Migdal et al, Equation (51)
Time bar (total: 22.0s)
| 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)
| 3.2s | 8 256× | 0 | valid |
| 2.2s | 3 512× | 1 | invalid |
| 882.0ms | 1 886× | 1 | exit |
| 268.0ms | 478× | 0 | invalid |
| 259.0ms | 455× | 2 | invalid |
| 65.0ms | 224× | 0 | exit |
ival-pow: 1.3s (27.4% of total)ival-mult: 1.3s (27.3% of total)ival-div: 558.0ms (12.1% of total)ival-sqrt: 526.0ms (11.4% of total)adjust: 377.0ms (8.2% of total)ival-sub: 303.0ms (6.6% of total)ival-pi: 263.0ms (5.7% of total)exact: 31.0ms (0.7% of total)ival-true: 23.0ms (0.5% of total)ival-assert: 12.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 3 | 81 | (1.0129691978293824e-132 1.3320117224157894e-129) | 0 | - | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
| 0 | 0 | - | 0 | - | k |
| 0 | 0 | - | 0 | - | n |
| 0 | 0 | - | 0 | - | (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 0 | 0 | - | 0 | - | (sqrt.f64 k) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| 0 | 0 | - | 0 | - | (-.f64 #s(literal 1 binary64) k) |
| 0 | 0 | - | 0 | - | (*.f64 #s(literal 2 binary64) (PI.f64)) |
| 0 | 0 | - | 0 | - | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 0 | 0 | - | 0 | - | (PI.f64) |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
pow.f64 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | sensitivity | 84 | 28 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 3 | 0 |
| - | 81 | 172 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 3 | 0 | 0 |
| - | 81 | 28 | 144 |
| number | freq |
|---|---|
| 0 | 172 |
| 1 | 84 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 110.0ms | 512× | 0 | valid |
Compiled 128 to 43 computations (66.4% saved)
ival-pow: 23.0ms (29.6% of total)ival-mult: 22.0ms (28.3% of total)ival-div: 13.0ms (16.7% of total)ival-sqrt: 8.0ms (10.3% of total)ival-sub: 6.0ms (7.7% of total)ival-pi: 3.0ms (3.9% of total)ival-true: 1.0ms (1.3% of total)exact: 1.0ms (1.3% of total)ival-assert: 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 | 0.11900044900415223 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | |
| accuracy | 0.217128759768442 | (*.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 | 0.2265625 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) | |
| accuracy | 0.27734375 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
| 63.0ms | 256× | 0 | valid |
Compiled 56 to 15 computations (73.2% saved)
ival-mult: 9.0ms (23.5% of total)ival-pow: 9.0ms (23.5% of total)ival-sqrt: 8.0ms (20.9% of total)ival-div: 6.0ms (15.7% of total)ival-pi: 2.0ms (5.2% of total)ival-sub: 2.0ms (5.2% of total)exact: 1.0ms (2.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (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 | |
|---|---|---|---|---|
| 83.0ms | 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)) |
| 54.0ms | 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)) |
| 14.0ms | 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)) |
| 6.0ms | 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)) |
| 5.0ms | 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)
13 alts after pruning (13 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 325 | 13 | 338 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 326 | 13 | 339 |
| Status | Accuracy | Program |
|---|---|---|
| 29.8% | (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) | |
| 99.4% | (*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| ▶ | 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)))) |
| 71.4% | (*.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))) | |
| ▶ | 99.4% | (*.f64 (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 99.4% | (*.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)))) | |
| ▶ | 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))))) |
| 95.9% | (*.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))))) | |
| 48.0% | (*.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))))) | |
| 47.5% | (*.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))))) | |
| 71.3% | (*.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)))) | |
| ▶ | 99.6% | #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)))) |
| ▶ | 34.9% | #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 598 to 482 computations (19.4% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (pow.f64 k #s(literal 1/4 binary64)) | |
| cost-diff | 0 | (pow.f64 k #s(literal -1/4 binary64)) | |
| cost-diff | 0 | (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) | |
| cost-diff | 0 | (*.f64 (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) | |
| 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 | (pow.f64 k #s(literal -1/2 binary64)) | |
| cost-diff | 0 | (*.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)))) | |
| cost-diff | 0 | #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)))) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (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 | (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 | 47 | 339 |
| 0 | 76 | 339 |
| 1 | 109 | 333 |
| 2 | 132 | 333 |
| 3 | 179 | 333 |
| 4 | 209 | 333 |
| 5 | 251 | 333 |
| 6 | 326 | 333 |
| 7 | 422 | 333 |
| 8 | 446 | 333 |
| 9 | 466 | 333 |
| 10 | 476 | 333 |
| 0 | 476 | 333 |
| 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)) #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 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) 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) |
#s(literal 1/2 binary64) |
(*.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)))) |
(pow.f64 k #s(literal -1/2 binary64)) |
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 #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) |
#s(literal 1 binary64) |
(*.f64 (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (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 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) |
(pow.f64 k #s(literal -1/4 binary64)) |
k |
#s(literal -1/4 binary64) |
(pow.f64 k #s(literal 1/4 binary64)) |
#s(literal 1/4 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 #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) |
#s(literal 1 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 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (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 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) |
(*.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)) #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 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) |
(*.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) |
#s(literal 1/2 binary64) |
(*.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)))) |
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) |
(pow.f64 k #s(literal -1/2 binary64)) |
