
Time bar (total: 11.1s)
| 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)
| 1.6s | 3 604× | 1 | invalid |
| 1.0s | 8 256× | 0 | valid |
| 400.0ms | 1 943× | 1 | exit |
| 152.0ms | 419× | 2 | invalid |
| 70.0ms | 523× | 0 | invalid |
| 37.0ms | 231× | 0 | exit |
ival-mult: 1.1s (40.9% of total)ival-pow: 571.0ms (22% of total)ival-div: 336.0ms (12.9% of total)adjust: 190.0ms (7.3% of total)ival-sqrt: 146.0ms (5.6% of total)ival-pi: 145.0ms (5.6% of total)ival-sub: 107.0ms (4.1% of total)exact: 19.0ms (0.7% of total)ival-true: 13.0ms (0.5% of total)ival-assert: 7.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 7 | 73 | (5.778167114658237e-246 2.817251554145798e+279) | 2 | (4.873996318183359e-17 3.1975295189893854e-43) | (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 | 78 | 22 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 5 | 2 |
| - | 73 | 176 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 5 | 2 | 0 |
| - | 73 | 20 | 156 |
| number | freq |
|---|---|
| 0 | 178 |
| 1 | 78 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 72.0ms | 512× | 0 | valid |
Compiled 128 to 43 computations (66.4% saved)
ival-pow: 10.0ms (27.6% of total)ival-mult: 9.0ms (24.8% of total)ival-div: 7.0ms (19.3% of total)ival-sqrt: 4.0ms (11% of total)ival-sub: 3.0ms (8.3% of total)ival-pi: 2.0ms (5.5% of total)exact: 1.0ms (2.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 88 |
| 1 | 71 | 76 |
| 2 | 145 | 74 |
| 3 | 227 | 74 |
| 4 | 296 | 74 |
| 5 | 363 | 74 |
| 6 | 428 | 74 |
| 7 | 501 | 74 |
| 8 | 528 | 74 |
| 9 | 541 | 74 |
| 10 | 547 | 74 |
| 0 | 13 | 16 |
| 0 | 22 | 16 |
| 1 | 37 | 14 |
| 2 | 50 | 14 |
| 3 | 67 | 14 |
| 4 | 80 | 14 |
| 5 | 98 | 14 |
| 6 | 132 | 14 |
| 7 | 202 | 14 |
| 8 | 227 | 14 |
| 9 | 247 | 14 |
| 10 | 257 | 14 |
| 0 | 257 | 14 |
| 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))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) |
Compiled 16 to 13 computations (18.8% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.5% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 16 to 13 computations (18.8% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 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: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 54 |
| 0 | 22 | 54 |
| 1 | 37 | 52 |
| 2 | 50 | 52 |
| 3 | 67 | 52 |
| 4 | 80 | 52 |
| 5 | 98 | 52 |
| 6 | 132 | 52 |
| 7 | 202 | 52 |
| 8 | 227 | 52 |
| 9 | 247 | 52 |
| 10 | 257 | 52 |
| 0 | 257 | 52 |
| 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))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(PI.f64) |
n |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.1328125 | (*.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 | 0.2232732627809995 | (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 #s(literal 1 binary64) (sqrt.f64 k)) | |
| accuracy | 0.265625 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 48.0ms | 256× | 0 | valid |
Compiled 56 to 15 computations (73.2% saved)
ival-pow: 5.0ms (26.4% of total)ival-mult: 4.0ms (21.2% of total)ival-div: 3.0ms (15.9% of total)ival-sub: 2.0ms (10.6% of total)ival-sqrt: 2.0ms (10.6% of total)ival-pi: 1.0ms (5.3% 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 #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) |
(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))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (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 (/ 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 | |
|---|---|---|---|---|
| 37.0ms | n | @ | -inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n)) |
| 33.0ms | n | @ | 0 | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n)) |
| 24.0ms | n | @ | inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 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 (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 (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 | 120 | 502 |
| 1 | 378 | 489 |
| 2 | 1377 | 453 |
| 3 | 4131 | 453 |
| 0 | 8166 | 441 |
| 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 (/ 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)))))) |
(* -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) |
(fma.f64 #s(literal 1 binary64) (*.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)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(fma.f64 (*.f64 (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))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/8 binary64)))) k (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (*.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) |
(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 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(+ (* 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))) |
(fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.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))) #s(literal 1/8 binary64)) k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.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)))) (* 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 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.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))) #s(literal 1/8 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)))))))) |
(* (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))) |
(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 (* (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 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))) |
(* 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 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.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))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 38 |
| 0 | 22 | 38 |
| 1 | 83 | 35 |
| 2 | 446 | 35 |
| 3 | 4007 | 29 |
| 0 | 8921 | 29 |
| 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 #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 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal -1/4 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))) |
(*.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (/.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) #s(literal 1 binary64)) |
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) |
(*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))) |
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (sqrt.f64 k))) |
(*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))) |
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (neg.f64 (sqrt.f64 k)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) |
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))) |
(/.f64 (*.f64 #s(literal 0 binary64) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 #s(literal 0 binary64) (*.f64 k #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 (*.f64 #s(literal 0 binary64) (sqrt.f64 n)) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (/.f64 (pow.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 n (*.f64 k #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 #s(literal 0 binary64) (sqrt.f64 n))) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64))) |
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) |
(/.f64 (*.f64 (*.f64 #s(literal 0 binary64) (sqrt.f64 n)) #s(literal -1 binary64)) (*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (*.f64 (*.f64 #s(literal 0 binary64) (sqrt.f64 n)) #s(literal 1 binary64)) (*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)) (sqrt.f64 k))) |
(/.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 0 binary64) (sqrt.f64 n))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sqrt.f64 n))) (*.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)))) |
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(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) |
(pow.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) (*.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) (*.f64 #s(literal 0 binary64) n)) |
(/.f64 (+.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64))) (fma.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)) (-.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) (*.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))))) |
(/.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 0 binary64)) |
(/.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 (PI.f64) (PI.f64) #s(literal 0 binary64))) |
(fma.f64 (*.f64 n (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 n (PI.f64))) |
(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 n (PI.f64))) |
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64)) (*.f64 n (PI.f64))) |
(fma.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 n (PI.f64))) |
(fma.f64 (*.f64 n #s(literal 2 binary64)) (cosh.f64 (log.f64 (PI.f64))) (*.f64 (*.f64 n #s(literal 2 binary64)) (sinh.f64 (log.f64 (PI.f64))))) |
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) n) (*.f64 n (PI.f64))) |
(fma.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) n)) (*.f64 n (PI.f64))) |
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)) (*.f64 n (PI.f64))) |
(fma.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64)) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 0 binary64) n) (*.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 0 binary64) n))) |
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 n (PI.f64))) |
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 n (PI.f64))) |
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)) (*.f64 n (PI.f64))) |
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n)) (*.f64 n (PI.f64))) |
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n) (*.f64 n (PI.f64))) |
(fma.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n (PI.f64)) (*.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n (PI.f64)))) |
(fma.f64 n (PI.f64) (*.f64 n (PI.f64))) |
(fma.f64 (PI.f64) n (*.f64 n (PI.f64))) |
(-.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) n))) |
(-.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (PI.f64)) n))) |
(-.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 n) (PI.f64))) |
(-.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) #s(literal 2 binary64))) |
(exp.f64 (log.f64 (*.f64 #s(literal 0 binary64) n))) |
(+.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 0 binary64) n)) (*.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 0 binary64) n))) |
(+.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64)))) |
(+.f64 (*.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n (PI.f64))) (*.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (cosh.f64 (log.f64 (PI.f64)))) (*.f64 (*.f64 n #s(literal 2 binary64)) (sinh.f64 (log.f64 (PI.f64))))) |
(+.f64 (cosh.f64 (log.f64 (*.f64 #s(literal 0 binary64) n))) (sinh.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)))) |
(+.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) |
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n #s(literal 2 binary64))))) |
(log.f64 (pow.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 0 binary64) n) n))) |
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) (*.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 2 binary64)))) |
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) (PI.f64)) (*.f64 (*.f64 n #s(literal 2 binary64)) (*.f64 n #s(literal 2 binary64))))) |
(log.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) n) (*.f64 #s(literal 0 binary64) n))) |
(log.f64 (pow.f64 (*.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) (exp.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))) n)) |
(log.f64 (/.f64 (pow.f64 (exp.f64 (PI.f64)) n) (pow.f64 (exp.f64 (PI.f64)) n))) |
(log.f64 (*.f64 (pow.f64 (exp.f64 (PI.f64)) n) (pow.f64 (exp.f64 (PI.f64)) n))) |
(log.f64 (pow.f64 #s(literal 1 binary64) n)) |
Compiled 7 537 to 1 169 computations (84.5% saved)
20 alts after pruning (20 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 318 | 20 | 338 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 319 | 20 | 339 |
| Status | Accuracy | Program |
|---|---|---|
| 28.5% | (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) | |
| 99.5% | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| 72.5% | (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))) | |
| ▶ | 72.5% | (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
| ▶ | 99.3% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 96.7% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64))))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| ▶ | 72.4% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) |
| 72.5% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))) | |
| 59.0% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.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))) #s(literal 1/8 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)))))))))) | |
| 53.6% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.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))) #s(literal 1/8 binary64)) k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) | |
| 99.5% | (*.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) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| 96.3% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))))) | |
| 42.3% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))) | |
| 41.2% | (*.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))))) | |
| 72.5% | (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| 96.6% | (*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| 50.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (*.f64 (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))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/8 binary64)))) k (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))) | |
