Migdal et al, Equation (51)
Time bar (total: 9.5s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50% | 0.1% | 0% | 50% | 0% | 2 |
| 50% | 25% | 25% | 0.1% | 0% | 50% | 0% | 3 |
| 50% | 25% | 25% | 0.1% | 0% | 50% | 0% | 4 |
| 50% | 25% | 25% | 0.1% | 0% | 50% | 0% | 5 |
| 50% | 25% | 25% | 0.1% | 0% | 50% | 0% | 6 |
| 51.6% | 25% | 23.4% | 0.1% | 0% | 51.5% | 0% | 7 |
| 52.5% | 25% | 22.6% | 0.1% | 0% | 52.3% | 0% | 8 |
| 53.8% | 25% | 21.5% | 0.1% | 0% | 53.5% | 0% | 9 |
| 54.5% | 25% | 20.9% | 0.1% | 0% | 54% | 0% | 10 |
| 55.3% | 25% | 20.2% | 0.1% | 0% | 54.7% | 0% | 11 |
| 55.7% | 25% | 19.9% | 0.1% | 0% | 55.1% | 0% | 12 |
Compiled 18 to 15 computations (16.7% saved)
| 1.2s | 8 256× | 0 | valid |
| 765.0ms | 3 494× | 1 | invalid |
| 365.0ms | 1 819× | 1 | exit |
| 132.0ms | 460× | 2 | invalid |
| 42.0ms | 497× | 0 | invalid |
| 27.0ms | 214× | 0 | exit |
ival-pow: 481.0ms (28% of total)ival-mult: 382.0ms (22.2% of total)ival-div: 253.0ms (14.7% of total)ival-sqrt: 235.0ms (13.7% of total)adjust: 135.0ms (7.9% of total)ival-sub: 110.0ms (6.4% of total)ival-pi: 85.0ms (4.9% of total)exact: 17.0ms (1% of total)ival-true: 13.0ms (0.8% of total)ival-assert: 6.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 9 | 89 | (8.321393231967652e-75 6.431970745949856e-273) | 2 | (1.0532386239520935e-8 1.0515116078801296e+56) | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
| 0 | 0 | - | 0 | - | k |
| 0 | 0 | - | 0 | - | n |
| 0 | 0 | - | 0 | - | (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 0 | 0 | - | 0 | - | (sqrt.f64 k) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| 0 | 0 | - | 0 | - | (-.f64 #s(literal 1 binary64) k) |
| 0 | 0 | - | 0 | - | (*.f64 #s(literal 2 binary64) (PI.f64)) |
| 0 | 0 | - | 0 | - | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 0 | 0 | - | 0 | - | (PI.f64) |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
pow.f64 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | sensitivity | 95 | 27 |
pow.f64 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | oflow-rescue | 1 | 0 |
| ↳ | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) | overflow | 1 | |
| ↳ | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | overflow | 65 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 7 | 2 |
| - | 89 | 158 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 7 | 2 | 0 |
| - | 89 | 25 | 133 |
| number | freq |
|---|---|
| 0 | 160 |
| 1 | 96 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 107.0ms | 512× | 0 | valid |
Compiled 182 to 56 computations (69.2% saved)
ival-sub: 52.0ms (61% of total)ival-pow: 11.0ms (12.9% of total)ival-mult: 9.0ms (10.6% of total)ival-div: 7.0ms (8.2% of total)ival-sqrt: 4.0ms (4.7% of total)ival-pi: 2.0ms (2.3% of total)ival-true: 1.0ms (1.2% of total)exact: 1.0ms (1.2% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 88 |
| 1 | 82 | 74 |
| 2 | 193 | 74 |
| 3 | 383 | 74 |
| 4 | 630 | 74 |
| 5 | 922 | 74 |
| 6 | 1089 | 74 |
| 7 | 1346 | 74 |
| 8 | 1405 | 74 |
| 9 | 1431 | 74 |
| 10 | 1449 | 74 |
| 11 | 1455 | 74 |
| 12 | 1455 | 74 |
| 0 | 13 | 16 |
| 0 | 22 | 16 |
| 1 | 37 | 14 |
| 2 | 54 | 14 |
| 3 | 75 | 14 |
| 4 | 93 | 14 |
| 5 | 108 | 14 |
| 6 | 129 | 14 |
| 7 | 156 | 14 |
| 8 | 165 | 14 |
| 9 | 168 | 14 |
| 0 | 168 | 13 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
Compiled 16 to 13 computations (18.8% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.0% | (*.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)))) |
Compiled 16 to 13 computations (18.8% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 1 | (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 54 |
| 0 | 22 | 54 |
| 1 | 37 | 52 |
| 2 | 54 | 52 |
| 3 | 75 | 52 |
| 4 | 93 | 52 |
| 5 | 108 | 52 |
| 6 | 129 | 52 |
| 7 | 156 | 52 |
| 8 | 165 | 52 |
| 9 | 168 | 52 |
| 0 | 168 | 49 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.2109375 | (*.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 | 0.26171875 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) | |
| accuracy | 0.2890625 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| accuracy | 0.4769578398336982 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
| 110.0ms | 256× | 0 | valid |
Compiled 110 to 28 computations (74.5% saved)
ival-pow: 87.0ms (86.5% of total)ival-mult: 4.0ms (4% of total)ival-div: 3.0ms (3% of total)ival-sqrt: 3.0ms (3% of total)ival-pi: 1.0ms (1% of total)ival-sub: 1.0ms (1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (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 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(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 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| Outputs |
|---|
(* (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) |
1/2 |
(+ 1/2 (* -1/2 k)) |
(sqrt (/ 1 k)) |
(sqrt 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))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* -1/2 k) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 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 (/ 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)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 52.0ms | n | @ | 0 | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n)) |
| 37.0ms | n | @ | -inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n)) |
| 8.0ms | n | @ | inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n)) |
| 3.0ms | k | @ | -inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n)) |
| 2.0ms | k | @ | 0 | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 128 | 517 |
| 1 | 345 | 504 |
| 2 | 1022 | 460 |
| 3 | 3355 | 433 |
| 4 | 5591 | 421 |
| 0 | 8473 | 406 |
| 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) |
1/2 |
(+ 1/2 (* -1/2 k)) |
(sqrt (/ 1 k)) |
(sqrt 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))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* -1/2 k) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 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 (/ 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)))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 k (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.f64 k k) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))) k) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/2 k)) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt k) |
(sqrt.f64 k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k (*.f64 k (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/8 binary64)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* -1/2 k) |
(*.f64 #s(literal -1/2 binary64) k) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(sqrt.f64 k) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 43 |
| 0 | 22 | 43 |
| 1 | 89 | 40 |
| 2 | 497 | 38 |
| 3 | 4478 | 38 |
| 0 | 8506 | 37 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(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 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| Outputs |
|---|
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64)))) |
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) |
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) |
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64)) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))) |
(*.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) |
(*.f64 (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))) |
(*.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))) |
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k)))) |
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) |
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(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))) #s(literal 2 binary64)))) |
(/.f64 (*.f64 (sqrt.f64 n) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 n)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (neg.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 (*.f64 k #s(literal 1/4 binary64)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 k #s(literal 1/4 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 k #s(literal 1 binary64)))) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) k))) |
(exp.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (PI.f64)) |
(*.f64 (*.f64 n (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (*.f64 n #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64))))) |
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (exp.f64 (log.f64 n))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)) |
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n)) |
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) n)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n)) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64)) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) |
(*.f64 (PI.f64) (*.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) |
(*.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64)) |
(exp.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
Compiled 9 931 to 1 555 computations (84.3% saved)
18 alts after pruning (18 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 413 | 18 | 431 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 414 | 18 | 432 |
| Status | Accuracy | Program |
|---|---|---|
| 52.1% | (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| 98.9% | (/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))) | |
| 77.3% | (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k))) | |
| 98.9% | (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))) | |
| 52.0% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) | |
| 51.8% | (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) | |
| 52.1% | (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) | |
| 51.6% | (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) | |
