k))> |
#<alt (sqrt k)> |
#<alt (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))> |
#<alt (/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))> |
#<alt (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))> |
#<alt (* 2 (* (PI) n))> |
#<alt (* (PI) n)> |
#<alt (* (* 2 (PI)) n)> |
#<alt (PI)> |
| 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 (* 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 (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)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 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 (* (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 (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 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 (* (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 (* 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 (* 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)))> |
39 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 35.0ms | n | @ | 0 | (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 23.0ms | n | @ | -inf | (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 14.0ms | n | @ | -inf | (* (PI) n) |
| 9.0ms | n | @ | 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 |
| 3146× | *-lowering-*.f32 |
| 3146× | *-lowering-*.f64 |
| 2906× | pow-lowering-pow.f64 |
| 2906× | pow-lowering-pow.f32 |
| 1394× | pow-unpow |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 20 | 68 |
| 1 | 100 | 68 |
| 2 | 478 | 64 |
| 3 | 3275 | 64 |
| 0 | 8262 | 64 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
(/ 1 (sqrt k)) |
(sqrt k) |
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) |
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k)) |
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) |
(* 2 (* (PI) n)) |
(* (PI) n) |
(* (* 2 (PI)) n) |
(PI) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (/.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 -2 binary64)))))) #s(literal -1 binary64))) |
(exp.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal -1/2 binary64) (log.f64 k)))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))))) |
(neg.f64 (neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))))) |
(neg.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) |
(neg.f64 (/.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 -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 -2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k)))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) |
(/.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))))) |
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64))))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))) |
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))) |
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
(/.f64 (neg.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))) |
(/.f64 (*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 n (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) #s(literal -1 binary64)) (sqrt.f64 k)) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64)))) (pow.f64 n (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k)) (pow.f64 n (/.f64 k #s(literal 2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64)))) |
(pow.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) #s(literal 1 binary64)) |
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(*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (log.f64 (pow.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64))))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (log.f64 (exp.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (log.f64 (exp.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))))) |
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 8/3 binary64)) #s(literal 1/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (exp.f64 (*.f64 #s(literal 2/3 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 (pow.f64 (PI.f64) #s(literal 8/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64))) |
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 5/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64))) |
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
| 1× | egg-herbie |
| 5256× | *-lowering-*.f32 |
| 5256× | *-lowering-*.f64 |
| 2382× | +-lowering-+.f64 |
| 2382× | +-lowering-+.f32 |
| 1466× | associate-*r* |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 139 | 2132 |
| 1 | 385 | 2094 |
| 2 | 1192 | 1806 |
| 3 | 4169 | 1722 |
| 4 | 7733 | 1722 |
| 0 | 8104 | 1722 |
| 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 (* 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))) |
(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))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 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 (* (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 (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 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 (* (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))) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* 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))) |
| 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)) (+.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.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)))))))) 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 (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (*.f64 k (*.f64 k k))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #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 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) 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 (+.f64 (*.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))) (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (*.f64 k (*.f64 k k))))) #s(literal -1/48 binary64))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) #s(literal 1/8 binary64)))) (*.f64 k k)) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 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))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
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(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 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 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+ (* 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))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (+.f64 (*.f64 (*.f64 k #s(literal 1/8 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 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))) |
(+.f64 (*.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))) (+.f64 (*.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 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 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))) |
(* 2 (* n (PI))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(* 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)) |
(* 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))) |
Compiled 17595 to 1734 computations (90.1% saved)
12 alts after pruning (11 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 858 | 11 | 869 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 1 | 2 |
| Done | 0 | 0 | 0 |
| Total | 859 | 12 | 871 |
| Status | Accuracy | Program |
|---|---|---|
| 99.6% | (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) | |
| ✓ | 99.5% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
| ▶ | 96.3% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))) |
| 98.9% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))) | |
| ▶ | 99.6% | (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
| 98.9% | (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) | |
| 73.3% | (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) | |
| 99.6% | (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) | |
| 74.0% | (*.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))) | |
| ▶ | 73.3% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64)))) |
| ▶ | 35.5% | (*.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 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 434 to 298 computations (31.3% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) |
| ✓ | cost-diff | 0 | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))) |
| ✓ | cost-diff | 6528 | (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))) |
| ✓ | cost-diff | 0 | (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) |
| ✓ | cost-diff | 128 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64)))) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 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 | (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64)))) |
| ✓ | cost-diff | 0 | (pow.f64 k #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
| 3560× | fnmadd-define |
| 3258× | fma-define |
| 1958× | fma-lowering-fma.f32 |
| 1958× | fma-lowering-fma.f64 |
| 1036× | *-lowering-*.f32 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 259 |
| 1 | 69 | 255 |
| 2 | 111 | 253 |
| 3 | 197 | 253 |
| 4 | 370 | 244 |
| 5 | 1119 | 244 |
| 6 | 3540 | 244 |
| 7 | 6576 | 244 |
| 0 | 8306 | 244 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))) |
(pow k -1/2) |
k |
-1/2 |
(pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))) |
(* 2 (* (PI) n)) |
2 |
(* (PI) n) |
(PI) |
n |
(- -1/2 (/ k -2)) |
(/ k -2) |
-2 |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(sqrt (/ (* n (PI)) k)) |
(/ (* n (PI)) k) |
(* n (PI)) |
n |
(PI) |
k |
(sqrt 2) |
2 |
(* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
(sqrt (/ 1 k)) |
(/ 1 k) |
1 |
k |
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) |
(* (* 2 (PI)) n) |
(* 2 (PI)) |
2 |
(PI) |
n |
(/ (- 1 k) 2) |
(- 1 k) |
(* (/ 1 (sqrt (/ k (* 2 (* (PI) n))))) (pow (* 2 (* (PI) n)) (/ k -2))) |
(/ 1 (sqrt (/ k (* 2 (* (PI) n))))) |
1 |
(sqrt (/ k (* 2 (* (PI) n)))) |
(/ k (* 2 (* (PI) n))) |
k |
(* 2 (* (PI) n)) |
2 |
(* (PI) n) |
(PI) |
n |
(pow (* 2 (* (PI) n)) (/ k -2)) |
(/ k -2) |
-2 |
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k)))) |
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) |
(* 2 (* (PI) n)) |
2 |
(* (PI) n) |
(PI) |
n |
(- 1/2 (/ k 2)) |
1/2 |
(/ k 2) |
k |
(exp (* 1/2 (log k))) |
(* 1/2 (log k)) |
(log k) |
| Outputs |
|---|
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) |
(pow k -1/2) |
(pow.f64 k #s(literal -1/2 binary64)) |
k |
-1/2 |
#s(literal -1/2 binary64) |
(pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) |
(* 2 (* (PI) n)) |
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) |
2 |
#s(literal 2 binary64) |
(* (PI) n) |
(*.f64 (PI.f64) n) |
(PI) |
(PI.f64) |
n |
(- -1/2 (/ k -2)) |
(+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) |
(/ k -2) |
(/.f64 k #s(literal -2 binary64)) |
-2 |
#s(literal -2 binary64) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt (/ (* n (PI)) k)) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(/ (* n (PI)) k) |
(/.f64 (*.f64 (PI.f64) n) k) |
(* n (PI)) |
(*.f64 (PI.f64) n) |
n |
(PI) |
(PI.f64) |