| 50.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.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)) | |
| ▶ | 99.5% | #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)))) |
| ▶ | 30.2% | #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 1 270 to 876 computations (31% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) k) | |
| cost-diff | 0 | (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) | |
| cost-diff | 0 | (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | |
| cost-diff | 0 | (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) | |
| cost-diff | 0 | (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| cost-diff | 4 | (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) | |
| 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 (*.f64 #s(literal 2 binary64) n) (PI.f64)) | |
| cost-diff | 0 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) | |
| cost-diff | 0 | (*.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))) | |
| cost-diff | 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)))) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 50 | 359 |
| 0 | 84 | 355 |
| 1 | 130 | 339 |
| 2 | 190 | 339 |
| 3 | 295 | 339 |
| 4 | 449 | 339 |
| 5 | 656 | 339 |
| 6 | 820 | 339 |
| 7 | 877 | 339 |
| 8 | 899 | 339 |
| 9 | 908 | 339 |
| 0 | 908 | 339 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#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)))) |
(*.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))) |
(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) n) (PI.f64)) |
(*.f64 #s(literal 2 binary64) n) |
#s(literal 2 binary64) |
n |
(PI.f64) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal -1/2 binary64) |
k |
#s(literal 1/2 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
#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 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.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 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) |
(*.f64 n #s(literal 2 binary64)) |
n |
#s(literal 2 binary64) |
(sqrt.f64 (PI.f64)) |
(PI.f64) |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.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 |
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 n #s(literal 2 binary64)) |
n |
#s(literal 2 binary64) |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(PI.f64) |
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
#s(literal 2 binary64) |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) |
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 n (PI.f64)) |
n |
(PI.f64) |
(pow.f64 k #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
| Outputs |
|---|
#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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 (*.f64 (*.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))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(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 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) n) (PI.f64)) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) n) |
(*.f64 n #s(literal 2 binary64)) |
#s(literal 2 binary64) |
n |
(PI.f64) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal -1/2 binary64) |
k |
#s(literal 1/2 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
#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) n) k)) (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) n) k)) (sqrt.f64 #s(literal 2 binary64))) |
(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 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) |
(*.f64 n #s(literal 2 binary64)) |
n |
#s(literal 2 binary64) |
(sqrt.f64 (PI.f64)) |
(PI.f64) |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) |
(/.f64 (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 n #s(literal 2 binary64)) |
n |
#s(literal 2 binary64) |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(PI.f64) |
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
#s(literal 2 binary64) |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 n (PI.f64)) |
(*.f64 (PI.f64) n) |
n |
(PI.f64) |
(pow.f64 k #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.20126761869777615 | (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | |
| accuracy | 0.203125 | (*.f64 n (PI.f64)) | |
| accuracy | 0.3834762695368841 | (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) | |
| accuracy | 16.468349061674505 | (PI.f64) | |
| accuracy | 0.19140625 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| accuracy | 0.34603500976844204 | (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| accuracy | 0.3984375 | (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | |
| accuracy | 16.468349061674505 | (PI.f64) | |
| accuracy | 0.21712875976844204 | (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) | |
| accuracy | 0.2232732627809995 | (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | |
| accuracy | 0.734375 | (sqrt.f64 (PI.f64)) | |
| accuracy | 16.468349061674505 | (PI.f64) | |
| accuracy | 0.29916000976844204 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) | |
| accuracy | 7.143489998520762 | (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) | |
| accuracy | 16.468349061674505 | (PI.f64) | |
| accuracy | 20.809547139878784 | #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 | 0.1328125 | (*.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))) | |
| accuracy | 0.203125 | (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) | |
| accuracy | 0.2232732627809995 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) | |
| accuracy | 16.468349061674505 | (PI.f64) |
| 81.0ms | 188× | 0 | valid |
| 32.0ms | 68× | 0 | exit |
Compiled 338 to 46 computations (86.4% saved)
ival-pow: 36.0ms (40.9% of total)ival-mult: 29.0ms (33% of total)ival-sqrt: 10.0ms (11.4% of total)ival-div: 8.0ms (9.1% of total)ival-pi: 1.0ms (1.1% of total)ival-add: 1.0ms (1.1% of total)ival-sub: 1.0ms (1.1% of total)exact: 1.0ms (1.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#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)))) |
(*.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))) |
(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) 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)))) |
(*.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 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(pow.f64 #s(literal 2 binary64) (/.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) k) |
(PI.f64) |
(sqrt.f64 (PI.f64)) |
(pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 n (PI.f64)) |
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #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 (* 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 (/ 1 k)) |
(sqrt k) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2))))))) k) |
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))) (* k (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2))))))))))))))) (* (sqrt (* n (PI))) (sqrt 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)) (+ (* -1/16 (* (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))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (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 2) |
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(+ (sqrt 2) (* k (+ (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2))))))) |
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1/2 |
(+ 1/2 (* -1/2 k)) |
1 |
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(sqrt (PI)) |
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(sqrt (* n (PI))) |
(+ (sqrt (* n (PI))) (* -1/2 (* (* k (log (* n (PI)))) (sqrt (* n (PI)))))) |
(+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* 1/8 (* (* k (pow (log (* n (PI))) 2)) (sqrt (* n (PI)))))))) |
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
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(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k)))))) |
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* n (PI)) |
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(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k)))))) |
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(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k)))) |
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(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
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(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 88.0ms | n | @ | -inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow k -1/2))) (pow 2 (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2))) |
| 85.0ms | n | @ | inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow k -1/2))) (pow 2 (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2))) |
| 75.0ms | n | @ | 0 | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow k -1/2))) (pow 2 (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2))) |
| 46.0ms | k | @ | 0 | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow k -1/2))) (pow 2 (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2))) |
| 25.0ms | k | @ | -inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow k -1/2))) (pow 2 (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 422 | 2411 |
| 1 | 1557 | 2173 |
| 2 | 6931 | 2128 |
| 0 | 8451 | 2030 |
| 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 (* 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 (/ 1 k)) |
(sqrt k) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2))))))) k) |
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
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(/ (+ (* (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)) (+ (* -1/16 (* (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))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (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 2) |
(+ (sqrt 2) (* -1/2 (* k (* (log 2) (sqrt 2))))) |
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1/2 |
(+ 1/2 (* -1/2 k)) |
1 |
(+ 1 (* -1 k)) |
(sqrt (PI)) |
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(sqrt (* n (PI))) |
(+ (sqrt (* n (PI))) (* -1/2 (* (* k (log (* n (PI)))) (sqrt (* n (PI)))))) |
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 n)) (- 1 k)))))) |
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 n)) (- 1 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (log (* n (PI))) (- 1 k)))))) |
(exp (* 1/2 (* (log 2) (- 1 k)))) |
(* -1/2 k) |
(* k (- (* 1/2 (/ 1 k)) 1/2)) |
(* -1 k) |
(* k (- (/ 1 k) 1)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(exp (* 1/2 (* (log (PI)) (- 1 k)))) |
(exp (* 1/2 (* (log (* n (PI))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(* (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))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 n)) (+ 1 (* -1 k))))))) |
(* (exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 n)) (+ 1 (* -1 k)))))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) (* (exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))) |
(exp (* 1/2 (* (log 2) (+ 1 (* -1 k))))) |
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) |
(* -1 (* k (- 1 (/ 1 k)))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k))))) |
(exp (* 1/2 (* (log (* n (PI))) (+ 1 (* -1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k)))))) |
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* n (PI)) |
(exp (* 1/2 (* (+ (log n) (log (PI))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k)))))) |
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (PI)) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -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)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k)))))) |
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(exp (* 1/2 (* (+ (log (* -1 (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 n (PI.f64)) k))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (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 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.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 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 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 (fma.f64 (*.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 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))) k (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 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)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (*.f64 k (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #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 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 k k) (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/48 binary64)) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) |
(sqrt (/ (* n (PI)) k)) |
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(sqrt k) |
(sqrt.f64 k) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2))))))) k) |