| 73.5% | (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))) | |
| ▶ | 51.6% | (*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
| ▶ | 49.8% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) |
| 52.7% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) | |
| 99.0% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))))) | |
| ▶ | 99.3% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
| ▶ | 99.0% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
| 52.6% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) | |
| 99.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| ▶ | 42.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
Compiled 754 to 584 computations (22.5% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) | |
| cost-diff | 0 | (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| cost-diff | 0 | (*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) | |
| cost-diff | 2 | (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 2 | (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| cost-diff | 0 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) | |
| cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) | |
| cost-diff | 0 | (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 53 | 361 |
| 0 | 87 | 355 |
| 1 | 140 | 341 |
| 2 | 205 | 341 |
| 3 | 276 | 335 |
| 4 | 354 | 335 |
| 5 | 373 | 335 |
| 6 | 394 | 335 |
| 7 | 427 | 335 |
| 8 | 439 | 335 |
| 9 | 443 | 335 |
| 0 | 443 | 335 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(*.f64 k #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(/.f64 (*.f64 (PI.f64) n) k) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
k |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) |
(*.f64 #s(literal -1/2 binary64) k) |
#s(literal -1/2 binary64) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) |
(*.f64 #s(literal -2 binary64) (PI.f64)) |
#s(literal -2 binary64) |
(PI.f64) |
(/.f64 #s(literal -1 binary64) n) |
#s(literal -1 binary64) |
n |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
#s(literal 2 binary64) |
(fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
k |
(sqrt.f64 k) |
(/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 n (PI.f64)) |
n |
(PI.f64) |
#s(literal 1 binary64) |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
(PI.f64) |
#s(literal 2 binary64) |
(*.f64 k #s(literal -1/2 binary64)) |
(*.f64 #s(literal -1/2 binary64) k) |
#s(literal -1/2 binary64) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) |
(/.f64 (*.f64 (PI.f64) n) k) |
(*.f64 (/.f64 (PI.f64) k) n) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
k |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) |
(*.f64 #s(literal -1/2 binary64) k) |
#s(literal -1/2 binary64) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 #s(literal -2 binary64) (PI.f64)) |
#s(literal -2 binary64) |
(PI.f64) |
(/.f64 #s(literal -1 binary64) n) |
#s(literal -1 binary64) |
n |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
#s(literal 2 binary64) |
(fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
k |
(sqrt.f64 k) |
(/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 n (PI.f64)) |
(*.f64 (PI.f64) n) |
n |
(PI.f64) |
#s(literal 1 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.2265625 | (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| accuracy | 0.512038839854648 | (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) | |
| accuracy | 0.9179646219124419 | (*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) | |
| accuracy | 15.015259438585579 | (PI.f64) | |
| accuracy | 0.2109375 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| accuracy | 0.2734375 | (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) | |
| accuracy | 0.4769578398336982 | (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) | |
| accuracy | 15.015259438585579 | (PI.f64) | |
| accuracy | 0.21484375 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) | |
| accuracy | 0.4769578398336982 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) | |
| accuracy | 15.015259438585579 | (PI.f64) | |
| accuracy | 34.06442680693078 | #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) | |
| accuracy | 0.42416000976844204 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) | |
| accuracy | 6.930179058353082 | (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) | |
| accuracy | 14.716500937698909 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) | |
| accuracy | 15.015259438585579 | (PI.f64) | |
| accuracy | 0.21484375 | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) | |
| accuracy | 0.24608824386619269 | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) | |
| accuracy | 0.33202582166578376 | (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) | |
| accuracy | 15.015259438585579 | (PI.f64) |
| 82.0ms | 194× | 0 | valid |
| 33.0ms | 62× | 0 | exit |
Compiled 685 to 100 computations (85.4% saved)
ival-mult: 25.0ms (29.5% of total)ival-pow: 23.0ms (27.1% of total)ival-div: 20.0ms (23.6% of total)ival-sqrt: 8.0ms (9.4% of total)ival-add: 3.0ms (3.5% of total)ival-sub: 3.0ms (3.5% of total)ival-pi: 1.0ms (1.2% of total)exact: 1.0ms (1.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(sqrt.f64 #s(literal 2 binary64)) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) |
(/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
(PI.f64) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
| Outputs |
|---|
(* (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)) |
(sqrt 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))) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (* n (PI))) |
(+ (sqrt (* n (PI))) (* 1/2 (* (* k (log (* n (PI)))) (sqrt (* n (PI)))))) |
(+ (sqrt (* n (PI))) (* k (+ (* 1/8 (* (* k (pow (log (* n (PI))) 2)) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (log (* n (PI)))))))) |
(+ (sqrt (* n (PI))) (* k (+ (* 1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* k (+ (* 1/48 (* (* k (pow (log (* n (PI))) 3)) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (pow (log (* n (PI))) 2)))))))) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k) |
(/ (+ (* k (+ (* (sqrt k) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* 1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (+ (* 1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (* 1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))))))))) (* (sqrt k) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (/ 1 k)) (sqrt 2)) |
(/ (+ (* 1/2 (* (sqrt (pow k 3)) (* (log 2) (sqrt 2)))) (* (sqrt k) (sqrt 2))) k) |
(/ (+ (* k (+ (* 1/8 (* (sqrt (pow k 3)) (* (pow (log 2) 2) (sqrt 2)))) (* 1/2 (* (sqrt k) (* (log 2) (sqrt 2)))))) (* (sqrt k) (sqrt 2))) k) |
(/ (+ (* k (+ (* 1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* k (+ (* 1/48 (* (sqrt (pow k 3)) (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (sqrt k) (* (pow (log 2) 2) (sqrt 2)))))))) (* (sqrt k) (sqrt 2))) k) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (* k (* (log 2) (sqrt 2))))) |
(+ (sqrt 2) (* k (+ (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2)))) (* 1/2 (* (log 2) (sqrt 2)))))) |
(+ (sqrt 2) (* k (+ (* 1/2 (* (log 2) (sqrt 2))) (* k (+ (* 1/48 (* k (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))))))) |
1 |
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2)))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2))))))) |
1/2 |
(+ 1/2 (* -1/2 k)) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log 2) (+ 1/2 (* 1/2 k))))) |
(exp (* (log 2) (+ 1/2 (* 1/2 k)))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(* -1/2 k) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (- 1/2 (* -1/2 k)))) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log 2) (- 1/2 (* -1/2 k))))) |
(exp (* (log 2) (- 1/2 (* -1/2 k)))) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* 2 (* n (PI))) |
(exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(* (sqrt (/ 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 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 54.0ms | n | @ | 0 | ((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* -2 (PI)) (/ -1 n)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1) (* (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1)) (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (pow 2 (+ (* 1/2 k) 1/2)) (PI) (sqrt (* n (* (PI) 2))) (pow (* n (* (PI) 2)) (* k -1/2)) (* n (* (PI) 2)) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (pow (* n (PI)) (+ (* 1/2 k) 1/2))) |
| 35.0ms | n | @ | -inf | ((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* -2 (PI)) (/ -1 n)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1) (* (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1)) (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (pow 2 (+ (* 1/2 k) 1/2)) (PI) (sqrt (* n (* (PI) 2))) (pow (* n (* (PI) 2)) (* k -1/2)) (* n (* (PI) 2)) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (pow (* n (PI)) (+ (* 1/2 k) 1/2))) |
| 33.0ms | n | @ | inf | ((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* -2 (PI)) (/ -1 n)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1) (* (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1)) (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (pow 2 (+ (* 1/2 k) 1/2)) (PI) (sqrt (* n (* (PI) 2))) (pow (* n (* (PI) 2)) (* k -1/2)) (* n (* (PI) 2)) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (pow (* n (PI)) (+ (* 1/2 k) 1/2))) |
| 6.0ms | k | @ | -inf | ((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* -2 (PI)) (/ -1 n)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1) (* (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1)) (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (pow 2 (+ (* 1/2 k) 1/2)) (PI) (sqrt (* n (* (PI) 2))) (pow (* n (* (PI) 2)) (* k -1/2)) (* n (* (PI) 2)) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (pow (* n (PI)) (+ (* 1/2 k) 1/2))) |