k |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
2 |
#s(literal 2 binary64) |
(* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)))) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
1 |
#s(literal 1 binary64) |
k |
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) |
(* (* 2 (PI)) n) |
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) |
(* 2 (PI)) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
2 |
#s(literal 2 binary64) |
(PI) |
(PI.f64) |
n |
(/ (- 1 k) 2) |
(+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) |
(- 1 k) |
(-.f64 #s(literal 1 binary64) k) |
(* (/ 1 (sqrt (/ k (* 2 (* (PI) n))))) (pow (* 2 (* (PI) n)) (/ k -2))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) |
(/ 1 (sqrt (/ k (* 2 (* (PI) n))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) |
1 |
#s(literal 1 binary64) |
(sqrt (/ k (* 2 (* (PI) n)))) |
(sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) |
(/ k (* 2 (* (PI) n))) |
(/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) |
k |
(* 2 (* (PI) n)) |
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) |
2 |
#s(literal 2 binary64) |
(* (PI) n) |
(*.f64 (PI.f64) n) |
(PI) |
(PI.f64) |
n |
(pow (* 2 (* (PI) n)) (/ k -2)) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal -2 binary64))) |
(/ k -2) |
(/.f64 k #s(literal -2 binary64)) |
-2 |
#s(literal -2 binary64) |
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k)))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) |
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) |
(* 2 (* (PI) n)) |
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) |
2 |
#s(literal 2 binary64) |
(* (PI) n) |
(*.f64 (PI.f64) n) |
(PI) |
(PI.f64) |
n |
(- 1/2 (/ k 2)) |
(+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(/ k 2) |
(/.f64 k #s(literal 2 binary64)) |
k |
(exp (* 1/2 (log k))) |
(sqrt.f64 k) |
(* 1/2 (log k)) |
(*.f64 #s(literal 1/2 binary64) (log.f64 k)) |
(log k) |
(log.f64 k) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.8% | (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.7% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))) |
| ✓ | accuracy | 94.4% | (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.7% | (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) |
| ✓ | accuracy | 88.6% | (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.8% | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| ✓ | accuracy | 99.8% | (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% | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.7% | (/.f64 (*.f64 n (PI.f64)) k) |
| ✓ | accuracy | 99.5% | (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 88.1% | (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.8% | (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64)))) |
| ✓ | accuracy | 99.8% | (*.f64 (PI.f64) n) |
| ✓ | accuracy | 99.8% | (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| 231.0ms | 64× | 5 | exit |
| 162.0ms | 190× | 0 | valid |
| 1.0ms | 2× | 0 | invalid |
Compiled 269 to 41 computations (84.8% saved)
ival-pow: 66.0ms (41% of total)backward-pass: 34.0ms (21.1% of total)ival-div: 19.0ms (11.8% of total)ival-mult: 18.0ms (11.2% of total)ival-sqrt: 9.0ms (5.6% of total)ival-sub: 5.0ms (3.1% of total)ival-log: 4.0ms (2.5% of total)ival-exp: 3.0ms (1.9% of total)const: 1.0ms (0.6% of total)ival-pi: 1.0ms (0.6% of total)| Inputs |
|---|
#<alt (/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))))> |
#<alt (pow k -1/2)> |
#<alt (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))> |
#<alt (* 2 (* (PI) n))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (/ (* n (PI)) k)> |
#<alt (* n (PI))> |
#<alt (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))> |
#<alt (sqrt (/ 1 k))> |
#<alt (/ 1 k)> |
#<alt (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))> |
#<alt (* (/ 1 (sqrt (/ k (* 2 (* (PI) n))))) (pow (* 2 (* (PI) n)) (/ k -2)))> |
#<alt (/ 1 (sqrt (/ k (* 2 (* (PI) n)))))> |
#<alt (sqrt (/ k (* 2 (* (PI) n))))> |
#<alt (/ k (* 2 (* (PI) n)))> |
#<alt (exp (* 1/2 (log k)))> |
#<alt (/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k))))> |
#<alt (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))> |
#<alt (PI)> |
#<alt (* (PI) n)> |
#<alt (* (* 2 (PI)) n)> |
| Outputs |
|---|
#<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)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (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 (/ 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 (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)))))> |
#<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 (/ (* 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)) 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))))) (pow (sqrt -1) 2)))> |
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))> |
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))> |
#<alt (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))> |
#<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)) (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 (* (+ (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)))))> |
#<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 (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (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 (+ (* -1/48 (* (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)))) (/ 1 (sqrt 1/2)))) k)> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt -1)) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt -1)) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt -1)) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt -1)) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt -1)) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt -1)) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt -1)) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt -1)) (sqrt -1/2))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<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)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))> |
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 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 (* (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 (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 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 (* (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 (* 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 (* 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)))> |
102 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 7.0ms | k | @ | inf | (sqrt (/ k (* 2 (* (PI) n)))) |
| 2.0ms | k | @ | 0 | (/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))) |
| 1.0ms | n | @ | 0 | (/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))) |
| 1.0ms | n | @ | inf | (/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))) |
| 1.0ms | n | @ | -inf | (/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))) |
| 1× | batch-egg-rewrite |
| 5090× | *-lowering-*.f32 |
| 5090× | *-lowering-*.f64 |
| 3042× | /-lowering-/.f32 |
| 3042× | /-lowering-/.f64 |
| 1980× | sum5-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 165 |
| 1 | 190 | 156 |
| 2 | 953 | 149 |
| 3 | 7300 | 149 |
| 0 | 8311 | 149 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2)))) |
(pow k -1/2) |
(pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))) |
(* 2 (* (PI) n)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(sqrt (/ (* n (PI)) k)) |
(/ (* n (PI)) k) |
(* n (PI)) |
(* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
(sqrt (/ 1 k)) |
(/ 1 k) |
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) |
(* (/ 1 (sqrt (/ k (* 2 (* (PI) n))))) (pow (* 2 (* (PI) n)) (/ k -2))) |
(/ 1 (sqrt (/ k (* 2 (* (PI) n))))) |
(sqrt (/ k (* 2 (* (PI) n)))) |
(/ k (* 2 (* (PI) n))) |
(exp (* 1/2 (log k))) |
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k)))) |
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) |
(PI) |
(* (PI) n) |
(* (* 2 (PI)) n) |
| Outputs |
|---|
(exp.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (log.f64 k)))) |
(exp.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) (*.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 k) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))) #s(literal -1 binary64))) |
(exp.f64 (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal -2 binary64) k)))) |
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal -2 binary64) k)) (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))))))) |
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(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64)))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64)))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 n (/.f64 k #s(literal -2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal -2 binary64)))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal -2 binary64)))) (pow.f64 n (/.f64 k #s(literal -2 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 n)) (pow.f64 n (/.f64 k #s(literal -2 binary64)))) |
(*.f64 (*.f64 (pow.f64 n (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 n (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal -2 binary64)))) |
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 n (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64)))) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64)))) |
(PI.f64) |
(log.f64 (exp.f64 (PI.f64))) |
(+.f64 (+.f64 (PI.f64) #s(literal 1 binary64)) #s(literal -1 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)) |
(-.f64 (+.f64 (PI.f64) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 (PI.f64) (PI.f64))) |
(cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) |
(expm1.f64 (log1p.f64 (PI.f64))) |
(log1p.f64 (expm1.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 (PI.f64) #s(literal 1 binary64)) |
(*.f64 (PI.f64) (log.f64 (E.f64))) |
(*.f64 #s(literal 1 binary64) (PI.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))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64))))) |
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) |
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal 1/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.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) (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n))) |
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n))) |
(*.f64 (PI.f64) n) |
(*.f64 (PI.f64) (neg.f64 (-.f64 #s(literal 0 binary64) n))) |
(*.f64 n (PI.f64)) |
(*.f64 n (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64)))) |
(*.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) |
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n (cbrt.f64 (PI.f64))))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 n (sqrt.f64 (PI.f64))))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 n (cbrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 n (sqrt.f64 (PI.f64)))) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 n (sqrt.f64 (PI.f64))))) |
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) n)) |
(*.f64 (-.f64 #s(literal 0 binary64) n) (-.f64 #s(literal 0 binary64) (PI.f64))) |