(/.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (log.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (fma.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/48 binary64)) (fma.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (log.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) k (*.f64 (*.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (log.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) (fma.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))))) k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))) (* k (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2))))))))))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (log.f64 (PI.f64))) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (fma.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/48 binary64)) (fma.f64 (pow.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) k))) k (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) (fma.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))))) k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(/ (+ (* (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) |
(/.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) 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) |
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(*.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))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (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 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1 binary64)) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k)))))) |
(*.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) (*.f64 (-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) (*.f64 (-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))) #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))) |
(*.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)) (*.f64 (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) #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)))) |
(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))))) |
(exp (* 1/2 (* (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 50 | 252 |
| 0 | 84 | 221 |
| 1 | 258 | 208 |
| 2 | 1212 | 208 |
| 0 | 8196 | 208 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#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)))) |
(*.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))) |
(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) 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)))) |
(*.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 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(pow.f64 #s(literal 2 binary64) (/.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) k) |
(PI.f64) |
(sqrt.f64 (PI.f64)) |
(pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 n (PI.f64)) |
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.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))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (sqrt.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 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (sqrt.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 (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (sqrt.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 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (sqrt.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 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (sqrt.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 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (sqrt.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 (*.f64 (neg.f64 (sqrt.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 (pow.f64 k #s(literal -1/4 binary64)))) (*.f64 (neg.f64 (sqrt.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 (pow.f64 k #s(literal -1/4 binary64))))) |
(*.f64 (*.f64 (neg.f64 (sqrt.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 (neg.f64 (sqrt.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 (sqrt.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 (pow.f64 k #s(literal -1/4 binary64)))) (*.f64 (sqrt.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 (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))) (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 k #s(literal -1/4 binary64)) (sqrt.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 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.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 (*.f64 (sqrt.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 (sqrt.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 k #s(literal -1/2 binary64)) (sqrt.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 (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 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (*.f64 k (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 (sqrt.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 (sqrt.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 (*.f64 n #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))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 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)))) |
(*.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))) |
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.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 2 binary64)) |
(pow.f64 (*.f64 (sqrt.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))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal -1 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))))) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 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))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (neg.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))) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (neg.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))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 #s(literal -1 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)))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 #s(literal 1 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)))) (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))) #s(literal -1 binary64)) (neg.f64 (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))) #s(literal 1 binary64)) (sqrt.f64 k)) |
(neg.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))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))) |
(neg.f64 (*.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))))) |
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64) (*.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))))) |
(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (*.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))))) |
(exp.f64 (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.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))))) |
(exp.f64 (fma.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 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.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 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.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 (log.f64 k) #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (sqrt.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 (sqrt.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 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 2 binary64)))) |
(*.f64 (neg.f64 (neg.f64 (sqrt.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 (neg.f64 (sqrt.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 (exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
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(*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64))) |
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(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
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(/.f64 (sqrt.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 k))) |
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(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))) |
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(+.f64 (cosh.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))) |
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(fma.f64 (neg.f64 (neg.f64 n)) (PI.f64) (*.f64 (PI.f64) n)) |
(fma.f64 (exp.f64 (log.f64 n)) (PI.f64) (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 (PI.f64) n)) |
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(fma.f64 (neg.f64 n) (neg.f64 (PI.f64)) (*.f64 (PI.f64) n)) |
(fma.f64 (neg.f64 (PI.f64)) (neg.f64 n) (*.f64 (PI.f64) n)) |
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(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (PI.f64) n)) |
(fma.f64 (PI.f64) (neg.f64 (neg.f64 n)) (*.f64 (PI.f64) n)) |
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(-.f64 (*.f64 (PI.f64) n) (*.f64 (neg.f64 n) (PI.f64))) |
(exp.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
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(*.f64 (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))) |
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(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))) |
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(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64))) |
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(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) |
Compiled 45 005 to 5 178 computations (88.5% saved)
18 alts after pruning (16 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 385 | 14 | 1 399 |
| Fresh | 13 | 2 | 15 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 0 | 0 |
| Total | 1 401 | 18 | 1 419 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 28.5% | (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) |
| ▶ | 99.7% | (/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
| 99.5% | (*.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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) | |
| 41.2% | (*.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))))) | |
| 99.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.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)) (sqrt.f64 k))) | |
| 41.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) | |
| ✓ | 99.5% | #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)))) |
| 99.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 k (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)))))) | |
| 99.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| ▶ | 99.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 72.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 30.1% | #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 n k)))) | |
| ▶ | 41.2% | #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)))) |
| 41.2% | #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))))) | |
| 30.2% | #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)))) | |
| ✓ | 30.2% | #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)))) |
| 41.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| ▶ | 30.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
Compiled 980 to 757 computations (22.8% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) | |
| cost-diff | 0 | (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) | |
| cost-diff | 2 | (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) | |
| cost-diff | 0 | (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)) | |
| cost-diff | 2 | (*.f64 #s(literal 0 binary64) n) | |
| cost-diff | 3 | (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) | |
| cost-diff | 6 | (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) | |
| cost-diff | 0 | (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) | |
| cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.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 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) | |
| cost-diff | 0 | (/.f64 (*.f64 (PI.f64) n) k) | |
| cost-diff | 0 | (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) | |
| cost-diff | 0 | (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) | |
| cost-diff | 0 | (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) | |
| cost-diff | 0 | (*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 48 | 342 |
| 0 | 77 | 317 |
| 1 | 120 | 311 |
| 2 | 181 | 311 |
| 3 | 267 | 311 |
| 4 | 320 | 311 |
| 5 | 381 | 311 |
| 6 | 493 | 311 |
| 7 | 722 | 311 |
| 8 | 867 | 311 |
| 9 | 923 | 311 |
| 10 | 953 | 311 |
| 0 | 953 | 311 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (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 -1/2 binary64)) k) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
#s(literal -1/2 binary64) |
k |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) |
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) |
(/.f64 (*.f64 (PI.f64) n) k) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
k |
#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 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
(sqrt.f64 k) |
k |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) |
(*.f64 #s(literal 0 binary64) n) |
#s(literal 0 binary64) |
n |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
#s(literal 8 binary64) |
(sqrt.f64 k) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 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) |
#s(literal 1 binary64) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) |
(/.f64 k #s(literal 2 binary64)) |
k |
(sqrt.f64 k) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64)) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) |
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64)) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64)) k)) |
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) |
(pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64)) k) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal -1/2 binary64)) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
#s(literal -1/2 binary64) |