| 6.0ms | k | @ | 0 | ((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* -2 (PI)) (/ -1 n)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1) (* (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) 1)) (/ (pow 2 (+ (* 1/2 k) 1/2)) (sqrt k)) (pow 2 (+ (* 1/2 k) 1/2)) (PI) (sqrt (* n (* (PI) 2))) (pow (* n (* (PI) 2)) (* k -1/2)) (* n (* (PI) 2)) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (pow (* n (PI)) (+ (* 1/2 k) 1/2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 347 | 1757 |
| 1 | 1104 | 1667 |
| 2 | 3666 | 1540 |
| 3 | 6760 | 1506 |
| 0 | 8372 | 1458 |
| 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)) |
(sqrt 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))) |
(sqrt (/ (* n (PI)) k)) |
(sqrt (* n (PI))) |
(+ (sqrt (* n (PI))) (* 1/2 (* (* k (log (* n (PI)))) (sqrt (* n (PI)))))) |
(+ (sqrt (* n (PI))) (* k (+ (* 1/8 (* (* k (pow (log (* n (PI))) 2)) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (log (* n (PI)))))))) |
(+ (sqrt (* n (PI))) (* k (+ (* 1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* k (+ (* 1/48 (* (* k (pow (log (* n (PI))) 3)) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (pow (log (* n (PI))) 2)))))))) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k) |
(/ (+ (* k (+ (* (sqrt k) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* 1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (+ (* 1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (* 1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))))))))) (* (sqrt k) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (/ 1 k)) (sqrt 2)) |
(/ (+ (* 1/2 (* (sqrt (pow k 3)) (* (log 2) (sqrt 2)))) (* (sqrt k) (sqrt 2))) k) |
(/ (+ (* k (+ (* 1/8 (* (sqrt (pow k 3)) (* (pow (log 2) 2) (sqrt 2)))) (* 1/2 (* (sqrt k) (* (log 2) (sqrt 2)))))) (* (sqrt k) (sqrt 2))) k) |
(/ (+ (* k (+ (* 1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* k (+ (* 1/48 (* (sqrt (pow k 3)) (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (sqrt k) (* (pow (log 2) 2) (sqrt 2)))))))) (* (sqrt k) (sqrt 2))) k) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (* k (* (log 2) (sqrt 2))))) |
(+ (sqrt 2) (* k (+ (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2)))) (* 1/2 (* (log 2) (sqrt 2)))))) |
(+ (sqrt 2) (* k (+ (* 1/2 (* (log 2) (sqrt 2))) (* k (+ (* 1/48 (* k (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))))))) |
1 |
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2)))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2))))))) |
1/2 |
(+ 1/2 (* -1/2 k)) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log 2) (+ 1/2 (* 1/2 k))))) |
(exp (* (log 2) (+ 1/2 (* 1/2 k)))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(* -1/2 k) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (- 1/2 (* -1/2 k)))) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log 2) (- 1/2 (* -1/2 k))))) |
(exp (* (log 2) (- 1/2 (* -1/2 k)))) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* 2 (* n (PI))) |
(exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(* (sqrt (/ 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 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (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) |
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1 |
#s(literal 1 binary64) |
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1/2 |
#s(literal 1/2 binary64) |
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(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) |
(exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))) |
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal -1/2 binary64)) k) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal -1/2 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal -1/2 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))) |
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal -1/2 binary64)) k) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(*.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -1/2 binary64) k)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -1/2 binary64) k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))) |
(pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (neg.f64 (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -1/2 binary64) k)) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 53 | 257 |
| 0 | 87 | 253 |
| 1 | 315 | 219 |
| 2 | 1862 | 217 |
| 0 | 8166 | 217 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(sqrt.f64 #s(literal 2 binary64)) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) |
(/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
(PI.f64) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
| Outputs |
|---|
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/4 binary64)))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 k #s(literal -1/4 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/4 binary64)))) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 k #s(literal -1/4 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 n (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1/2 binary64)) k) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 n (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) (/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1/2 binary64)) k) #s(literal 1 binary64))) |
(*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 n (*.f64 #s(literal -1/2 binary64) k))) #s(literal 1 binary64)) (/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1/2 binary64)) k) (sqrt.f64 k))) |
(*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n)) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) |
(*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (neg.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (neg.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (neg.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (neg.f64 n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 (neg.f64 n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 k #s(literal -1/4 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
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(pow.f64 (*.f64 (PI.f64) n) (fma.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) |
(/.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))) |
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1 binary64)) |
(/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (neg.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (neg.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) (neg.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(exp.f64 (neg.f64 (neg.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 (PI.f64) n)) (*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 n) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 n) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (neg.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) n) (neg.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) |
Compiled 31 838 to 3 944 computations (87.6% saved)
25 alts after pruning (23 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 170 | 22 | 1 192 |
| Fresh | 12 | 1 | 13 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 0 | 0 |
| Total | 1 185 | 25 | 1 210 |
| Status | Accuracy | Program |
|---|---|---|
| 99.1% | (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| 49.8% | (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) | |
| 99.0% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| 79.8% | (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| ▶ | 99.3% | (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))) |
| ✓ | 99.3% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
| 52.7% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* n (* (PI) 2)) (* k -1/2)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) | |
| ▶ | 52.6% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
| 98.6% | (*.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) | |
| 52.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))) | |
| 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) | |
| 99.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 52.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) | |
| 52.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) | |
| 42.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| 42.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) | |
| 52.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))) | |
| 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) | |
| ▶ | 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))) | |
| 42.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) | |
| ▶ | 53.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
| 42.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)))) | |
| ✓ | 42.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
| ▶ | 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
Compiled 1 177 to 962 computations (18.3% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) | |
| cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) | |
| cost-diff | 0 | #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) | |
| cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) | |
| cost-diff | 0 | (/.f64 n k) | |
| cost-diff | 0 | (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))) | |
| cost-diff | 0 | (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64)))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| cost-diff | 0 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) | |
| cost-diff | 0 | (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) | |
| cost-diff | 0 | (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))) | |
| cost-diff | 2 | (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 46 | 318 |