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) |
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))) n) |
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) n)) (PI.f64)) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.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)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(*.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))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64))) |
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) |
(-.f64 #s(literal 0 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal -2 binary64)))) |
(neg.f64 (*.f64 n (*.f64 (PI.f64) #s(literal -2 binary64)))) |
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) |
(/.f64 (*.f64 n (*.f64 (PI.f64) #s(literal -2 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))) |
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) |
(*.f64 (PI.f64) (/.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64))) |
(*.f64 (PI.f64) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) n))) |
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) |
(*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1 binary64))) |
(*.f64 n (neg.f64 (*.f64 (PI.f64) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1 binary64)) |
(*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n))) |
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n #s(literal 1 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 (-.f64 #s(literal 0 binary64) n))) |
(*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal -2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 2 binary64) n))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))) n)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n)) |
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)) #s(literal -2 binary64)) |
(*.f64 (-.f64 #s(literal 0 binary64) n) (*.f64 (PI.f64) #s(literal -2 binary64))) |
(*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) n)) |
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) #s(literal 1 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 n (cbrt.f64 (PI.f64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 n (sqrt.f64 (PI.f64)))) |
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) |
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64)))) |
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n))) |
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) n)) (*.f64 #s(literal 2 binary64) (PI.f64))) |
(*.f64 (neg.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) n) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)) (PI.f64)) |
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) |
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
| 1× | egg-herbie |
| 5380× | *-lowering-*.f32 |
| 5380× | *-lowering-*.f64 |
| 2876× | +-lowering-+.f64 |
| 2876× | +-lowering-+.f32 |
| 1388× | fma-lowering-fma.f32 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 294 | 5071 |
| 1 | 935 | 4812 |
| 2 | 3307 | 4497 |
| 3 | 7571 | 4481 |
| 0 | 8038 | 4481 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (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) |
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(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(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)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 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 (* (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 (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 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 (* (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)))) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* n (PI)) |
(* 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))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k (*.f64 (*.f64 k k) n))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 1/2 binary64)))) 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) |
(/.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (+.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n))))))) 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) |
(/.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (+.f64 (*.f64 (/.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)))) (*.f64 (-.f64 #s(literal 0 binary64) k) (+.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (*.f64 #s(literal -1/24 binary64) (sqrt.f64 (*.f64 k (*.f64 k k))))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/8 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))))))))) k) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1 (* (+ 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)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 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)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
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(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 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)) (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k (*.f64 (*.f64 k k) n))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) 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 (+.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 k (*.f64 (*.f64 k k) n)))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))))) 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 (+.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 k (*.f64 (*.f64 k k) n)))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))))))))) 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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* -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 (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 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 (*.f64 k (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 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))) |
(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)))) (*.f64 k k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) |
(* 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)) |
(* 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))) |
Compiled 62216 to 5392 computations (91.3% saved)
29 alts after pruning (25 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2956 | 25 | 2981 |
| Fresh | 6 | 0 | 6 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 1 | 1 |
| Total | 2964 | 29 | 2993 |
| Status | Accuracy | Program |
|---|---|---|
| 36.1% | (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) | |
| 88.0% | (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) | |
| 74.1% | (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))) #s(literal -1/2 binary64)) | |
| 73.4% | (/.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) | |
| 98.9% | (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) | |
| ✓ | 99.5% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
| ✓ | 96.3% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))) |
| ✓ | 99.6% | (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
| 47.2% | (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) | |
| 35.3% | (/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) | |
| ▶ | 99.6% | (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
| 47.2% | (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) | |
| 36.0% | (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) | |
| 36.0% | (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64))) | |
| 47.2% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))) | |
| ▶ | 47.2% | (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
| 47.1% | (*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64))) | |
| 35.9% | (*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64))) | |
| 47.2% | (*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) | |
| ▶ | 47.1% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
| 47.2% | (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) | |
| 74.4% | (*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64)))) | |
| ✓ | 35.5% | (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
| ▶ | 35.5% | (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
| 47.2% | (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) | |
| 35.4% | (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) | |
| 47.2% | (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) | |
| ▶ | 35.6% | (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
| 33.4% | (exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64))) |
Compiled 757 to 594 computations (21.5% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) |
| ✓ | cost-diff | 128 | (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
| ✓ | cost-diff | 0 | (/.f64 k #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 k #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) |
| ✓ | cost-diff | 128 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
| ✓ | cost-diff | 0 | (/.f64 n k) |
| ✓ | cost-diff | 0 | (*.f64 (/.f64 n k) (PI.f64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 (PI.f64) n) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
| 148× | sum3-define |
| 130× | fma-define |
| 120× | *-lowering-*.f32 |
| 120× | *-lowering-*.f64 |
| 86× | /-lowering-/.f32 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 37 | 189 |
| 1 | 66 | 186 |
| 2 | 111 | 185 |
| 3 | 165 | 183 |
| 4 | 205 | 183 |
| 5 | 238 | 183 |
| 6 | 288 | 183 |
| 7 | 326 | 183 |
| 8 | 343 | 183 |
| 9 | 373 | 183 |
| 10 | 472 | 183 |
| 0 | 472 | 183 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))) |
(sqrt (/ 1 k)) |
(/ 1 k) |
1 |
k |
(pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))) |
(* n (* (PI) 2)) |
n |
(* (PI) 2) |
(PI) |
2 |
(+ -1/2 (* k 1/2)) |
-1/2 |
(* k 1/2) |
1/2 |
(sqrt (/ (/ (* (PI) n) 1/2) k)) |
(/ (/ (* (PI) n) 1/2) k) |
(/ (* (PI) n) 1/2) |
(* (PI) n) |
(PI) |
n |
1/2 |
k |
(* (sqrt (* (/ n k) (PI))) (sqrt 2)) |
(sqrt (* (/ n k) (PI))) |
(* (/ n k) (PI)) |
(/ n k) |
n |
k |
(PI) |
(sqrt 2) |
2 |
(* (/ 1 (sqrt (/ k 2))) (sqrt (* (PI) n))) |
(/ 1 (sqrt (/ k 2))) |
1 |
(sqrt (/ k 2)) |
(/ k 2) |
k |
2 |
(sqrt (* (PI) n)) |
(* (PI) n) |
(PI) |
n |
(/ -1 (* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k)))) |
-1 |
(* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k))) |
(sqrt (/ 1/2 (* (PI) n))) |
(/ 1/2 (* (PI) n)) |
1/2 |
(* (PI) n) |
(PI) |
n |
(- 0 (sqrt k)) |
0 |
(sqrt k) |
k |
| Outputs |
|---|
(/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
1 |
#s(literal 1 binary64) |
k |
(pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(* n (* (PI) 2)) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
n |
(* (PI) 2) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI) |
(PI.f64) |
2 |
#s(literal 2 binary64) |
(+ -1/2 (* k 1/2)) |
(+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))) |
-1/2 |
#s(literal -1/2 binary64) |
(* k 1/2) |
(*.f64 k #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(sqrt (/ (/ (* (PI) n) 1/2) k)) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) k)) |
(/ (/ (* (PI) n) 1/2) k) |