k |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) |
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) |
(/.f64 (*.f64 (PI.f64) n) k) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
k |
#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 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
(*.f64 (PI.f64) n) |
(PI.f64) |
n |
(sqrt.f64 k) |
k |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) |
#s(literal 0 binary64) |
(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) |
#s(literal 0 binary64) |
(*.f64 #s(literal 0 binary64) n) |
#s(literal 0 binary64) |
#s(literal 0 binary64) |
n |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
#s(literal 8 binary64) |
(sqrt.f64 k) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)) |
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) |
(/.f64 k #s(literal 2 binary64)) |
k |
(sqrt.f64 k) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.04296875 | (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) | |
| accuracy | 0.11328125 | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) | |
| accuracy | 0.16796875 | (/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) | |
| accuracy | 35.842877369526924 | (PI.f64) | |
| accuracy | 0.0 | (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)) | |
| accuracy | 0.0 | (-.f64 #s(literal 1 binary64) k) | |
| accuracy | 0.0 | (*.f64 #s(literal 0 binary64) n) | |
| accuracy | 0.0 | (sqrt.f64 k) | |
| accuracy | 0.1171875 | (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) | |
| accuracy | 0.17806625976844204 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) | |
| accuracy | 1.4354895321793715 | #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)))) | |
| accuracy | 35.842877369526924 | (PI.f64) | |
| accuracy | 0.11328125 | (*.f64 (PI.f64) n) | |
| accuracy | 1.4354895321793715 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) | |
| accuracy | 7.100240972503172 | (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) | |
| accuracy | 35.842877369526924 | (PI.f64) | |
| accuracy | 0.0625 | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) | |
| accuracy | 0.11328125 | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) | |
| accuracy | 0.1328125 | (*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) | |
| accuracy | 35.842877369526924 | (PI.f64) |
| 63.0ms | 108× | 0 | valid |
| 57.0ms | 148× | 0 | invalid |
Compiled 302 to 44 computations (85.4% saved)
ival-div: 36.0ms (37.5% of total)ival-pow: 25.0ms (26.1% of total)ival-mult: 21.0ms (21.9% of total)ival-sqrt: 11.0ms (11.5% of total)ival-pi: 1.0ms (1% of total)ival-sub: 1.0ms (1% of total)exact: 1.0ms (1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (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 -1/2 binary64)) k) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) |
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) |
(/.f64 (*.f64 (PI.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 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) |
(sqrt.f64 #s(literal 2 binary64)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) |
(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) |
(*.f64 #s(literal 0 binary64) n) |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)) |
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(PI.f64) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
(*.f64 (PI.f64) n) |
(sqrt.f64 k) |
(-.f64 #s(literal 1 binary64) k) |
| 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 (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k) |
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI))))) |
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) |
1 |
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))))) |
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))) |
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))) |
(* 2 (/ (* n (PI)) k)) |
(/ (* n (PI)) k) |
(sqrt (/ (* n (PI)) k)) |
(exp (* 1/8 (+ (log 0) (* 20 (log k))))) |
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))) |
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) |
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (+ (log 0) (* 20 (log k)))))) |
(/ (+ (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))) k) |
(/ (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))))) (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k) |
1/8 |
(+ 1/8 (* -1/8 k)) |
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* 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)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(sqrt k) |
(+ 1 (* -1 k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))) |
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))) |
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k) |
(exp (* 1/8 (* (log 0) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (- 1 k))))) |
(* -1/8 k) |
(* k (- (* 1/8 (/ 1 k)) 1/8)) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))) |
(* -1 k) |
(* k (- (/ 1 k) 1)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(exp (* 1/8 (* (log 0) (+ 1 (* -1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (+ 1 (* -1 k)))))) |
(* -1 (* k (- 1/8 (* 1/8 (/ 1 k))))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* k (- 1 (/ 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2))) |
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2))) |
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) |
(exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* 1/8 (* n (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* n (+ (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* n (+ (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))) (* n (+ (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k))))))) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))) |
(+ (* 1/8 (* (sqrt (/ 1 k)) (* n (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))))) |
(+ (* n (+ (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))) (* (sqrt (/ 1 k)) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))))) |
(+ (* n (+ (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))) (* n (+ (* (sqrt (/ 1 k)) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))))) |
0 |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(* n (PI)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2)))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)) (+ (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) (pow n 3)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2))))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) |
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))))) |
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (+ (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2))))) |
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (+ (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) (+ (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) (pow n 3))) (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2)))))) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (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) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k))))) |
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) 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 (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n))) |
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(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))) n)) (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))))) n))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))) |
(+ (* -1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))) |
(+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n))) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))) n)) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 131.0ms | n | @ | -inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt k) (- 1 k)) |
| 51.0ms | n | @ | 0 | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt k) (- 1 k)) |
| 39.0ms | n | @ | inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt k) (- 1 k)) |
| 7.0ms | k | @ | -inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt k) (- 1 k)) |
| 7.0ms | k | @ | 0 | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt k) (- 1 k)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 486 | 3741 |
| 1 | 1774 | 3470 |
| 0 | 8041 | 3265 |
| 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 (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k) |
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI))))) |
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) |
1 |
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))))) |
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))) |
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))) |
(* 2 (/ (* n (PI)) k)) |
(/ (* n (PI)) k) |
(sqrt (/ (* n (PI)) k)) |
(exp (* 1/8 (+ (log 0) (* 20 (log k))))) |
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))) |
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) |
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (+ (log 0) (* 20 (log k)))))) |
(/ (+ (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))) k) |
(/ (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))))) (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k) |
1/8 |
(+ 1/8 (* -1/8 k)) |
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* 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)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(sqrt k) |
(+ 1 (* -1 k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))) |
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))) |
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k) |
(exp (* 1/8 (* (log 0) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (- 1 k))))) |
(* -1/8 k) |
(* k (- (* 1/8 (/ 1 k)) 1/8)) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))) |
(* -1 k) |
(* k (- (/ 1 k) 1)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(exp (* 1/8 (* (log 0) (+ 1 (* -1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (+ 1 (* -1 k)))))) |
(* -1 (* k (- 1/8 (* 1/8 (/ 1 k))))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* -1 (* k (- 1 (/ 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2))) |
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2))) |
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) |
(exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* 1/8 (* n (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* n (+ (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))))) |
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(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))) |
(+ (* 1/8 (* (sqrt (/ 1 k)) (* n (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))))) |
(+ (* n (+ (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))) (* (sqrt (/ 1 k)) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))))) |
(+ (* n (+ (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))) (* n (+ (* (sqrt (/ 1 k)) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))))) |
0 |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(* n (PI)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2)))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)) (+ (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) (pow n 3)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2))))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) |
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))))) |
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (+ (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2))))) |
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (+ (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) (+ (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) (pow n 3))) (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2)))))) |
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (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) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k))))) |
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) 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 (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n)) (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))))) n))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))) n)) (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))))) n))) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))) |
(+ (* -1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))) |
(+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n))) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))) n)) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (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 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.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 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 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 (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.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 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k) |
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 k k) (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) k) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64))))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))))) |
(fma.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k #s(literal 1 binary64)) |
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))) |
(fma.f64 (fma.f64 (*.f64 k #s(literal 1/2 binary64)) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))) k #s(literal 1 binary64)) |