| 0 | 74 | 314 |
| 1 | 119 | 306 |
| 2 | 169 | 306 |
| 3 | 214 | 306 |
| 4 | 260 | 306 |
| 5 | 274 | 306 |
| 6 | 295 | 306 |
| 7 | 322 | 306 |
| 8 | 331 | 306 |
| 9 | 334 | 306 |
| 0 | 334 | 301 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 #s(literal 2 binary64) n) |
#s(literal 2 binary64) |
n |
(PI.f64) |
(*.f64 #s(literal -1/2 binary64) k) |
#s(literal -1/2 binary64) |
k |
(sqrt.f64 k) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) |
#s(literal 1 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64)))) |
(*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))) |
(/.f64 n k) |
n |
k |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
#s(literal 2 binary64) |
(PI.f64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) |
(sqrt.f64 n) |
n |
(sqrt.f64 (/.f64 (PI.f64) k)) |
(/.f64 (PI.f64) k) |
(PI.f64) |
k |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(pow.f64 k #s(literal -1/2 binary64)) |
k |
#s(literal -1/2 binary64) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
| Outputs |
|---|
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) |
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) n) |
(*.f64 n #s(literal 2 binary64)) |
#s(literal 2 binary64) |
n |
(PI.f64) |
(*.f64 #s(literal -1/2 binary64) k) |
(*.f64 k #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
k |
(sqrt.f64 k) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
#s(literal 1 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) |
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64)))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k)) |
(*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))) |
(/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k) |
(/.f64 n k) |
n |
k |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(PI.f64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) |
(sqrt.f64 n) |
n |
(sqrt.f64 (/.f64 (PI.f64) k)) |
(/.f64 (PI.f64) k) |
(PI.f64) |
k |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(pow.f64 k #s(literal -1/2 binary64)) |
k |
#s(literal -1/2 binary64) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.37109313724614595 | (sqrt.f64 (*.f64 (PI.f64) n)) | |
| accuracy | 0.41634750976844204 | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) | |
| accuracy | 0.533535009768442 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) | |
| accuracy | 29.86749073970137 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) | |
| accuracy | 0.2890625 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| accuracy | 0.37109313724614595 | (sqrt.f64 (*.f64 (PI.f64) n)) | |
| accuracy | 0.40462875976844204 | (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) | |
| accuracy | 29.878366562688164 | #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) | |
| accuracy | 0.26953125 | (/.f64 (PI.f64) k) | |
| accuracy | 0.320976269536884 | (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) | |
| accuracy | 0.533535009768442 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))) | |
| accuracy | 29.86749073970137 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) | |
| accuracy | 0.0 | (PI.f64) | |
| accuracy | 0.28353500976844204 | (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))) | |
| accuracy | 13.433545487693971 | (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64)))) | |
| accuracy | 29.86749073970137 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| accuracy | 0.203125 | (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))) | |
| accuracy | 0.24608824386619269 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) | |
| accuracy | 0.26171875 | (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) | |
| accuracy | 0.37499457166578376 | (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) |
| 89.0ms | 256× | 0 | valid |
Compiled 590 to 87 computations (85.3% saved)
ival-pow: 21.0ms (32.9% of total)ival-mult: 19.0ms (29.8% of total)ival-sqrt: 11.0ms (17.2% of total)ival-div: 9.0ms (14.1% of total)ival-pi: 1.0ms (1.6% of total)ival-sub: 1.0ms (1.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64)))) |
(*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))) |
(/.f64 n k) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))) |
(sqrt.f64 #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(PI.f64) |
(/.f64 (PI.f64) k) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
| Outputs |
|---|
(* (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)) |
(/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k) |
1 |
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2)))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2))))))) |
(* 2 (/ (* n (PI)) k)) |
(/ n k) |
(sqrt (/ (* n (PI)) k)) |
(sqrt 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))) |
(/ (PI) k) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 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 (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* 2 (* n (PI))) |
(sqrt (* n (PI))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 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)))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 13.0ms | n | @ | inf | ((/ (sqrt (* (* 2 n) (PI))) 1) (* (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (/ (sqrt (* (* 2 n) (PI))) 1)) (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (pow (* (* 2 n) (PI)) (* -1/2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ n k) (* 2 (PI)))) (* (/ n k) (* 2 (PI))) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (pow k -1/2) (sqrt (* (PI) n)))) (* (pow k -1/2) (sqrt (* (PI) n))) (sqrt (* (* 2 n) (PI))) (* (* 2 n) (PI)) (PI) (/ (PI) k) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n))) |
| 12.0ms | n | @ | -inf | ((/ (sqrt (* (* 2 n) (PI))) 1) (* (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (/ (sqrt (* (* 2 n) (PI))) 1)) (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (pow (* (* 2 n) (PI)) (* -1/2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ n k) (* 2 (PI)))) (* (/ n k) (* 2 (PI))) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (pow k -1/2) (sqrt (* (PI) n)))) (* (pow k -1/2) (sqrt (* (PI) n))) (sqrt (* (* 2 n) (PI))) (* (* 2 n) (PI)) (PI) (/ (PI) k) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n))) |
| 10.0ms | n | @ | 0 | ((/ (sqrt (* (* 2 n) (PI))) 1) (* (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (/ (sqrt (* (* 2 n) (PI))) 1)) (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (pow (* (* 2 n) (PI)) (* -1/2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ n k) (* 2 (PI)))) (* (/ n k) (* 2 (PI))) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (pow k -1/2) (sqrt (* (PI) n)))) (* (pow k -1/2) (sqrt (* (PI) n))) (sqrt (* (* 2 n) (PI))) (* (* 2 n) (PI)) (PI) (/ (PI) k) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n))) |
| 6.0ms | k | @ | inf | ((/ (sqrt (* (* 2 n) (PI))) 1) (* (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (/ (sqrt (* (* 2 n) (PI))) 1)) (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (pow (* (* 2 n) (PI)) (* -1/2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ n k) (* 2 (PI)))) (* (/ n k) (* 2 (PI))) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (pow k -1/2) (sqrt (* (PI) n)))) (* (pow k -1/2) (sqrt (* (PI) n))) (sqrt (* (* 2 n) (PI))) (* (* 2 n) (PI)) (PI) (/ (PI) k) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n))) |
| 5.0ms | k | @ | -inf | ((/ (sqrt (* (* 2 n) (PI))) 1) (* (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (/ (sqrt (* (* 2 n) (PI))) 1)) (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (pow (* (* 2 n) (PI)) (* -1/2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ n k) (* 2 (PI)))) (* (/ n k) (* 2 (PI))) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (pow k -1/2) (sqrt (* (PI) n)))) (* (pow k -1/2) (sqrt (* (PI) n))) (sqrt (* (* 2 n) (PI))) (* (* 2 n) (PI)) (PI) (/ (PI) k) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 201 | 994 |
| 1 | 573 | 970 |
| 2 | 1756 | 900 |
| 3 | 2745 | 897 |
| 4 | 5340 | 882 |
| 0 | 8555 | 858 |
| 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)) |
(/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k) |
1 |
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2)))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2))))))) |
(* 2 (/ (* n (PI)) k)) |
(/ n k) |
(sqrt (/ (* n (PI)) k)) |
(sqrt 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))) |
(/ (PI) k) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 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 (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* 2 (* n (PI))) |
(sqrt (* n (PI))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 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)))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (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 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64))))) k (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k) |
(/.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k) |
(/.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal 1/8 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 k)))) k (sqrt.f64 k)) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal -1/48 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 k)))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 k)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))) k (sqrt.f64 k)) k) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2)))))) |
(fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))) k #s(literal 1 binary64)) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2))))))) |
(fma.f64 (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/8 binary64))) k (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))) k #s(literal 1 binary64)) |
(* 2 (/ (* n (PI)) k)) |
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) |