(/.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) k) |
(/ (* (PI) n) 1/2) |
(/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) |
(* (PI) n) |
(*.f64 n (PI.f64)) |
(PI) |
(PI.f64) |
n |
1/2 |
#s(literal 1/2 binary64) |
k |
(* (sqrt (* (/ n k) (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt (* (/ n k) (PI))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) |
(* (/ n k) (PI)) |
(*.f64 (PI.f64) (/.f64 n k)) |
(/ n k) |
(/.f64 n k) |
n |
k |
(PI) |
(PI.f64) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
2 |
#s(literal 2 binary64) |
(* (/ 1 (sqrt (/ k 2))) (sqrt (* (PI) n))) |
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) |
(/ 1 (sqrt (/ k 2))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) |
1 |
#s(literal 1 binary64) |
(sqrt (/ k 2)) |
(sqrt.f64 (/.f64 k #s(literal 2 binary64))) |
(/ k 2) |
(/.f64 k #s(literal 2 binary64)) |
k |
2 |
#s(literal 2 binary64) |
(sqrt (* (PI) n)) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(* (PI) n) |
(*.f64 n (PI.f64)) |
(PI) |
(PI.f64) |
n |
(/ -1 (* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))) |
-1 |
#s(literal -1 binary64) |
(* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) |
(sqrt (/ 1/2 (* (PI) n))) |
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) |
(/ 1/2 (* (PI) n)) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
1/2 |
#s(literal 1/2 binary64) |
(* (PI) n) |
(*.f64 n (PI.f64)) |
(PI) |
(PI.f64) |
n |
(- 0 (sqrt k)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 k)) |
0 |
#s(literal 0 binary64) |
(sqrt k) |
(sqrt.f64 k) |
k |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.7% | (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
| ✓ | accuracy | 99.7% | (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.8% | (*.f64 (PI.f64) n) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.6% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.7% | (*.f64 (/.f64 n k) (PI.f64)) |
| ✓ | accuracy | 99.5% | (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 88.1% | (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.8% | (*.f64 (PI.f64) n) |
| ✓ | accuracy | 99.7% | (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k) |
| ✓ | accuracy | 88.1% | (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.8% | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.8% | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
| ✓ | accuracy | 99.8% | (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| 547.0ms | 64× | 5 | exit |
| 174.0ms | 190× | 0 | valid |
| 1.0ms | 2× | 0 | invalid |
Compiled 202 to 38 computations (81.2% saved)
ival-sqrt: 58.0ms (40.2% of total)backward-pass: 32.0ms (22.2% of total)ival-div: 21.0ms (14.5% of total)ival-mult: 17.0ms (11.8% of total)ival-pow: 10.0ms (6.9% of total)ival-sub: 2.0ms (1.4% of total)ival-add: 2.0ms (1.4% of total)const: 1.0ms (0.7% of total)ival-pi: 1.0ms (0.7% of total)| Inputs |
|---|
#<alt (/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))))> |
#<alt (sqrt (/ 1 k))> |
#<alt (/ 1 k)> |
#<alt (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))> |
#<alt (sqrt (/ (/ (* (PI) n) 1/2) k))> |
#<alt (/ (/ (* (PI) n) 1/2) k)> |
#<alt (/ (* (PI) n) 1/2)> |
#<alt (* (PI) n)> |
#<alt (* (sqrt (* (/ n k) (PI))) (sqrt 2))> |
#<alt (sqrt (* (/ n k) (PI)))> |
#<alt (* (/ n k) (PI))> |
#<alt (/ n k)> |
#<alt (* (/ 1 (sqrt (/ k 2))) (sqrt (* (PI) n)))> |
#<alt (/ 1 (sqrt (/ k 2)))> |
#<alt (sqrt (/ k 2))> |
#<alt (/ k 2)> |
#<alt (/ -1 (* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k))))> |
#<alt (* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k)))> |
#<alt (sqrt (/ 1/2 (* (PI) n)))> |
#<alt (/ 1/2 (* (PI) n))> |
#<alt (PI)> |
#<alt (* n (* (PI) 2))> |
| Outputs |
|---|
#<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)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))> |
#<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 (/ 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 (* (+ (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 (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 (/ (* 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) (sqrt -1)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) 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 (* 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)) 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 k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (/ n k)> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt k) (sqrt 1/2))> |
#<alt (* (sqrt k) (sqrt 1/2))> |
#<alt (* (sqrt k) (sqrt 1/2))> |
#<alt (* (sqrt k) (sqrt 1/2))> |
#<alt (* (sqrt k) (sqrt 1/2))> |
#<alt (* (sqrt k) (sqrt 1/2))> |
#<alt (* (sqrt k) (sqrt 1/2))> |
#<alt (* (sqrt k) (sqrt 1/2))> |
#<alt (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* 1/2 k)> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* 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)))> |
96 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | k | @ | inf | (sqrt (/ (/ (* (PI) n) 1/2) k)) |
| 1.0ms | n | @ | -inf | (/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))) |
| 1.0ms | n | @ | -inf | (sqrt (/ (/ (* (PI) n) 1/2) k)) |
| 1.0ms | n | @ | inf | (/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))) |
| 1.0ms | n | @ | 0 | (/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))) |
| 1× | batch-egg-rewrite |
| 4656× | *-lowering-*.f32 |
| 4656× | *-lowering-*.f64 |
| 2640× | /-lowering-/.f32 |
| 2640× | /-lowering-/.f64 |
| 1376× | sum4-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 37 | 130 |
| 1 | 171 | 126 |
| 2 | 918 | 125 |
| 3 | 6906 | 125 |
| 0 | 8222 | 125 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2)))) |
(sqrt (/ 1 k)) |
(/ 1 k) |
(pow (* n (* (PI) 2)) (+ -1/2 (* k 1/2))) |
(sqrt (/ (/ (* (PI) n) 1/2) k)) |
(/ (/ (* (PI) n) 1/2) k) |
(/ (* (PI) n) 1/2) |
(* (PI) n) |
(* (sqrt (* (/ n k) (PI))) (sqrt 2)) |
(sqrt (* (/ n k) (PI))) |
(* (/ n k) (PI)) |
(/ n k) |
(* (/ 1 (sqrt (/ k 2))) (sqrt (* (PI) n))) |
(/ 1 (sqrt (/ k 2))) |
(sqrt (/ k 2)) |
(/ k 2) |
(/ -1 (* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k)))) |
(* (sqrt (/ 1/2 (* (PI) n))) (- 0 (sqrt k))) |
(sqrt (/ 1/2 (* (PI) n))) |
(/ 1/2 (* (PI) n)) |
(PI) |
(* n (* (PI) 2)) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal -1 binary64))) |
(exp.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) |
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))))) |
(exp.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 #s(literal 1/2 binary64) (log.f64 k)))) |
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) (/.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) |
(neg.f64 (/.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
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(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(exp.f64 (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) |
(neg.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) |
(neg.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(neg.f64 (/.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) |
(/.f64 #s(literal 1 binary64) (exp.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))) |
(/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) |
(/.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) n)) |
(/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) |
(/.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) n)) |
(/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) |
(/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) |
(/.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64)))) |
(/.f64 (-.f64 #s(literal 0 binary64) n) (/.f64 #s(literal -1/2 binary64) (PI.f64))) |
(/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64))) |
(/.f64 (exp.f64 (log.f64 (*.f64 n (PI.f64)))) (exp.f64 (log.f64 #s(literal 1/2 binary64)))) |
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) (*.f64 n (PI.f64))))) (exp.f64 (log.f64 #s(literal -1/2 binary64)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64)))) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(*.f64 n (/.f64 (PI.f64) #s(literal 1/2 binary64))) |
(*.f64 n (/.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 n (neg.f64 (*.f64 (PI.f64) #s(literal -2 binary64)))) |
(*.f64 n (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -2 binary64))) |
(*.f64 (PI.f64) (/.f64 n #s(literal 1/2 binary64))) |
(*.f64 (PI.f64) (exp.f64 (log.f64 (/.f64 n #s(literal 1/2 binary64))))) |
(*.f64 (PI.f64) (*.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (PI.f64) (/.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) |
(*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) n) |
(*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) n) #s(literal -1 binary64))) |
(*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n #s(literal 1 binary64))) |
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) |
(*.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 n #s(literal 1/2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))) n)) |
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))) |
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1 binary64))) |
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 n (PI.f64))) #s(literal -2 binary64)) |
(*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 n (PI.f64)))) |
(*.f64 #s(literal -2 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))) #s(literal -1 binary64))) |
(*.f64 #s(literal -2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 n (PI.f64))) #s(literal 1 binary64))) |
(*.f64 (-.f64 #s(literal 0 binary64) n) (*.f64 (PI.f64) #s(literal -2 binary64))) |
(*.f64 (-.f64 #s(literal 0 binary64) n) (/.f64 (PI.f64) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 n #s(literal 1/2 binary64)) (PI.f64)) |
(*.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 (PI.f64) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) |
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 n #s(literal -1/2 binary64))) |
(*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) n)) |
(*.f64 (/.f64 n #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 n (cbrt.f64 (PI.f64)))) |
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64)))) |
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) |
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) |
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 n (sqrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))) #s(literal -1 binary64)) #s(literal -2 binary64)) |
(*.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) #s(literal -1 binary64)) #s(literal 2 binary64)) |
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(*.f64 (exp.f64 (log.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (exp.f64 (log.f64 n))) |
(*.f64 (exp.f64 (log.f64 (*.f64 n (PI.f64)))) (exp.f64 (log.f64 #s(literal 2 binary64)))) |
(*.f64 (*.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1 binary64)) (PI.f64)) |
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))) (/.f64 n #s(literal 1/2 binary64))) |