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) k) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 3 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) #s(literal 1/2 binary64))) k (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))) k #s(literal 1 binary64)) |
(* 2 (/ (* n (PI)) k)) |
(*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)) |
(/ (* n (PI)) k) |
(/.f64 (*.f64 n (PI.f64)) k) |
(sqrt (/ (* n (PI)) k)) |
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
(exp (* 1/8 (+ (log 0) (* 20 (log k))))) |
(pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) |
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))) |
(fma.f64 (*.f64 k (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))))) |
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) |
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(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1 binary64)) |
(exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n))) |
(fma.f64 (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 1 binary64) k)) (/.f64 (NAN.f64) n)) #s(literal -1/8 binary64) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n)) (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))))) n))) |
(-.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 1 binary64) k))) (NAN.f64) (*.f64 (neg.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (*.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (NAN.f64) (NAN.f64)) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) n))) n)) |
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))) n)) (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))))) n))) |
(-.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (NAN.f64) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))))) (-.f64 #s(literal 1 binary64) k) (/.f64 (fma.f64 (neg.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (NAN.f64)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64)) #s(literal 1/128 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n) (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (fma.f64 (*.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (NAN.f64) (NAN.f64)) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))))) (neg.f64 n))) n)) |
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(+ (* -1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))) |
(fma.f64 (*.f64 (*.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 1 binary64) k)) (/.f64 (NAN.f64) n)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n))) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))) |
(fma.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 1 binary64) k))) (NAN.f64) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (*.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (NAN.f64) (NAN.f64)) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) n))) (neg.f64 n))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))) n)) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))) |
(fma.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (NAN.f64) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))))) (-.f64 #s(literal 1 binary64) k) (/.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (fma.f64 (*.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (NAN.f64) (NAN.f64)) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (NAN.f64)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64)) #s(literal 1/128 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n))) (neg.f64 n))) (neg.f64 n))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))) |
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) |
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 48 | 260 |
| 0 | 77 | 229 |
| 1 | 236 | 201 |
| 2 | 1045 | 100 |
| 0 | 9791 | 97 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (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 -1/2 binary64)) k) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) |
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) |
(/.f64 (*.f64 (PI.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 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) |
(sqrt.f64 #s(literal 2 binary64)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) |
(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) |
(*.f64 #s(literal 0 binary64) n) |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)) |
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(PI.f64) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
(*.f64 (PI.f64) n) |
(sqrt.f64 k) |
(-.f64 #s(literal 1 binary64) k) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n))) #s(literal 0 binary64)) |
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) #s(literal 0 binary64)) |
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 n (*.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) |
(*.f64 (*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n))) #s(literal 0 binary64)) |
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(*.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 n)) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 n)) #s(literal 0 binary64)) |
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) #s(literal 1 binary64)) #s(literal 0 binary64)) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 n))) #s(literal 0 binary64)) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 #s(literal 0 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 #s(literal 0 binary64) (pow.f64 (pow.f64 n #s(literal -1/2 binary64)) k)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) |
(*.f64 (*.f64 #s(literal 0 binary64) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) k)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) k)) |
(*.f64 (*.f64 #s(literal 0 binary64) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) k)) |
(*.f64 (*.f64 #s(literal 0 binary64) (pow.f64 n (*.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k))) |
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(*.f64 (*.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (neg.f64 (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) k)))) |
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#s(literal 0 binary64) |
#s(literal 0 binary64) |
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(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64))))) |
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(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)) |
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(pow.f64 (PI.f64) #s(literal 1 binary64)) |
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(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(exp.f64 (log.f64 (PI.f64))) |
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(PI.f64) |
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(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal -1/4 binary64)) (pow.f64 (PI.f64) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal -1/4 binary64)) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal -1/4 binary64)) (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64))) (neg.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)))) |
(*.f64 (pow.f64 n #s(literal -1/4 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/4 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)) (pow.f64 (PI.f64) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 n #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 n #s(literal -1/2 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64))) |
(*.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (*.f64 (pow.f64 n #s(literal -1/2 binary64)) (pow.f64 n #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (fabs.f64 (pow.f64 n #s(literal -1/4 binary64)))) |
(*.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (pow.f64 n #s(literal -1/8 binary64))) |
(*.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (pow.f64 n #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (pow.f64 n #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64))) |
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal 0 binary64))) |
(pow.f64 (neg.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64))) #s(literal 2 binary64)) |
(pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) |
(pow.f64 #s(literal 0 binary64) #s(literal -1/4 binary64)) |
(pow.f64 #s(literal 0 binary64) #s(literal -1 binary64)) |
(pow.f64 #s(literal 0 binary64) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) #s(literal 4 binary64)) |
(pow.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64))))) (*.f64 (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))))) (-.f64 (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))))) |
(/.f64 (+.f64 (pow.f64 (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (-.f64 (*.f64 (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64))))) (*.f64 (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))))))) |
(neg.f64 (neg.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)))) |
(fma.f64 (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (*.f64 (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)))) |
(fma.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (*.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))))) |
(sqrt.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64))) |
(fabs.f64 (neg.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)))) |
(fabs.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 #s(literal 0 binary64)) #s(literal -1/8 binary64))) |
(exp.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) |
(+.f64 (*.f64 (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64))) (*.f64 (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)))) |
(+.f64 (*.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64))))) (*.f64 (pow.f64 #s(literal 0 binary64) #s(literal -1/8 binary64)) (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))))) |
(+.f64 (cosh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64)))) (sinh.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 0 binary64))))) |
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64)))) |
(*.f64 (*.f64 n (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (*.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (neg.f64 (neg.f64 n)) (PI.f64)) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n))) |
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))) |
(*.f64 (neg.f64 n) (neg.f64 (PI.f64))) |
(*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) n))) |
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) n)) |
(*.f64 (neg.f64 (PI.f64)) (neg.f64 n)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n)) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n)) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n)) |
(*.f64 (PI.f64) (neg.f64 (neg.f64 n))) |
(*.f64 (PI.f64) n) |
(*.f64 n (PI.f64)) |
(neg.f64 (*.f64 (neg.f64 n) (PI.f64))) |
(fma.f64 (cosh.f64 (log.f64 (PI.f64))) n (*.f64 (sinh.f64 (log.f64 (PI.f64))) n)) |
(fma.f64 n (cosh.f64 (log.f64 (PI.f64))) (*.f64 n (sinh.f64 (log.f64 (PI.f64))))) |
(+.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) n) (*.f64 (sinh.f64 (log.f64 (PI.f64))) n)) |
(+.f64 (*.f64 n (cosh.f64 (log.f64 (PI.f64)))) (*.f64 n (sinh.f64 (log.f64 (PI.f64))))) |
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n)) |
(*.f64 (neg.f64 (pow.f64 k #s(literal 1/4 binary64))) (neg.f64 (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (fabs.f64 (pow.f64 k #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 k)) |
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 k) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 k) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(pow.f64 (exp.f64 (log.f64 k)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 k k) #s(literal 1/4 binary64)) |
(pow.f64 k #s(literal 1/2 binary64)) |
(neg.f64 (neg.f64 (sqrt.f64 k))) |
(sqrt.f64 k) |
(exp.f64 (log.f64 (sqrt.f64 k))) |
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 k))) (sinh.f64 (log.f64 (sqrt.f64 k)))) |
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))))) (+.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))))) |
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))) (+.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))) |
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))))))) |
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))))) |
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k))) (neg.f64 (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k))) (+.f64 k #s(literal 1 binary64))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))))) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))) (*.f64 (+.f64 k #s(literal 1 binary64)) (*.f64 k k))) (*.f64 (+.f64 k #s(literal 1 binary64)) (+.f64 k #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))) |
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k)) (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (neg.f64 (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 k #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (neg.f64 (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) |
(neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k))) |
(-.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64)))) |
(-.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) k) |
(+.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 k) k) (+.f64 k #s(literal 1 binary64)))) |
(+.f64 #s(literal 1 binary64) (neg.f64 k)) |
Compiled 48 800 to 5 836 computations (88% saved)
26 alts after pruning (21 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 586 | 12 | 1 598 |