(/ n k) |
(/.f64 n k) |
(sqrt (/ (* n (PI)) k)) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(sqrt k) |
(sqrt.f64 k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (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 (PI.f64) n)) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) k (fma.f64 k (*.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(/ (PI) k) |
(/.f64 (PI.f64) k) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal -2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(sqrt.f64 k) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) |
(* 2 (* n (PI))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(sqrt (* n (PI))) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(*.f64 (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 #s(literal -1/2 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n))) (-.f64 #s(literal 1 binary64) k)) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 46 | 261 |
| 0 | 74 | 241 |
| 1 | 231 | 227 |
| 2 | 1175 | 220 |
| 0 | 9148 | 220 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64)))) |
(*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))) |
(/.f64 n k) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))) |
(sqrt.f64 #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(PI.f64) |
(/.f64 (PI.f64) k) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
| Outputs |
|---|
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 (PI.f64))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 n #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (pow.f64 n #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64))) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (pow.f64 n #s(literal 1/4 binary64)) (*.f64 (pow.f64 n #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal -1 binary64))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (sqrt.f64 n) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) #s(literal -1 binary64)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) #s(literal -1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(exp.f64 (neg.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1/2 binary64))) |
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)) (/.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) (/.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))) |
(*.f64 (/.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k) #s(literal -1/2 binary64))) #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) |
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) #s(literal -1 binary64)) (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) |
(*.f64 (/.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) |
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(*.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64))) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (pow.f64 n #s(literal 1/4 binary64)) (*.f64 (pow.f64 n #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal -1 binary64))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (sqrt.f64 n) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) #s(literal -1 binary64)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) #s(literal -1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(exp.f64 (neg.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 n (sqrt.f64 (PI.f64)))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (pow.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 n))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 n #s(literal 1/4 binary64)) (*.f64 (pow.f64 n #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64)))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (sqrt.f64 n))) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) n))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) |
(pow.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) |
Compiled 36 961 to 4 603 computations (87.5% saved)
48 alts after pruning (42 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 292 | 33 | 1 325 |
| Fresh | 9 | 9 | 18 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 2 | 2 |
| Total | 1 302 | 48 | 1 350 |
| Status | Accuracy | Program |
|---|---|---|
| 99.1% | (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| 49.8% | (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) | |
| 52.7% | (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)) | |
| 99.0% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| ▶ | 52.6% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
| 79.8% | (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| 99.2% | (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) | |
| ▶ | 99.3% | (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
| ✓ | 99.3% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
| ✓ | 52.6% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
| 52.7% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) | |
| 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n)))) | |
| 53.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))) | |
| 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) | |
| 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))) | |
| 99.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 99.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 52.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) | |
| ▶ | 52.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
| 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))) | |
| ▶ | 53.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
| 42.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) | |
| 53.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) | |
| 42.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) | |
| 42.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) | |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))) | |
| 53.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))) | |
| 52.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) | |
| 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) | |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) | |
| 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))) | |
| ✓ | 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))) | |
| ✓ | 53.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k)))))) | |
| ✓ | 42.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
| 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))) | |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) | |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))) | |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))) | |
| 42.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) k) (sqrt.f64 (PI.f64))))) | |
| 42.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))))))) | |
| ✓ | 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 k n)) (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) | |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (neg.f64 n) (/.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| ▶ | 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
| 42.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))) |
Compiled 2 313 to 1 884 computations (18.5% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) | |
| cost-diff | 0 | (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) | |
| cost-diff | 2 | (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) | |
| cost-diff | 2 | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) | |
| cost-diff | 0 | (/.f64 (PI.f64) k) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 (PI.f64) k)) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) | |
| cost-diff | 0 | (*.f64 (PI.f64) n) | |
| cost-diff | 0 | (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)) | |
| cost-diff | 0 | (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) | |
| cost-diff | 0 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) | |
| cost-diff | 0 | (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) | |
| cost-diff | 0 | (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 326 |
| 0 | 72 | 320 |
| 1 | 114 | 314 |
| 2 | 156 | 312 |
| 3 | 201 | 312 |
| 4 | 271 | 312 |
| 5 | 298 | 312 |
| 6 | 325 | 312 |
| 7 | 382 | 312 |
| 8 | 401 | 312 |
| 9 | 410 | 312 |
| 0 | 410 | 306 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 #s(literal 2 binary64) n) |
#s(literal 2 binary64) |
n |
(PI.f64) |
(*.f64 #s(literal -1/2 binary64) k) |
#s(literal -1/2 binary64) |
k |
(sqrt.f64 k) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(*.f64 n #s(literal 2 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))) |
(*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
(/.f64 #s(literal 2 binary64) k) |
#s(literal 2 binary64) |
k |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) |
(sqrt.f64 (/.f64 (PI.f64) k)) |
(/.f64 (PI.f64) k) |
(PI.f64) |
k |
(sqrt.f64 (*.f64 n #s(literal 2 binary64))) |
(*.f64 n #s(literal 2 binary64)) |
n |
#s(literal 2 binary64) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(literal 1 binary64) |
(/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(sqrt.f64 k) |
k |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(PI.f64) |
(*.f64 n #s(literal 2 binary64)) |
n |
#s(literal 2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(sqrt.f64 k) |
k |
(/.f64 (sqrt.f64 n) #s(literal 1 binary64)) |
(sqrt.f64 n) |
n |
#s(literal 1 binary64) |
| Outputs |
|---|
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 k #s(literal -1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) |
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 k #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) |
(*.f64 #s(literal 2 binary64) n) |
(*.f64 n #s(literal 2 binary64)) |
#s(literal 2 binary64) |
n |
(PI.f64) |
(*.f64 #s(literal -1/2 binary64) k) |
(*.f64 k #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