(*.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 (PI.f64) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (/.f64 (PI.f64) #s(literal 1/2 binary64))) |
(*.f64 (neg.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) n) |
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 #s(literal -2 binary64) n) (-.f64 #s(literal 0 binary64) (PI.f64))) |
(*.f64 (*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) n)) (PI.f64)) |
(*.f64 (*.f64 (/.f64 n #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (PI.f64))) (-.f64 #s(literal 0 binary64) n)) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 n #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) |
(*.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64))) |
(*.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64))) |
| 1× | egg-herbie |
| 3362× | *-lowering-*.f32 |
| 3362× | *-lowering-*.f64 |
| 1960× | fnmadd-define |
| 1820× | fma-lowering-fma.f32 |
| 1820× | fma-lowering-fma.f64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 177 | 3303 |
| 1 | 537 | 3196 |
| 2 | 1842 | 3106 |
| 3 | 5374 | 3094 |
| 0 | 8080 | 3094 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (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)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(* (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 (/ 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 (* (+ (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 (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 (/ (* 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 -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) 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))) |
(* 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)) 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 k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(/ n k) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))) |
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ 1 k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ 1 k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt k) (sqrt 1/2)) |
(* (sqrt k) (sqrt 1/2)) |
(* (sqrt k) (sqrt 1/2)) |
(* (sqrt k) (sqrt 1/2)) |
(* (sqrt k) (sqrt 1/2)) |
(* (sqrt k) (sqrt 1/2)) |
(* (sqrt k) (sqrt 1/2)) |
(* (sqrt k) (sqrt 1/2)) |
(* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt k) (* (sqrt -1) (sqrt -1/2)))) |
(* 1/2 k) |
(* 1/2 k) |
(* 1/2 k) |
(* 1/2 k) |
(* 1/2 k) |
(* 1/2 k) |
(* 1/2 k) |
(* 1/2 k) |
(* 1/2 k) |
(* 1/2 k) |
(* 1/2 k) |
(* 1/2 k) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* 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))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))) 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) |
(/.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (+.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))))))) 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) |
(/.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (-.f64 (*.f64 (/.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) (*.f64 k (+.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) #s(literal -1/24 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/8 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))))))))) k) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))) |
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(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #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))))) |
(* (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))))) |
(* (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))))) |
(* (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))))) |
(* (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))))) |
(* (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))))) |
(* (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))))) |
(* (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))))) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64)))) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64)))) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64)))) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64)))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(* 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))) |
Compiled 31960 to 4489 computations (86% saved)
51 alts after pruning (45 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2184 | 31 | 2215 |
| Fresh | 6 | 14 | 20 |
| Picked | 1 | 4 | 5 |
| Done | 2 | 2 | 4 |
| Total | 2193 | 51 | 2244 |
| Status | Accuracy | Program |
|---|---|---|
| 36.0% | (pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) | |
| 74.1% | (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))) #s(literal -1/2 binary64)) | |
| 73.4% | (/.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) | |
| 35.3% | (/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) | |
| ▶ | 35.8% | (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) |
| 99.5% | (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) | |
| 47.3% | (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) | |
| 98.9% | (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) | |
| ✓ | 96.3% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))) |
| 47.2% | (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) | |
| 47.2% | (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) | |
| ▶ | 35.3% | (/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
| ▶ | 99.6% | (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
| 47.2% | (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) | |
| 36.0% | (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) | |
| ▶ | 36.0% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
| 35.5% | (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) | |
| 35.9% | (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) | |
| ✓ | 47.2% | (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
| 99.6% | (*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) | |
| 47.2% | (*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) | |
| 47.2% | (*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) | |
| 47.1% | (*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64))) | |
| 47.2% | (*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) | |
| 47.2% | (*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) | |
| 47.1% | (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) | |
| ✓ | 47.1% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
| 47.1% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n))) | |
| 47.2% | (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) | |
| 74.4% | (*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64)))) | |
| ✓ | 35.5% | (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
| 35.4% | (*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))) | |
| 47.2% | (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) | |
| ✓ | 35.5% | (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
| 35.4% | (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) | |
| 47.2% | (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))))) | |
| 47.2% | (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) | |
| 35.6% | (sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) | |
| 35.5% | (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) | |
| 35.6% | (sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) | |
| 35.6% | (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k)) | |
| 35.5% | (sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) | |
| 35.6% | (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) | |
| 35.6% | (sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k))) | |
| 35.5% | (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) | |
| 35.6% | (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n)) | |
| 35.6% | (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) | |
| ▶ | 35.6% | (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
| 35.6% | (sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))) | |
| 33.4% | (exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64))) |
Compiled 1275 to 1001 computations (21.5% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (PI.f64) |
| ✓ | cost-diff | 0 | (/.f64 (PI.f64) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 64 | (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #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 1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) |
| ✓ | cost-diff | 0 | (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
| ✓ | cost-diff | 0 | (*.f64 n (PI.f64)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 2 binary64) k) |
| ✓ | cost-diff | 0 | (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
| ✓ | cost-diff | 0 | (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -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 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
| 116× | *-lowering-*.f32 |
| 116× | *-lowering-*.f64 |
| 74× | /-lowering-/.f32 |
| 74× | /-lowering-/.f64 |
| 46× | *-commutative |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 170 |
| 1 | 53 | 170 |
| 2 | 81 | 170 |
| 3 | 113 | 170 |
| 4 | 132 | 170 |
| 5 | 142 | 170 |
| 6 | 142 | 170 |
| 0 | 142 | 170 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))) |
(sqrt (/ 1 k)) |
(/ 1 k) |
1 |
k |
(pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))) |
(/ 1/2 (* n (PI))) |
1/2 |
(* n (PI)) |
n |
(PI) |
(+ 1/2 (/ k -2)) |
(/ k -2) |
-2 |
(sqrt (* (/ 2 k) (* n (PI)))) |
(* (/ 2 k) (* n (PI))) |
(/ 2 k) |
2 |
k |
(* n (PI)) |
n |
(PI) |
(/ 1 (sqrt (/ k (/ n (/ 1/2 (PI)))))) |
1 |
(sqrt (/ k (/ n (/ 1/2 (PI))))) |
(/ k (/ n (/ 1/2 (PI)))) |
k |
(/ n (/ 1/2 (PI))) |
n |
(/ 1/2 (PI)) |
1/2 |
(PI) |
(/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2)) |
(sqrt (/ (* n (PI)) k)) |
(/ (* n (PI)) k) |
(* n (PI)) |
n |
(PI) |
k |
(sqrt 1/2) |
1/2 |
(/ (pow (/ (PI) 1/2) 1/2) (pow (/ k n) 1/2)) |
(pow (/ (PI) 1/2) 1/2) |
(/ (PI) 1/2) |
(PI) |
1/2 |
(pow (/ k n) 1/2) |
(/ k n) |
k |
n |
| Outputs |
|---|
(/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/ 1 k) |
(/.f64 #s(literal 1 binary64) k) |
1 |
#s(literal 1 binary64) |
k |
(pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))) |
(pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
1/2 |
#s(literal 1/2 binary64) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
n |
(PI) |
(PI.f64) |
(+ 1/2 (/ k -2)) |
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) |
(/ k -2) |
(/.f64 k #s(literal -2 binary64)) |
-2 |
#s(literal -2 binary64) |
(sqrt (* (/ 2 k) (* n (PI)))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))) |
(* (/ 2 k) (* n (PI))) |
(*.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k)) |
(/ 2 k) |
(/.f64 #s(literal 2 binary64) k) |
2 |
#s(literal 2 binary64) |
k |
(* n (PI)) |
(*.f64 n (PI.f64)) |
n |
(PI) |
(PI.f64) |
(/ 1 (sqrt (/ k (/ n (/ 1/2 (PI)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))))) |
1 |
#s(literal 1 binary64) |
(sqrt (/ k (/ n (/ 1/2 (PI))))) |
(sqrt.f64 (/.f64 k (/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))) |
(/ k (/ n (/ 1/2 (PI)))) |