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))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) |
(*.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) |
#s(literal 1 binary64) |
(*.f64 (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 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 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) |
(pow.f64 k #s(literal -1/4 binary64)) |
k |
#s(literal -1/4 binary64) |
(pow.f64 k #s(literal 1/4 binary64)) |
#s(literal 1/4 binary64) |
(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 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) |
(*.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) |
#s(literal 1 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.11900044900415223 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | |
| accuracy | 0.217128759768442 | (*.f64 (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| accuracy | 0.2265625 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) | |
| accuracy | 0.359375 | (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) | |
| accuracy | 0.0 | (PI.f64) | |
| accuracy | 0.11900044900415223 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | |
| accuracy | 0.217128759768442 | (*.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)))) | |
| accuracy | 0.2265625 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) | |
| accuracy | 0.11900044900415223 | (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 | 0.217128759768442 | (*.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))))) | |
| accuracy | 0.2265625 | (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) | |
| accuracy | 0.27734375 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| accuracy | 0.2265625 | (*.f64 (PI.f64) n) | |
| accuracy | 0.39291000976844204 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) | |
| accuracy | 16.782764215530452 | (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) | |
| accuracy | 33.32823650251268 | #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 | 0.11900044900415223 | (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 | 0.12890625 | (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) | |
| accuracy | 0.217128759768442 | (*.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 | 0.2265625 | (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
| 283.0ms | 256× | 0 | valid |
Compiled 298 to 38 computations (87.2% saved)
ival-pow: 68.0ms (34.1% of total)ival-div: 47.0ms (23.6% of total)ival-sqrt: 43.0ms (21.6% of total)ival-mult: 32.0ms (16% of total)ival-pi: 2.0ms (1% of total)ival-add: 2.0ms (1% of total)ival-sub: 2.0ms (1% of total)exact: 2.0ms (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 (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 #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 #s(literal 1 binary64) (sqrt.f64 k)) |
(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 (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)))) |
(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))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (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 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) |
(pow.f64 k #s(literal -1/4 binary64)) |
(pow.f64 k #s(literal 1/4 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(*.f64 (PI.f64) n) |
(PI.f64) |
| 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) |
(pow (/ 1 k) 1/4) |
(pow (* 1 k) 1/4) |
(* (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)))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ 1 k)) (* (exp (* (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))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt -1))) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(exp (* 1/4 (+ (log -1) (log (/ -1 k))))) |
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -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))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* n (PI)) |
(* (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)))))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -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))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 190.0ms | 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)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* (/ (pow k -1/4) (pow k 1/4)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow k -1/4) (pow k 1/4)) (pow k -1/4) (pow k 1/4) (sqrt (/ 1 k)) (* (PI) n) (PI)) |
| 162.0ms | 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)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* (/ (pow k -1/4) (pow k 1/4)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow k -1/4) (pow k 1/4)) (pow k -1/4) (pow k 1/4) (sqrt (/ 1 k)) (* (PI) n) (PI)) |
| 82.0ms | 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)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* (/ (pow k -1/4) (pow k 1/4)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow k -1/4) (pow k 1/4)) (pow k -1/4) (pow k 1/4) (sqrt (/ 1 k)) (* (PI) n) (PI)) |
| 73.0ms | 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)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* (/ (pow k -1/4) (pow k 1/4)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow k -1/4) (pow k 1/4)) (pow k -1/4) (pow k 1/4) (sqrt (/ 1 k)) (* (PI) n) (PI)) |
| 72.0ms | 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)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* (/ (pow k -1/4) (pow k 1/4)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow k -1/4) (pow k 1/4)) (pow k -1/4) (pow k 1/4) (sqrt (/ 1 k)) (* (PI) n) (PI)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 165 | 800 |
| 1 | 535 | 767 |
| 2 | 2188 | 686 |
| 3 | 6632 | 670 |
| 0 | 8175 | 658 |
| 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) |
(pow (/ 1 k) 1/4) |
(pow (* 1 k) 1/4) |
(* (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)))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ 1 k)) (* (exp (* (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))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt -1))) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(exp (* 1/4 (+ (log -1) (log (/ -1 k))))) |
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -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))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* n (PI)) |
(* (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)))))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -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))) |