k |
(sqrt.f64 k) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) |
(*.f64 n #s(literal 2 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (/.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) |
(*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)) |
(/.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
(/.f64 #s(literal 2 binary64) k) |
#s(literal 2 binary64) |
k |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) |
(sqrt.f64 (/.f64 (PI.f64) k)) |
(/.f64 (PI.f64) k) |
(PI.f64) |
k |
(sqrt.f64 (*.f64 n #s(literal 2 binary64))) |
(*.f64 n #s(literal 2 binary64)) |
n |
#s(literal 2 binary64) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))) |
(sqrt.f64 k) |
k |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) |
(PI.f64) |
(*.f64 n #s(literal 2 binary64)) |
n |
#s(literal 2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(sqrt.f64 k) |
k |
(/.f64 (sqrt.f64 n) #s(literal 1 binary64)) |
(sqrt.f64 n) |
(sqrt.f64 n) |
n |
#s(literal 1 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.24447250976844204 | (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) | |
| accuracy | 0.546875 | (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) | |
| accuracy | 1.6495638017354044 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) | |
| accuracy | 28.09306604638599 | (PI.f64) | |
| accuracy | 0.171875 | (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) | |
| accuracy | 0.30077582166578376 | (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) | |
| accuracy | 1.6435845960484612 | #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) | |
| accuracy | 28.09306604638599 | (PI.f64) | |
| accuracy | 0.16796875 | (/.f64 (PI.f64) k) | |
| accuracy | 0.18587875976844204 | (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) | |
| accuracy | 1.6495638017354044 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) | |
| accuracy | 28.09306604638599 | (PI.f64) | |
| accuracy | 0.16015625 | (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)) | |
| accuracy | 1.6495638017354044 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) | |
| accuracy | 6.875210005291345 | (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))) | |
| accuracy | 28.09306604638599 | (PI.f64) | |
| accuracy | 0.203125 | (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) | |
| accuracy | 0.24608824386619269 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) | |
| accuracy | 0.30077582166578376 | (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) | |
| accuracy | 28.09306604638599 | (PI.f64) |
| 47.0ms | 116× | 0 | exit |
| 43.0ms | 140× | 0 | valid |
Compiled 601 to 88 computations (85.4% saved)
ival-mult: 31.0ms (45.6% of total)ival-div: 14.0ms (20.6% of total)ival-sqrt: 11.0ms (16.2% of total)ival-pow: 9.0ms (13.2% of total)ival-pi: 1.0ms (1.5% of total)ival-sub: 1.0ms (1.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))) |
(*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)) |
(*.f64 (PI.f64) n) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) |
(sqrt.f64 (/.f64 (PI.f64) k)) |
(/.f64 (PI.f64) k) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
(/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(sqrt.f64 k) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 n) #s(literal 1 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) |
(PI.f64) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
| Outputs |
|---|
(* (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)) |
(/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k) |
1 |
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2)))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2))))))) |
(* 2 (/ (* n (PI)) k)) |
(sqrt (/ (PI) k)) |
(/ (PI) k) |
(* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))) |
(+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/48 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))))))))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(sqrt k) |
(* (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))) |
(* (sqrt (/ (PI) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 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 (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (PI) k)) (pow (sqrt -1) 2)) |
(* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* n (PI)) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(sqrt n) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(* -1 (* (sqrt n) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 14.0ms | n | @ | inf | ((* (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt (* (PI) (* n 2)))) (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (pow (* (* 2 n) (PI)) (* -1/2 k)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) n) (/ 2 k))) (* (* (PI) n) (/ 2 k)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* n 2))) (sqrt (/ (PI) k)) (/ (PI) k) (/ 1 (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt n) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt (* (PI) 2)) (sqrt k)) (/ (sqrt n) 1)) (/ (sqrt (* (PI) 2)) (sqrt k)) (PI) (sqrt (* (PI) (* n 2))) (sqrt (* (PI) 2))) |
| 13.0ms | n | @ | 0 | ((* (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt (* (PI) (* n 2)))) (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (pow (* (* 2 n) (PI)) (* -1/2 k)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) n) (/ 2 k))) (* (* (PI) n) (/ 2 k)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* n 2))) (sqrt (/ (PI) k)) (/ (PI) k) (/ 1 (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt n) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt (* (PI) 2)) (sqrt k)) (/ (sqrt n) 1)) (/ (sqrt (* (PI) 2)) (sqrt k)) (PI) (sqrt (* (PI) (* n 2))) (sqrt (* (PI) 2))) |
| 12.0ms | n | @ | -inf | ((* (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt (* (PI) (* n 2)))) (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (pow (* (* 2 n) (PI)) (* -1/2 k)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) n) (/ 2 k))) (* (* (PI) n) (/ 2 k)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* n 2))) (sqrt (/ (PI) k)) (/ (PI) k) (/ 1 (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt n) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt (* (PI) 2)) (sqrt k)) (/ (sqrt n) 1)) (/ (sqrt (* (PI) 2)) (sqrt k)) (PI) (sqrt (* (PI) (* n 2))) (sqrt (* (PI) 2))) |
| 6.0ms | k | @ | -inf | ((* (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt (* (PI) (* n 2)))) (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (pow (* (* 2 n) (PI)) (* -1/2 k)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) n) (/ 2 k))) (* (* (PI) n) (/ 2 k)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* n 2))) (sqrt (/ (PI) k)) (/ (PI) k) (/ 1 (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt n) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt (* (PI) 2)) (sqrt k)) (/ (sqrt n) 1)) (/ (sqrt (* (PI) 2)) (sqrt k)) (PI) (sqrt (* (PI) (* n 2))) (sqrt (* (PI) 2))) |
| 4.0ms | k | @ | 0 | ((* (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt (* (PI) (* n 2)))) (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (pow (* (* 2 n) (PI)) (* -1/2 k)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) n) (/ 2 k))) (* (* (PI) n) (/ 2 k)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* n 2))) (sqrt (/ (PI) k)) (/ (PI) k) (/ 1 (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt n) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt (* (PI) 2)) (sqrt k)) (/ (sqrt n) 1)) (/ (sqrt (* (PI) 2)) (sqrt k)) (PI) (sqrt (* (PI) (* n 2))) (sqrt (* (PI) 2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 254 | 1320 |
| 1 | 758 | 1260 |
| 2 | 2510 | 1192 |
| 3 | 5482 | 1183 |
| 0 | 8485 | 1153 |
| 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)) |
(/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k) |
1 |
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2)))))) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2))))))) |
(* 2 (/ (* n (PI)) k)) |
(sqrt (/ (PI) k)) |
(/ (PI) k) |
(* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))) |
(+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/48 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))))))))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(sqrt k) |
(* (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))) |
(* (sqrt (/ (PI) k)) (sqrt 2)) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 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 (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (PI) k)) (pow (sqrt -1) 2)) |
(* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* n (PI)) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(sqrt n) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(* -1 (* (sqrt n) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (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 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64))))) k (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k) |
(/.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k) |
(/.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal 1/8 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 k)))) k (sqrt.f64 k)) k) |
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal -1/48 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 k)))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 k)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))) k (sqrt.f64 k)) k) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2)))))) |
(fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))) k #s(literal 1 binary64)) |
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2))))))) |
(fma.f64 (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/8 binary64))) k (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))) k #s(literal 1 binary64)) |
(* 2 (/ (* n (PI)) k)) |