(/.f64 k (/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64))) |
k |
(/ n (/ 1/2 (PI))) |
(/.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) |
n |
(/ 1/2 (PI)) |
(/.f64 #s(literal 1/2 binary64) (PI.f64)) |
1/2 |
#s(literal 1/2 binary64) |
(PI) |
(PI.f64) |
(/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2)) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(sqrt (/ (* n (PI)) k)) |
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
(/ (* n (PI)) k) |
(/.f64 (*.f64 n (PI.f64)) k) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
n |
(PI) |
(PI.f64) |
k |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(/ (pow (/ (PI) 1/2) 1/2) (pow (/ k n) 1/2)) |
(/.f64 (sqrt.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64))) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) |
(pow (/ (PI) 1/2) 1/2) |
(sqrt.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64))) |
(/ (PI) 1/2) |
(/.f64 (PI.f64) #s(literal 1/2 binary64)) |
(PI) |
(PI.f64) |
1/2 |
#s(literal 1/2 binary64) |
(pow (/ k n) 1/2) |
(pow.f64 (/.f64 k n) #s(literal 1/2 binary64)) |
(/ k n) |
(/.f64 k n) |
k |
n |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.4% | (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 98.8% | (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 88.6% | (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.7% | (/.f64 (*.f64 n (PI.f64)) k) |
| ✓ | accuracy | 99.4% | (/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
| ✓ | accuracy | 88.1% | (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
| ✓ | accuracy | 99.6% | (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) |
| ✓ | accuracy | 88.6% | (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.8% | (*.f64 n (PI.f64)) |
| ✓ | accuracy | 99.6% | (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))) |
| ✓ | accuracy | 88.1% | (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| ✓ | accuracy | 99.8% | (*.f64 n (PI.f64)) |
| ✓ | accuracy | 99.8% | (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
| ✓ | accuracy | 75.0% | (PI.f64) |
| 231.0ms | 64× | 5 | exit |
| 111.0ms | 190× | 0 | valid |
| 1.0ms | 2× | 0 | invalid |
Compiled 182 to 33 computations (81.9% saved)
ival-div: 35.0ms (34% of total)backward-pass: 25.0ms (24.3% of total)ival-pow: 22.0ms (21.4% of total)ival-sqrt: 11.0ms (10.7% of total)ival-mult: 4.0ms (3.9% of total)ival-add: 2.0ms (1.9% of total)const: 1.0ms (1% of total)ival-pi: 1.0ms (1% of total)| Inputs |
|---|
#<alt (/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))))> |
#<alt (sqrt (/ 1 k))> |
#<alt (/ 1 k)> |
#<alt (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))> |
#<alt (sqrt (* (/ 2 k) (* n (PI))))> |
#<alt (* (/ 2 k) (* n (PI)))> |
#<alt (/ 2 k)> |
#<alt (* n (PI))> |
#<alt (/ 1 (sqrt (/ k (/ n (/ 1/2 (PI))))))> |
#<alt (sqrt (/ k (/ n (/ 1/2 (PI)))))> |
#<alt (/ k (/ n (/ 1/2 (PI))))> |
#<alt (/ n (/ 1/2 (PI)))> |
#<alt (/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2))> |
#<alt (sqrt (/ (* n (PI)) k))> |
#<alt (/ (* n (PI)) k)> |
#<alt (pow (/ (PI) 1/2) 1/2)> |
#<alt (/ (pow (/ (PI) 1/2) 1/2) (pow (/ k n) 1/2))> |
#<alt (/ (PI) 1/2)> |
#<alt (PI)> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (pow (/ k n) 1/2)> |
| Outputs |
|---|
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (/ (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (/ 1/2 (* 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 (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)> |
#<alt (/ (+ (* k (+ (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/48 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/2 (* (log (/ 1/2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))))> |
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))> |
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))> |
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))> |
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))))> |
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (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 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n)))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))> |
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))> |
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))> |
#<alt (+ (* -1/2 (* (* k (* (log (/ 1/2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))> |
#<alt (+ (* k (+ (* -1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* 1/8 (* (* k (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))> |
#<alt (+ (* k (+ (* -1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))> |
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k))))> |
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k))))> |
#<alt (exp (* (log (/ 1/2 (* 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 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (* (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 (* -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 (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (* 2 (/ (* n (PI)) k))> |
#<alt (/ 2 k)> |
#<alt (/ 2 k)> |
#<alt (/ 2 k)> |
#<alt (/ 2 k)> |
#<alt (/ 2 k)> |
#<alt (/ 2 k)> |
#<alt (/ 2 k)> |
#<alt (/ 2 k)> |
#<alt (/ 2 k)> |
#<alt (/ 2 k)> |
#<alt (/ 2 k)> |
#<alt (/ 2 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)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* n (PI))))> |
#<alt (* 1/2 (/ k (* 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 (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))> |
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))> |
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (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 (* -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 (* (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 (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (/ 1/2 (* n (PI)))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (sqrt (/ k n))> |
#<alt (* (sqrt (/ k n)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ k n)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ k n)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ k n)) (pow (sqrt -1) 2))> |
90 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 42.0ms | n | @ | 0 | (/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))) |
| 17.0ms | n | @ | -inf | (/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))) |
| 7.0ms | n | @ | inf | (/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))) |
| 3.0ms | k | @ | -inf | (/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))) |
| 2.0ms | k | @ | 0 | (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))) |
| 1× | batch-egg-rewrite |
| 4518× | *-lowering-*.f32 |
| 4518× | *-lowering-*.f64 |
| 3152× | /-lowering-/.f32 |
| 3152× | /-lowering-/.f64 |
| 972× | sum5-define |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 124 |
| 1 | 183 | 120 |
| 2 | 1057 | 120 |
| 3 | 7701 | 120 |
| 0 | 8207 | 120 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (sqrt (/ 1 k)) (pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2)))) |
(sqrt (/ 1 k)) |
(/ 1 k) |
(pow (/ 1/2 (* n (PI))) (+ 1/2 (/ k -2))) |
(sqrt (* (/ 2 k) (* n (PI)))) |
(* (/ 2 k) (* n (PI))) |
(/ 2 k) |
(* n (PI)) |
(/ 1 (sqrt (/ k (/ n (/ 1/2 (PI)))))) |
(sqrt (/ k (/ n (/ 1/2 (PI))))) |
(/ k (/ n (/ 1/2 (PI)))) |
(/ n (/ 1/2 (PI))) |
(/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2)) |
(sqrt (/ (* n (PI)) k)) |
(/ (* n (PI)) k) |
(pow (/ (PI) 1/2) 1/2) |
(/ (pow (/ (PI) 1/2) 1/2) (pow (/ k n) 1/2)) |
(/ (PI) 1/2) |
(PI) |
(/ 1/2 (* n (PI))) |
(pow (/ k n) 1/2) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal -1 binary64))) |
(exp.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))))) |
(exp.f64 (+.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))))) |
(exp.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))) |
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) |
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) |
(/.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))) |
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) |
(/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal -1/2 binary64) (PI.f64)))) (*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) |
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(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))))) |
(exp.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (PI.f64) (/.f64 k n)))) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))))) |
(exp.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) |
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(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))) |
(/.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 n)) (*.f64 (sqrt.f64 k) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) n) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 k) (pow.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 n)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) n) #s(literal 1/2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) #s(literal 1/2 binary64)))) |
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(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
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(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal 1 binary64) n)) (cbrt.f64 (PI.f64))) |
(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) n)) (sqrt.f64 (PI.f64))) |
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) |
(/.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))) |
(/.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64)))) |
(/.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) n) (sqrt.f64 (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))) |
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64))) |
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) |
(/.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64))) |
(/.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(/.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) |
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) n)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 (/.f64 #s(literal 1 binary64) n) #s(literal 1 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) n)) |
(*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) n)) |
(*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) n))) |
(*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) n) #s(literal 1 binary64))) |
(*.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 #s(literal 1/2 binary64) (PI.f64))) |
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) #s(literal 1/2 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) n) (/.f64 #s(literal 1 binary64) (PI.f64))) |
(*.f64 (/.f64 #s(literal -1/2 binary64) n) (/.f64 #s(literal -1 binary64) (PI.f64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) (/.f64 #s(literal -1/2 binary64) n)) |
(*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) (/.f64 (/.f64 #s(literal 1 binary64) n) #s(literal -2 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) n) (/.f64 #s(literal -1/2 binary64) (PI.f64))) |