| Fresh | 2 | 9 | 11 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 2 | 2 |
| Total | 1 590 | 26 | 1 616 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.7% | (/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
| ▶ | 99.5% | (*.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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
| 28.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) | |
| 99.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.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)) (sqrt.f64 k))) | |
| 41.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) | |
| ✓ | 99.5% | #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)))) |
| 99.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 k (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)))))) | |
| 99.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 72.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| ▶ | 99.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 41.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| ▶ | 30.1% | #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 n k)))) |
| ✓ | 41.2% | #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)))) |
| 41.2% | #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))))) | |
| ✓ | 30.2% | #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)))) |
| 41.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| ▶ | 30.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
| ✓ | 30.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
| 30.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) | |
| 4.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) | |
| 4.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) | |
| 30.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64)))) | |
| 30.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) | |
| 30.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) | |
| 75.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (*.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) k) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))))) | |
| ▶ | 32.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
Compiled 1 451 to 1 113 computations (23.3% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 2 | (*.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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) | |
| cost-diff | 0 | (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)) | |
| cost-diff | 0 | (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) | |
| cost-diff | 4 | (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) | |
| cost-diff | 0 | (*.f64 (PI.f64) #s(literal 2 binary64)) | |
| cost-diff | 0 | (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) | |
| cost-diff | 0 | #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 n k)))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) | |
| cost-diff | 0 | (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) | |
| cost-diff | 0 | (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) | |
| cost-diff | 0 | (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 413 |
| 0 | 88 | 409 |
| 1 | 128 | 383 |
| 2 | 185 | 383 |
| 3 | 364 | 383 |
| 4 | 677 | 383 |
| 5 | 1150 | 383 |
| 6 | 1535 | 383 |
| 7 | 1750 | 383 |
| 8 | 1867 | 383 |
| 9 | 1870 | 383 |
| 10 | 1870 | 383 |
| 0 | 1870 | 383 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) |
#s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) |
#s(literal 1 binary64) |
(*.f64 n (PI.f64)) |
n |
(PI.f64) |
k |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#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 n k)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 n k)) |
(/.f64 n k) |
n |
k |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))) |
(*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)) |
(/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) |
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 n (sqrt.f64 (PI.f64))) |
n |
(sqrt.f64 (PI.f64)) |
(PI.f64) |
k |
#s(literal 2 binary64) |
(*.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 (-.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 |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
#s(literal -2 binary64) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) k))) |
(*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) k)) |
(*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) k)) |
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) |
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) k) |
#s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) |
#s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) |
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) |
#s(literal 1 binary64) |
(*.f64 n (PI.f64)) |
(*.f64 (PI.f64) n) |
n |
(PI.f64) |
k |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#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 n k)))) |
#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))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 n k)) |
(/.f64 n k) |
n |
k |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) |
(/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) |
(*.f64 (/.f64 n k) (PI.f64)) |
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 (PI.f64) n) |
(*.f64 n (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (PI.f64)) n) |
n |
(sqrt.f64 (PI.f64)) |
(PI.f64) |
k |
#s(literal 2 binary64) |
(*.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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) 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 |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) |
n |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)) |
(-.f64 #s(literal 1 binary64) k) |
#s(literal -2 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.19140625 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| accuracy | 0.203125 | (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) | |
| accuracy | 0.22500860515192628 | (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) | |
| accuracy | 16.468349061674505 | (PI.f64) | |
| accuracy | 0.734375 | (sqrt.f64 (PI.f64)) | |
| accuracy | 7.139303472503172 | (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))) | |
| accuracy | 16.468349061674505 | (PI.f64) | |
| accuracy | 20.809547139878784 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) | |
| accuracy | 0.734375 | (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) | |
| accuracy | 7.140029582818521 | (sqrt.f64 (/.f64 n k)) | |
| accuracy | 16.468349061674505 | (PI.f64) | |
| accuracy | 20.809547139878784 | #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 n k)))) | |
| accuracy | 26.786522553618177 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) | |
| accuracy | 0.203125 | (*.f64 n (PI.f64)) | |
| accuracy | 0.21875 | (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) | |
| accuracy | 0.3756637695368841 | (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) | |
| accuracy | 16.468349061674505 | (PI.f64) |
| 108.0ms | 188× | 0 | valid |
| 32.0ms | 68× | 0 | exit |
Compiled 318 to 47 computations (85.2% saved)
ival-mult: 29.0ms (34.6% of total)ival-sqrt: 20.0ms (23.9% of total)ival-pow: 18.0ms (21.5% of total)ival-div: 13.0ms (15.5% of total)ival-pi: 1.0ms (1.2% of total)ival-sub: 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 |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#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 n k)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(*.f64 (*.f64 n (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 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))) |
(*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)) |
(*.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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) |
(PI.f64) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) |
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) |
(*.f64 n (PI.f64)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt.f64 (PI.f64)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) |
(*.f64 n (*.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 (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k) |
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI))))) |
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) |
1 |
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))))) |
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))) |
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))) |
(* 2 (/ (* n (PI)) k)) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(sqrt (/ 1 k)) |
(sqrt k) |
(* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))) |
(+ (* -1/2 (* (/ (* k (log (* 2 (* n (PI))))) (sqrt 1/2)) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))) |
(+ (* k (- (* -1 (* k (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))) |
(+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))) |
(sqrt (/ n k)) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))) |
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))) |
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 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)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ n 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))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2))) |
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2))) |
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) |
(* n (PI)) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))) |
(/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(/ 1 (* n (PI))) |
(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))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 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)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k))))) |
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))) |
(/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 62.0ms | n | @ | inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (* n (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2)) (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2))) (PI) (* (sqrt 1/2) (sqrt (/ 1 (* n (PI))))) (/ 1 (* n (PI))) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (pow (* n (* (PI) 2)) (/ (- 1 k) -2)) (* n (* (PI) 2))) |
| 25.0ms | k | @ | -inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (* n (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2)) (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2))) (PI) (* (sqrt 1/2) (sqrt (/ 1 (* n (PI))))) (/ 1 (* n (PI))) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (pow (* n (* (PI) 2)) (/ (- 1 k) -2)) (* n (* (PI) 2))) |
| 24.0ms | n | @ | -inf | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (* n (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2)) (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2))) (PI) (* (sqrt 1/2) (sqrt (/ 1 (* n (PI))))) (/ 1 (* n (PI))) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (pow (* n (* (PI) 2)) (/ (- 1 k) -2)) (* n (* (PI) 2))) |
| 18.0ms | n | @ | 0 | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (* n (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2)) (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2))) (PI) (* (sqrt 1/2) (sqrt (/ 1 (* n (PI))))) (/ 1 (* n (PI))) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (pow (* n (* (PI) 2)) (/ (- 1 k) -2)) (* n (* (PI) 2))) |
| 5.0ms | k | @ | 0 | ((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (* n (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2)) (* (/ (* (* n (sqrt (PI))) (sqrt (PI))) k) 2) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (/ (- 1 k) -2))) (PI) (* (sqrt 1/2) (sqrt (/ 1 (* n (PI))))) (/ 1 (* n (PI))) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (pow (* n (* (PI) 2)) (/ (- 1 k) -2)) (* n (* (PI) 2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 313 | 1853 |
| 1 | 1084 | 1765 |
| 2 | 4392 | 1724 |
| 0 | 8124 | 1680 |
| 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 (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k) |
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI))))) |
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) |
1 |
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))))) |
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))) |
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))) |
(* 2 (/ (* n (PI)) k)) |
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k) |
(sqrt (/ 1 k)) |
(sqrt k) |
(* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))) |
(+ (* -1/2 (* (/ (* k (log (* 2 (* n (PI))))) (sqrt 1/2)) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))) |
(+ (* k (- (* -1 (* k (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))) |
(+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))) |
(sqrt (/ n k)) |
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) |
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))) |
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))) |
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 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)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ n 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))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2))) |
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2))) |
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) |
(* n (PI)) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))) |
(/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(/ 1 (* n (PI))) |