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) |
(sqrt (/ (PI) k)) |
(sqrt.f64 (/.f64 (PI.f64) k)) |
(/ (PI) k) |
(/.f64 (PI.f64) k) |
(* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))) |
(/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(fma.f64 (*.f64 (/.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64)))) #s(literal 1/8 binary64) (*.f64 (*.f64 (/.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) k (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/48 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))))))))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k)) #s(literal 1/8 binary64) (*.f64 (neg.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/8 binary64)) #s(literal 1/2 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/24 binary64))))) k (*.f64 (*.f64 (/.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) k (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))) |
(sqrt k) |
(sqrt.f64 k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (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 (PI.f64) n)) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) k (fma.f64 k (*.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(* (sqrt (/ (PI) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1/2 (* k (log (* 2 (* n (PI))))))) |
(pow.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)) k) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 k #s(literal 1 binary64))) (sqrt.f64 k)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* (sqrt (/ (PI) k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 (PI.f64) k))) |
(* -1 (* (sqrt k) (/ (pow (sqrt -1) 2) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 k #s(literal 1 binary64))) (sqrt.f64 k)) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(sqrt.f64 k) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) |
(pow.f64 (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal -1/2 binary64)) |
(* 2 (* n (PI))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* n (PI)) |
(*.f64 (PI.f64) n) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (-.f64 k #s(literal 1 binary64))) (sqrt.f64 k)) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) k)) |
(sqrt n) |
(sqrt.f64 n) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(pow.f64 (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal -1/2 binary64)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (-.f64 k #s(literal 1 binary64))) (sqrt.f64 k)) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) k)) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(*.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))) #s(literal -1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.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 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
(* (sqrt k) (/ 1 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))) |
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 k #s(literal 1 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 k)) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) |
(* -1 (* (sqrt n) (pow (sqrt -1) 2))) |
(sqrt.f64 n) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 257 |
| 0 | 72 | 244 |
| 1 | 238 | 231 |
| 2 | 1240 | 223 |
| 0 | 8398 | 223 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))) |
(*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)) |
(*.f64 (PI.f64) n) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) |
(sqrt.f64 (/.f64 (PI.f64) k)) |
(/.f64 (PI.f64) k) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
(/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(sqrt.f64 k) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 n) #s(literal 1 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) |
(PI.f64) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
| Outputs |
|---|
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(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))))) |
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(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 k))) |
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(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(exp.f64 (log.f64 (PI.f64))) |
(log.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (PI.f64))))) |
(log.f64 (exp.f64 (PI.f64))) |
(PI.f64) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 n)) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 n #s(literal -1/2 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 n #s(literal -1/2 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) |
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1 binary64)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 n))) |
(*.f64 (neg.f64 (sqrt.f64 n)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 2 binary64)) #s(literal 1/4 binary64)) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 n #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 n #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 1 binary64)) |
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) |
(exp.f64 (fma.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64) (*.f64 (log.f64 n) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 n) #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 1/2 binary64))) |
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64))) |
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (PI.f64)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(pow.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
Compiled 35 180 to 4 370 computations (87.6% saved)
62 alts after pruning (55 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 217 | 35 | 1 252 |
| Fresh | 17 | 20 | 37 |
| Picked | 2 | 3 | 5 |
| Done | 2 | 4 | 6 |
| Total | 1 238 | 62 | 1 300 |
| Status | Accuracy | Program |
|---|---|---|
| 99.1% | (/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| 77.7% | (/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) | |
| 49.8% | (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) | |
| 99.3% | (/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (sqrt.f64 k)) | |
| 52.7% | (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 k)) | |
| 52.6% | (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) | |
| 99.0% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) | |
| 52.8% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))) | |
| 52.6% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) | |
| 52.8% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))) | |
| ✓ | 52.6% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
| 98.9% | (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 k #s(literal 1 binary64))) (sqrt.f64 k)))) | |
| 79.8% | (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| ✓ | 99.3% | (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
| 52.7% | (*.f64 (/.f64 #s(approx (pow (* (* 2 n) (PI)) (* -1/2 k)) #s(literal 1 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) | |
| ✓ | 52.6% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
| 99.3% | (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/2 binary64) k)))) | |
| 52.7% | (*.f64 #s(approx (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) | |
| 52.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)))) | |
| 52.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))) | |
| 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n)))) | |
| 53.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64))))) | |
| 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) | |
| 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))) | |
| 99.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) | |
| 52.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n))) | |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal -1 binary64)))) | |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) | |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) | |
| 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))) | |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) | |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) | |
| 53.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) | |
| 52.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) | |
| 52.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) | |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) | |
| 42.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) | |
| 52.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))) | |
| 53.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) | |
| 42.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) | |
| 42.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) | |
| 53.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) | |
| 42.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))) | |
| 53.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) | |
| 53.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))) | |
| 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) | |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) | |
| ✓ | 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
| 52.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k)))))) | |
| ✓ | 42.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
| 52.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))) | |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k))) | |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))) | |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))) | |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) | |
| ✓ | 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 k n)) (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) | |
| ✓ | 42.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
| 42.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))) | |
| 42.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 #s(literal 2 binary64) k) n))))) |