(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 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(fma.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 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.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))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 #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))))) 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))))) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.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)))) k (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (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 (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.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))) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 1 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) |
(pow (/ 1 k) 1/4) |
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) |
(pow (* 1 k) 1/4) |
(pow.f64 k #s(literal 1/4 binary64)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) 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 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))) |
(*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt -1))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/4 (+ (log -1) (log (/ -1 k))))) |
(pow.f64 (*.f64 (/.f64 #s(literal -1 binary64) k) #s(literal -1 binary64)) #s(literal 1/4 binary64)) |
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 k)))))) |
(pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) k)) #s(literal 1/4 binary64)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* 2 (* n (PI))) |
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(*.f64 (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* -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)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 47 | 234 |
| 0 | 76 | 226 |
| 1 | 216 | 212 |
| 2 | 1033 | 210 |
| 0 | 8741 | 210 |
| 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 #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 #s(literal 1 binary64) (sqrt.f64 k)) |
(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 (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)))) |
(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))) |
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(*.f64 (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (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 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) |
(pow.f64 k #s(literal -1/4 binary64)) |
(pow.f64 k #s(literal 1/4 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(*.f64 (PI.f64) n) |
(PI.f64) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.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 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (/.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 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64)))) |
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(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) |
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(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) |
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(fma.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.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 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 n (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64))) (*.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 (neg.f64 n)) (PI.f64) (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (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)) |
(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)) |
(fma.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.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 (PI.f64) (neg.f64 (neg.f64 n)) (*.f64 (PI.f64) n)) |
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n)) |
(fma.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (cosh.f64 (log.f64 (PI.f64))) (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (sinh.f64 (log.f64 (PI.f64))))) |
(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 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(+.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(+.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (cosh.f64 (log.f64 (PI.f64)))) (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (sinh.f64 (log.f64 (PI.f64))))) |
(+.f64 (cosh.f64 (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))))) (sinh.f64 (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) |
(log.f64 (pow.f64 (pow.f64 (exp.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 (PI.f64) n) k) #s(literal 2 binary64)))) |
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(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64)))) |
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(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) |
(*.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))) |
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (neg.f64 n)) (PI.f64))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (log.f64 (sqrt.f64 k)))) |
(exp.f64 (fma.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) |
(*.f64 (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) |
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(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) |
(sqrt.f64 #s(literal 2 binary64)) |
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(+.f64 (cosh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64)))) |
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(*.f64 (fabs.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 n) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n k))) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)) #s(literal 1/2 binary64))) |
(pow.f64 (exp.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 k)) |
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(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 (neg.f64 n) (PI.f64))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) |
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))) |
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(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64))) |
(+.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)))) |
(*.f64 (*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -3/8 binary64))) (pow.f64 k #s(literal -1/8 binary64))) |
(*.f64 (*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/8 binary64))) (pow.f64 k #s(literal -3/8 binary64))) |
(*.f64 (*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.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)))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))) |
(*.f64 (*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #s(literal 1 binary64)) |
(*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))) |
(/.f64 (neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) (sqrt.f64 k)) |
(/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