(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))))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 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)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k))))) |
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))) |
(/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(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 n (PI.f64)) k))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (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 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.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 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 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 (fma.f64 (*.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 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))) k (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k) |
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
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(*.f64 (*.f64 n (PI.f64)) #s(literal 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 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (/ 1 (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 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(/ 1 (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 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) |
(exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k))) |
(* (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) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k))))) |
(*.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) k)) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k))))) |
(*.f64 (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) k)) |
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k) |
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.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 n (PI.f64)) 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 n (PI.f64)) k)))) |
(* (sqrt (/ 1 k)) (/ 1 (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 (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))))) |
(* (sqrt (/ 1 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2))) |
(*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) |
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 n k)) #s(literal 1 binary64)) |
(exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 320 |
| 0 | 88 | 294 |
| 1 | 243 | 270 |
| 2 | 1068 | 266 |
| 0 | 8478 | 266 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#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 n k)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(*.f64 (*.f64 n (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 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))) |
(*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)) |
(*.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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) |
(PI.f64) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) |
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) |
(*.f64 n (PI.f64)) |
(sqrt.f64 (/.f64 n k)) |
(sqrt.f64 (PI.f64)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) |
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (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 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 n)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n)) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)))) (neg.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)))) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 n))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) (*.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) |
(*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) 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 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) (*.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 n)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (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)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (pow.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)))) |
(*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) (/.f64 (/.f64 k #s(literal -2 binary64)) #s(literal -2 binary64))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) (/.f64 (/.f64 k #s(literal -2 binary64)) #s(literal -2 binary64))) (*.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))))) |
(*.f64 (neg.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) (*.f64 (neg.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (pow.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (sqrt.f64 n) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) |
(*.f64 (sqrt.f64 n) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (pow.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) |
(*.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (*.f64 (sqrt.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (pow.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (sqrt.f64 n) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (pow.f64 k #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) #s(literal 1 binary64)) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k)) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (pow.f64 k #s(literal -1/2 binary64)))) |
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(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (cbrt.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) |
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64)))) |
(*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (exp.f64 (log.f64 n))) |
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) |
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n) (sqrt.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 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) n)) |
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (PI.f64)) n)) |
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) n))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (*.f64 (sqrt.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 (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))) n)) |
(*.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 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 (cbrt.f64 (PI.f64)) n (*.f64 (cbrt.f64 (PI.f64)) n))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) n)) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) n))) |
(*.f64 (cbrt.f64 (PI.f64)) (fma.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) |
(*.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 #s(literal 2 binary64) n))) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n)) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) |
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) |
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (-.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64))) (fma.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n) (-.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))))) |
(/.f64 (*.f64 n #s(literal 0 binary64)) #s(literal 0 binary64)) |
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (PI.f64) (PI.f64) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))) (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (PI.f64) n)) |
(fma.f64 (neg.f64 (*.f64 (neg.f64 n) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)) (*.f64 (PI.f64) n)) |
(fma.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 n #s(literal 2 binary64)) (cosh.f64 (log.f64 (PI.f64))) (*.f64 (*.f64 n #s(literal 2 binary64)) (sinh.f64 (log.f64 (PI.f64))))) |
(fma.f64 (*.f64 #s(literal 2 binary64) n) (cosh.f64 (log.f64 (PI.f64))) (*.f64 (*.f64 #s(literal 2 binary64) n) (sinh.f64 (log.f64 (PI.f64))))) |
(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 (neg.f64 n) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) n)) |
(fma.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) n)) (*.f64 (PI.f64) n)) |
(fma.f64 (neg.f64 (PI.f64)) (neg.f64 n) (*.f64 (PI.f64) n)) |
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 n) (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) n)) |
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)) (*.f64 (PI.f64) n)) |
(fma.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64)) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) n) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) n))) |
(fma.f64 (neg.f64 n) (neg.f64 (PI.f64)) (*.f64 (PI.f64) n)) |
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 (PI.f64) n)) |
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n)) (*.f64 (PI.f64) n)) |
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)) (*.f64 (PI.f64) n)) |
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n) (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64)) (*.f64 (PI.f64) n)) |
(fma.f64 (sqrt.f64 (PI.f64)) (neg.f64 (*.f64 (neg.f64 n) (sqrt.f64 (PI.f64)))) (*.f64 (PI.f64) n)) |
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (PI.f64) n)) |
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n)) |
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n)) |
(-.f64 (*.f64 (PI.f64) n) (*.f64 (neg.f64 n) (PI.f64))) |
(exp.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) |
(+.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64)))) |
(+.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) n)) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) n))) |
(+.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (cosh.f64 (log.f64 (PI.f64)))) (*.f64 (*.f64 n #s(literal 2 binary64)) (sinh.f64 (log.f64 (PI.f64))))) |
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (cosh.f64 (log.f64 (PI.f64)))) (*.f64 (*.f64 #s(literal 2 binary64) n) (sinh.f64 (log.f64 (PI.f64))))) |
(+.f64 (cosh.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sinh.f64 (log.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) |
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) |
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64)))) |
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))) |
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)) n)) |
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) #s(literal 2 binary64))) |
(log.f64 (*.f64 (pow.f64 (exp.f64 (PI.f64)) n) (pow.f64 (exp.f64 (PI.f64)) n))) |
Compiled 80 334 to 9 373 computations (88.3% saved)
27 alts after pruning (22 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2 137 | 15 | 2 152 |
| Fresh | 9 | 7 | 16 |
| Picked | 3 | 2 | 5 |
| Done | 2 | 3 | 5 |
| Total | 2 151 | 27 | 2 178 |
| Status | Accuracy | Program |
|---|---|---|
| 75.2% | (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64)))) | |
| 99.7% | (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) | |
| 99.4% | (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) (sqrt.f64 k))) | |
| 99.5% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) | |
| 99.5% | (*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) | |
| 28.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) | |
| 99.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.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)) (sqrt.f64 k))) | |
| 41.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))) | |
| ✓ | 99.5% | #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)))) |
| 75.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))) | |
| 30.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) | |
| 41.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64))))) | |
| 41.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) | |
| 41.1% | #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 n) (sqrt.f64 k)))) | |
| 41.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) | |
| 41.2% | #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))))) | |
| ✓ | 30.2% | #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)))) |
| 41.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| ✓ | 30.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
| ✓ | 30.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
| 30.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))))) | |
| 30.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) | |
| 4.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) | |
| 4.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) | |
| 30.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) | |
| 30.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) | |
| ✓ | 32.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
Compiled 2 538 to 900 computations (64.5% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#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 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) |
#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 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (*.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 (PI.f64) n)) (sqrt.f64 k)))) |
#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 n) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))) |
#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 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 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 (*.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)) (sqrt.f64 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) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(*.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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (*.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) k) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 k (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 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (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 (*.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)) |