Compiled 4 300 to 1 737 computations (59.6% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (neg.f64 n) (/.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 k n)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
(*.f64 #s(approx (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(approx (pow (* (* 2 n) (PI)) (* -1/2 k)) #s(literal 1 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* n (* (PI) 2)) (* k -1/2)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 #s(literal 2 binary64) k) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) k) (sqrt.f64 (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 k #s(literal 1 binary64))) (sqrt.f64 k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/2 binary64) k)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k))) |
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/2 binary64) k)))) |
4 calls:
| 55.0ms | n |
| 37.0ms | k |
| 32.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 29.0ms | (*.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 |
|---|---|---|
| 99.3% | 1 | k |
| 99.3% | 1 | n |
| 99.3% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 99.3% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (neg.f64 n) (/.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 k n)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
(*.f64 #s(approx (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(approx (pow (* (* 2 n) (PI)) (* -1/2 k)) #s(literal 1 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* n (* (PI) 2)) (* k -1/2)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 #s(literal 2 binary64) k) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) k) (sqrt.f64 (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 k #s(literal 1 binary64))) (sqrt.f64 k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
| Outputs |
|---|
(/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (sqrt.f64 k)) |
4 calls:
| 35.0ms | k |
| 31.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 29.0ms | n |
| 26.0ms | (*.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 |
|---|---|---|
| 99.3% | 1 | k |
| 99.3% | 1 | n |
| 99.3% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 99.3% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (neg.f64 n) (/.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 k n)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
(*.f64 #s(approx (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(approx (pow (* (* 2 n) (PI)) (* -1/2 k)) #s(literal 1 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* n (* (PI) 2)) (* k -1/2)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 #s(literal 2 binary64) k) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) k) (sqrt.f64 (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 k #s(literal 1 binary64))) (sqrt.f64 k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
| Outputs |
|---|
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
4 calls:
| 37.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 31.0ms | k |
| 27.0ms | n |
| 26.0ms | (*.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 |
|---|---|---|
| 99.3% | 1 | k |
| 99.3% | 1 | n |
| 99.3% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 99.3% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (neg.f64 n) (/.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 k n)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
(*.f64 #s(approx (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(approx (pow (* (* 2 n) (PI)) (* -1/2 k)) #s(literal 1 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* n (* (PI) 2)) (* k -1/2)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 #s(literal 2 binary64) k) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) k) (sqrt.f64 (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 k #s(literal 1 binary64))) (sqrt.f64 k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
| Outputs |
|---|
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
4 calls:
| 33.0ms | n |
| 33.0ms | k |
| 26.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 25.0ms | (*.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 |
|---|---|---|
| 99.1% | 1 | k |
| 99.1% | 1 | n |
| 99.1% | 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)))) |
| 99.1% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (neg.f64 n) (/.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 k n)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
(*.f64 #s(approx (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(approx (pow (* (* 2 n) (PI)) (* -1/2 k)) #s(literal 1 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* n (* (PI) 2)) (* k -1/2)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 #s(literal 2 binary64) k) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) k) (sqrt.f64 (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)) |
4 calls:
| 33.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 25.0ms | n |
| 24.0ms | k |
| 23.0ms | (*.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 |
|---|---|---|
| 97.9% | 2 | k |
| 62.2% | 5 | n |
| 97.5% | 3 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 62.2% | 5 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (neg.f64 n) (/.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 k n)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
(*.f64 #s(approx (/ (pow (* (* 2 n) (PI)) (* -1/2 k)) (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(approx (pow (* (* 2 n) (PI)) (* -1/2 k)) #s(literal 1 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 #s(approx (pow (* n (* (PI) 2)) (* k -1/2)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 #s(literal 2 binary64) k) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) k) (sqrt.f64 (PI.f64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
4 calls:
| 23.0ms | (*.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)))) |
| 22.0ms | n |
| 22.0ms | k |
| 21.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| Accuracy | Segments | Branch |
|---|---|---|
| 53.1% | 1 | n |
| 53.1% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 53.1% | 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)))) |
| 53.1% | 1 | k |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (neg.f64 n) (/.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
4 calls:
| 6.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 5.0ms | n |
| 5.0ms | k |
| 5.0ms | (*.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 |
|---|---|---|
| 53.0% | 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)))) |
| 53.0% | 1 | k |
| 53.0% | 1 | n |
| 53.0% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (neg.f64 n) (/.f64 #s(literal -1 binary64) k)) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
4 calls:
| 47.0ms | n |
| 4.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 4.0ms | k |
| 4.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 42.5% | 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)))) |
| 42.5% | 1 | k |
| 42.5% | 1 | n |
| 42.5% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
4 calls:
| 39.0ms | (*.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)))) |
| 2.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 2.0ms | n |
| 2.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 42.5% | 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)))) |
| 42.5% | 1 | k |
| 42.5% | 1 | n |
| 42.5% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
Total -0.0b remaining (-0.1%)
Threshold costs -0b (-0.1%)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
4 calls:
| 1.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 1.0ms | (*.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)))) |
| 1.0ms | n |
| 1.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 42.5% | 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)))) |
| 42.5% | 1 | k |
| 42.5% | 1 | n |
| 42.5% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 15.0ms | 0.026729992301662803 | 2.985828119755369 |
| 10.0ms | 112× | 0 | valid |
Compiled 327 to 291 computations (11% saved)
ival-mult: 2.0ms (26.4% of total)ival-pow: 2.0ms (26.4% of total)ival-div: 1.0ms (13.2% of total)ival-sqrt: 1.0ms (13.2% of total)ival-pi: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-sub: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 71 | 247 |
| 1 | 96 | 235 |
| 2 | 132 | 233 |
| 3 | 187 | 233 |
| 4 | 272 | 233 |
| 5 | 406 | 233 |
| 6 | 669 | 233 |
| 7 | 1834 | 233 |
| 8 | 4616 | 233 |
| 9 | 6821 | 233 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/2 binary64) k)))) |
(/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (sqrt.f64 k)) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(if (<=.f64 k #s(literal 1 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/2 binary64) k)))) |
(/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) (sqrt.f64 k)) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 k)) |
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) |
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(if (<=.f64 k #s(literal 1 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 53 | 257 |
| 0 | 87 | 253 |
| 1 | 315 | 219 |
| 2 | 1862 | 217 |
| 0 | 8166 | 217 |
| 0 | 45 | 257 |
| 0 | 72 | 244 |
| 1 | 238 | 231 |
| 2 | 1240 | 223 |
| 0 | 8398 | 223 |
| 0 | 128 | 517 |
| 1 | 345 | 504 |
| 2 | 1022 | 460 |
| 3 | 3355 | 433 |
| 4 | 5591 | 421 |
| 0 | 8473 | 406 |
| 0 | 46 | 261 |
| 0 | 74 | 241 |
| 1 | 231 | 227 |
| 2 | 1175 | 220 |
| 0 | 9148 | 220 |
| 0 | 13 | 43 |
| 0 | 22 | 43 |
| 1 | 89 | 40 |
| 2 | 497 | 38 |
| 3 | 4478 | 38 |
| 0 | 8506 | 37 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 1 095 to 604 computations (44.8% saved)
Compiled 522 to 168 computations (67.8% saved)
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