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) n) (cbrt.f64 (PI.f64)))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) n) (sqrt.f64 (PI.f64)))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (/.f64 #s(literal 1 binary64) (cbrt.f64 (PI.f64)))) |
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (*.f64 n (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 n #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (PI.f64))) |
(*.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) (exp.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (cbrt.f64 (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) |
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (PI.f64))) |
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) n) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (PI.f64))) |
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 #s(literal -1 binary64) (PI.f64))) #s(literal -1/2 binary64)) |
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) n) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) (PI.f64))) |
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (PI.f64))) |
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (PI.f64))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k n)))) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))) |
(sqrt.f64 (/.f64 k n)) |
(neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(/.f64 (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))) |
(/.f64 (sqrt.f64 k) (sqrt.f64 n)) |
(/.f64 (sqrt.f64 k) (*.f64 #s(literal 1 binary64) (sqrt.f64 n))) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(/.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) n) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) n) #s(literal 1/2 binary64)))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) (/.f64 n k)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (neg.f64 (sqrt.f64 n))) |
(/.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (-.f64 #s(literal 0 binary64) n) #s(literal 1/2 binary64)))) |
(pow.f64 (/.f64 k n) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 n k) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 k n))) |
(*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))) |
(*.f64 (sqrt.f64 k) (pow.f64 n #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 k) (/.f64 (pow.f64 n #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 n #s(literal -1/2 binary64)) (sqrt.f64 k)) |
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) n))) |
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) n) #s(literal 1/2 binary64)))) |
| 1× | egg-herbie |
| 3708× | *-lowering-*.f32 |
| 3708× | *-lowering-*.f64 |
| 1900× | fma-lowering-fma.f32 |
| 1900× | fma-lowering-fma.f64 |
| 1518× | sum3-define |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 169 | 3229 |
| 1 | 506 | 3049 |
| 2 | 1779 | 3022 |
| 3 | 5476 | 2950 |
| 0 | 8097 | 2950 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/ (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (/ 1/2 (* 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 (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/ (+ (* k (+ (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/48 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/2 (* (log (/ 1/2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (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) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(+ (* -1/2 (* (* k (* (log (/ 1/2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* -1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* 1/8 (* (* k (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* -1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(exp (* (log (/ 1/2 (* 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)) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (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)) |
(* -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)))) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(* 2 (/ (* n (PI)) k)) |
(/ 2 k) |
(/ 2 k) |
(/ 2 k) |
(/ 2 k) |
(/ 2 k) |
(/ 2 k) |
(/ 2 k) |
(/ 2 k) |
(/ 2 k) |
(/ 2 k) |
(/ 2 k) |
(/ 2 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)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt -1) (sqrt -1/2)))) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(* -1 (* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) |
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* (sqrt (/ k (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* n (PI)))) |
(* 1/2 (/ k (* 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))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))) |
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (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)) |
(* -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) |
(* (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))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(/ 1/2 (* n (PI))) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2))) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(sqrt (/ k n)) |
(* (sqrt (/ k n)) (pow (sqrt -1) 2)) |
(* (sqrt (/ k n)) (pow (sqrt -1) 2)) |
(* (sqrt (/ k n)) (pow (sqrt -1) 2)) |
(* (sqrt (/ k n)) (pow (sqrt -1) 2)) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(/ (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64)))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (+.f64 (/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (pow.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64))))))) k) |
(/ (+ (* k (+ (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (log (/ 1/2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/48 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/2 (* (log (/ 1/2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 1/2))))))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (+.f64 (/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 k (-.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k k))) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (pow.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/8 binary64)))) (*.f64 (/.f64 (pow.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/24 binary64)))))))))) k) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (/ 1/2 (* n (PI)))) (- 1/2 (* 1/2 k)))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* (log (/ 1/2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (/.f64 #s(literal -1 binary64) n) (/.f64 #s(literal -1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (/.f64 #s(literal -1 binary64) n) (/.f64 #s(literal -1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (/.f64 #s(literal -1 binary64) n) (/.f64 #s(literal -1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (/.f64 #s(literal -1 binary64) n) (/.f64 #s(literal -1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 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)) (pow (sqrt -1) 2)) |
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(*.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))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))) |
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))) |
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))) |
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))) |
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(/ 1/2 (* n (PI))) |
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 k n)) |
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 k n)) |
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 k n)) |
(* -1 (* (sqrt (/ k n)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(sqrt (/ k n)) |
(sqrt.f64 (/.f64 k n)) |
(* (sqrt (/ k n)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k n))) |
(* (sqrt (/ k n)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k n))) |
(* (sqrt (/ k n)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k n))) |
(* (sqrt (/ k n)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k n))) |
Compiled 35827 to 5375 computations (85% saved)
64 alts after pruning (56 fresh and 8 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2460 | 28 | 2488 |
| Fresh | 12 | 28 | 40 |
| Picked | 2 | 3 | 5 |
| Done | 1 | 5 | 6 |
| Total | 2475 | 64 | 2539 |
| Status | Accuracy | Program |
|---|---|---|
| 36.0% | (pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) | |
| 74.1% | (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))) #s(literal -1/2 binary64)) | |
| 72.9% | (/.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))) | |
| 35.3% | (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64))) | |
| 35.9% | (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)))) | |
| 35.8% | (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n))) | |
| 99.5% | (/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) | |
| 47.3% | (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) | |
| 98.9% | (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) | |
| ✓ | 96.3% | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))) |
| 47.2% | (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) | |
| 99.6% | (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) | |
| 47.2% | (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) | |
| 35.3% | (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) | |
| ✓ | 35.3% | (/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
| 35.3% | (/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64))) | |
| 35.3% | (/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) | |
| ✓ | 99.6% | (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
| 35.4% | (/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) | |
| 47.2% | (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) | |
| 47.3% | (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64))))) | |
| 36.0% | (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) | |
| 47.1% | (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) | |
| 47.2% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n))) | |
| 35.5% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) | |
| 47.2% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) | |
| 35.9% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) | |
| 35.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k)))) | |
| 36.0% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))) | |
| ✓ | 36.0% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
| 36.0% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) | |
| 36.0% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) | |
| 33.9% | (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))))) | |
| 99.6% | (*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) | |
| 47.2% | (*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) | |
| 47.2% | (*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) | |
| 47.2% | (*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) | |
| 47.2% | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) | |
| 47.1% | (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) | |
| ✓ | 47.1% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