(*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.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))) #s(literal 1/8 binary64)) k (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64))))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.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))) #s(literal 1/8 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)))))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (*.f64 (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))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/8 binary64)))) k (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
4 calls:
| 21.0ms | n |
| 21.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 18.0ms | (*.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)))) |
| 17.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | k |
| 99.8% | 1 | n |
| 99.8% | 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)))) |
| 99.8% | 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))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#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 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) |
#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 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (*.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 (PI.f64) n)) (sqrt.f64 k)))) |
#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 n) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))) |
#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 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 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 (*.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)) (sqrt.f64 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) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(*.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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (*.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) k) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
4 calls:
| 25.0ms | n |
| 15.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 13.0ms | k |
| 11.0ms | (*.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 |
|---|---|---|
| 99.8% | 1 | k |
| 99.8% | 1 | n |
| 99.8% | 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)))) |
| 99.8% | 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))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#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 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) |
#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 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (*.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 (PI.f64) n)) (sqrt.f64 k)))) |
#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 n) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))) |
#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 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 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 (*.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)) (sqrt.f64 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) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(*.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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
| Outputs |
|---|
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))) |
4 calls:
| 45.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 40.0ms | n |
| 11.0ms | k |
| 10.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | k |
| 99.7% | 1 | n |
| 99.7% | 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)))) |
| 99.7% | 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))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#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 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) |
#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 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (*.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 (PI.f64) n)) (sqrt.f64 k)))) |
#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 n) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))) |
#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 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 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 (*.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)) (sqrt.f64 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) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))) (sqrt.f64 k))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(*.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
(*.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 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64)))) |
| Outputs |
|---|
#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)))) |
4 calls:
| 53.0ms | n |
| 20.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 11.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 11.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | k |
| 99.5% | 1 | n |
| 99.5% | 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)))) |
| 99.5% | 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))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#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 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) |
#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 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (*.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 (PI.f64) n)) (sqrt.f64 k)))) |
#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 n) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))) |
#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 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
4 calls:
| 13.0ms | k |
| 9.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 9.0ms | n |
| 8.0ms | (*.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 |
|---|---|---|
| 74.9% | 3 | k |
| 58.5% | 2 | n |
| 97.2% | 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)))) |
| 58.5% | 2 | (*.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))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#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 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) |
#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 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (*.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 (PI.f64) n)) (sqrt.f64 k)))) |
#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 n) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))) |
#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 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
2 calls:
| 8.0ms | k |
| 7.0ms | (*.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 |
|---|---|---|
| 70.7% | 2 | k |
| 70.8% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 17 to 15 computations (11.8% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#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 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) |
#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 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (*.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 (PI.f64) n)) (sqrt.f64 k)))) |
#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 n) (sqrt.f64 k)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 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 2 binary64) k)))) |
1 calls:
| 24.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 70.8% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 16 to 13 computations (18.8% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#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 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) |
#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 n k)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) |
1 calls:
| 4.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 70.8% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 16 to 13 computations (18.8% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#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)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
2 calls:
| 3.0ms | k |
| 3.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 59.7% | 2 | k |
| 59.8% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 17 to 15 computations (11.8% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
4 calls:
| 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 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 1.0ms | k |
| 1.0ms | n |
| Accuracy | Segments | Branch |
|---|---|---|
| 32.0% | 1 | n |
| 32.0% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 33.8% | 2 | k |
| 34.1% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 23 to 23 computations (0% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
4 calls:
| 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 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 1.0ms | n |
| 1.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 32.0% | 1 | n |
| 32.0% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 32.0% | 1 | k |
| 32.0% | 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)))) |
Compiled 23 to 23 computations (0% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 2.0826522937397566e+268 | +inf |
| 0.0ms | 0.0 | 9.081821480916652e-125 |
Compiled 19 to 18 computations (5.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 9.081821480916652e-125 |
Compiled 19 to 18 computations (5.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 9.081821480916652e-125 |
Compiled 19 to 18 computations (5.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 9.081821480916652e-125 |
Compiled 19 to 18 computations (5.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 9.081821480916652e-125 |
Compiled 19 to 18 computations (5.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 9.081821480916652e-125 |
Compiled 19 to 18 computations (5.3% saved)
| 1× | egg-herbie |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 98 | 599 |
| 1 | 119 | 565 |
| 2 | 134 | 565 |
| 3 | 155 | 565 |
| 4 | 172 | 565 |
| 5 | 191 | 565 |
| 6 | 225 | 565 |
| 7 | 296 | 565 |
| 8 | 327 | 565 |
| 9 | 360 | 565 |
| 10 | 370 | 565 |
| 1× | saturated |
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 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)))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) (if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 39999999999999998937528994166409092235100742444912950023748503679485838560977786267761776179074747560605966704919852367606632983360925877640733989572365418529924904538372564282961571672462773168785953956301720167915620487511778795854816831741326539736938915682603499520 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 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 2 binary64) k))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 #s(approx (pow (* n (* (PI) 2)) -1/2) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal -1 binary64))))) k) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 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 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) (if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 39999999999999998937528994166409092235100742444912950023748503679485838560977786267761776179074747560605966704919852367606632983360925877640733989572365418529924904538372564282961571672462773168785953956301720167915620487511778795854816831741326539736938915682603499520 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) (if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 39999999999999998937528994166409092235100742444912950023748503679485838560977786267761776179074747560605966704919852367606632983360925877640733989572365418529924904538372564282961571672462773168785953956301720167915620487511778795854816831741326539736938915682603499520 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) |
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64)))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 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 2 binary64) k))))) |
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 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 2 binary64) k))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) |
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))) |
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) |
(if (<=.f64 (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 320 |
| 0 | 88 | 294 |
| 1 | 243 | 270 |
| 2 | 1068 | 266 |
| 0 | 8478 | 266 |
| 0 | 120 | 502 |
| 1 | 378 | 489 |
| 2 | 1377 | 453 |
| 3 | 4131 | 453 |
| 0 | 8166 | 441 |
| 0 | 486 | 3741 |
| 1 | 1774 | 3470 |
| 0 | 8041 | 3265 |
| 0 | 13 | 38 |
| 0 | 22 | 38 |
| 1 | 83 | 35 |
| 2 | 446 | 35 |
| 3 | 4007 | 29 |
| 0 | 8921 | 29 |
| 0 | 50 | 252 |
| 0 | 84 | 221 |
| 1 | 258 | 208 |
| 2 | 1212 | 208 |
| 0 | 8196 | 208 |
| 0 | 48 | 260 |
| 0 | 77 | 229 |
| 1 | 236 | 201 |
| 2 | 1045 | 100 |
| 0 | 9791 | 97 |
| 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× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 1 366 to 738 computations (46% saved)
Compiled 1 230 to 230 computations (81.3% saved)
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