| 47.1% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n))) | |
| 47.2% | (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) | |
| 74.4% | (*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64)))) | |
| ✓ | 35.5% | (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
| 47.2% | (*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n)) | |
| 35.4% | (*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))) | |
| 47.2% | (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) | |
| ✓ | 35.5% | (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
| 35.4% | (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) | |
| 47.2% | (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) | |
| 35.5% | (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) | |
| 35.6% | (sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) | |
| 35.6% | (sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) | |
| 35.6% | (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k)) | |
| 35.5% | (sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) | |
| 35.6% | (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) | |
| 35.6% | (sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k))) | |
| 35.5% | (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) | |
| 35.6% | (sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) | |
| 35.6% | (sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k))) | |
| ✓ | 35.6% | (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
| 35.5% | (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) | |
| 33.4% | (exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64))) | |
| 33.9% | (exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64))) |
Compiled 1994 to 977 computations (51% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) |
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) |
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n)) |
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k))) |
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) |
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) |
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(/.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 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n))) |
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64))) #s(literal -1/2 binary64)) |
(*.f64 (sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64)))) |
(/.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 k #s(literal 2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))) |
(/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))) |
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
| Outputs |
|---|
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
4 calls:
| 31.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 27.0ms | n |
| 27.0ms | k |
| 24.0ms | (*.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 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) |
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) |
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n)) |
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k))) |
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) |
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) |
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(/.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 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n))) |
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 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 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
4 calls:
| 26.0ms | n |
| 26.0ms | k |
| 23.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 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)))) |
| 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 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) |
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) |
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n)) |
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k))) |
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) |
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) |
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(/.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 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n))) |
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
| Outputs |
|---|
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
2 calls:
| 23.0ms | k |
| 20.0ms | n |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | k |
| 99.6% | 1 | n |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) |
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) |
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n)) |
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k))) |
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) |
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) |
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(/.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 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n))) |
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)) |
| Outputs |
|---|
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
2 calls:
| 22.0ms | n |
| 20.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | k |
| 99.5% | 1 | n |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) |
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) |
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n)) |
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k))) |
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) |
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) |
(*.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))))) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) n) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(/.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 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 n))) |
(/.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))) |
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))))) |
(/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)))) |
| Outputs |
|---|
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64))))) |
2 calls:
| 21.0ms | n |
| 20.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 47.3% | 1 | n |
| 47.3% | 1 | k |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) |
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) |
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n)) |
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k))) |
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))))) |
2 calls:
| 11.0ms | n |
| 11.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 47.2% | 1 | k |
| 47.2% | 1 | n |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) |
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) |
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n)) |
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k))) |
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) |
2 calls:
| 8.0ms | n |
| 8.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 47.2% | 1 | n |
| 47.2% | 1 | k |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) |
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) |
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) n)) |
(sqrt.f64 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 n (PI.f64))) k))) |
(sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) n)) (PI.f64)) k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 n k)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) (/.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) n) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))) |
| Outputs |
|---|
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
2 calls:
| 8.0ms | n |
| 8.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 36.1% | 1 | n |
| 36.1% | 1 | k |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) |
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) |
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
| Outputs |
|---|
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
2 calls:
| 5.0ms | n |
| 4.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 36.0% | 1 | k |
| 36.0% | 1 | n |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) n)) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) |
(sqrt.f64 (/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))) |
(sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64))) k)) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) |
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k)) |
| Outputs |
|---|
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
2 calls:
| 4.0ms | n |
| 4.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 35.6% | 1 | k |
| 35.6% | 1 | n |
Compiled 6 to 4 computations (33.3% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
| Outputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
2 calls:
| 4.0ms | k |
| 1.0ms | n |
| Accuracy | Segments | Branch |
|---|---|---|
| 35.5% | 1 | k |
| 35.5% | 1 | n |
Compiled 6 to 4 computations (33.3% saved)
| 1× | egg-herbie |
| 32× | *-commutative_binary64 |
| 18× | +-commutative_binary64 |
| 14× | sub-neg_binary64 |
| 10× | neg-sub0_binary64 |
| 10× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 121 |
| 1 | 79 | 121 |
| 2 | 93 | 121 |
| 3 | 103 | 121 |
| 4 | 111 | 121 |
| 5 | 114 | 121 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) |
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
| Outputs |
|---|
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (/.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) |
(pow.f64 (/.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) (PI.f64)) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 (/.f64 k (*.f64 n #s(literal 2 binary64))) (PI.f64)) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 k (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))) |
| 5380× | *-lowering-*.f32 |
| 5380× | *-lowering-*.f64 |
| 5256× | *-lowering-*.f32 |
| 5256× | *-lowering-*.f64 |
| 5090× | *-lowering-*.f32 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 124 |
| 1 | 183 | 120 |
| 2 | 1057 | 120 |
| 3 | 7701 | 120 |
| 0 | 8207 | 120 |
| 0 | 20 | 68 |
| 1 | 100 | 68 |
| 2 | 478 | 64 |
| 3 | 3275 | 64 |
| 0 | 8262 | 64 |
| 0 | 40 | 165 |
| 1 | 190 | 156 |
| 2 | 953 | 149 |
| 3 | 7300 | 149 |
| 0 | 8311 | 149 |
| 0 | 13 | 14 |
| 1 | 30 | 14 |
| 2 | 47 | 14 |
| 3 | 69 | 14 |
| 4 | 90 | 13 |
| 5 | 113 | 13 |
| 6 | 149 | 13 |
| 7 | 188 | 13 |
| 8 | 214 | 13 |
| 9 | 228 | 13 |
| 10 | 229 | 13 |
| 0 | 229 | 13 |
| 0 | 37 | 130 |
| 1 | 171 | 126 |
| 2 | 918 | 125 |
| 3 | 6906 | 125 |
| 0 | 8222 | 125 |
| 0 | 139 | 2132 |
| 1 | 385 | 2094 |
| 2 | 1192 | 1806 |
| 3 | 4169 | 1722 |
| 4 | 7733 | 1722 |
| 0 | 8104 | 1722 |
| 0 | 294 | 5071 |
| 1 | 935 | 4812 |
| 2 | 3307 | 4497 |
| 3 | 7571 | 4481 |
| 0 | 8038 | 4481 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 385 to 271 computations (29.6% saved)
Compiled 282 to 142 computations (49.6% saved)
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