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(+.f64 (cosh.f64 (*.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64)) #s(literal 2 binary64))) (sinh.f64 (*.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64)) #s(literal 2 binary64)))) |
(+.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (sinh.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(+.f64 (cosh.f64 (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))) |
(+.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 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 (*.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 (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 (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 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (*.f64 (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 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64))))) |
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))) |
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64))) (cbrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 (PI.f64)))) |
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64)))) |
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(*.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (neg.f64 (cbrt.f64 (PI.f64)))) |
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64))))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (PI.f64))) |
(pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/3 binary64)) |
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)) |
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64)) |
(pow.f64 (PI.f64) #s(literal 1 binary64)) |
(/.f64 (-.f64 (*.f64 (cosh.f64 (log.f64 (PI.f64))) (cosh.f64 (log.f64 (PI.f64)))) (*.f64 (sinh.f64 (log.f64 (PI.f64))) (sinh.f64 (log.f64 (PI.f64))))) (-.f64 (cosh.f64 (log.f64 (PI.f64))) (sinh.f64 (log.f64 (PI.f64))))) |
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (PI.f64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (PI.f64))) (cosh.f64 (log.f64 (PI.f64))) (-.f64 (*.f64 (sinh.f64 (log.f64 (PI.f64))) (sinh.f64 (log.f64 (PI.f64)))) (*.f64 (cosh.f64 (log.f64 (PI.f64))) (sinh.f64 (log.f64 (PI.f64))))))) |
(neg.f64 (neg.f64 (PI.f64))) |
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) |
(sqrt.f64 (*.f64 (PI.f64) (PI.f64))) |
(fabs.f64 (neg.f64 (PI.f64))) |
(fabs.f64 (PI.f64)) |
(exp.f64 (/.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) #s(literal 1/3 binary64))) |
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(exp.f64 (log.f64 (PI.f64))) |
(+.f64 (cosh.f64 (log.f64 (PI.f64))) (sinh.f64 (log.f64 (PI.f64)))) |
(log.f64 (exp.f64 (PI.f64))) |
(PI.f64) |
Compiled 40 666 to 3 887 computations (90.4% saved)
25 alts after pruning (23 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 206 | 19 | 1 225 |
| Fresh | 4 | 4 | 8 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 0 | 0 |
| Total | 1 213 | 25 | 1 238 |
| Status | Accuracy | Program |
|---|---|---|
| 29.8% | (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k)) | |
| 27.9% | (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) | |
| 99.2% | (*.f64 (pow.f64 (pow.f64 k #s(literal -1/8 binary64)) #s(literal 4 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| ▶ | 99.5% | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
| 94.7% | (*.f64 (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| 29.6% | (*.f64 (/.f64 (/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))))) (-.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| 26.8% | (*.f64 (/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) (-.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| 56.3% | (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (pow.f64 k #s(literal 1/4 binary64)) (cosh.f64 (*.f64 (log.f64 k) #s(literal 1/4 binary64)))) (*.f64 (pow.f64 k #s(literal 1/4 binary64)) (sinh.f64 (*.f64 (log.f64 k) #s(literal 1/4 binary64)))))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| ▶ | 99.4% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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))))) |
| 95.9% | (*.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))))) | |
| 48.0% | (*.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))))) | |
| 47.5% | (*.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))))) | |
| 5.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) | |
| 96.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (exp.f64 (log.f64 n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 70.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))) | |
| ▶ | 71.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
| 34.8% | #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)))) | |
| 47.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) | |
| 47.5% | #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))))) | |
| 34.9% | #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)))) | |
| ✓ | 34.9% | #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)))) |
| ▶ | 47.6% | #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)))) |
| ▶ | 35.0% | #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)))) |
| 33.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
Compiled 1 501 to 1 134 computations (24.5% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (pow.f64 k #s(literal -1/2 binary64)) | |
| cost-diff | 0 | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| cost-diff | 0 | (sqrt.f64 k) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| cost-diff | 4 | (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) | |
| cost-diff | 0 | #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) | |
| cost-diff | 0 | (*.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))) | |
| cost-diff | 0 | #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)))) | |
| 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 (*.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 | #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)))) | |
| cost-diff | 0 | (pow.f64 k #s(literal -1/2 binary64)) | |
| cost-diff | 0 | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 442 |
| 0 | 88 | 430 |
| 1 | 133 | 422 |
| 2 | 183 | 422 |
| 3 | 260 | 418 |
| 4 | 347 | 418 |
| 5 | 567 | 418 |
| 6 | 1167 | 418 |
| 7 | 1764 | 418 |
| 8 | 1872 | 418 |
| 9 | 1970 | 418 |
| 10 | 1970 | 418 |
| 0 | 1970 | 418 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
k |
#s(literal -1/2 binary64) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) 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) |
#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 #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 #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))) |
#s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(*.f64 n (PI.f64)) |
n |
(PI.f64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) |
(*.f64 (sqrt.f64 (PI.f64)) n) |
(sqrt.f64 (PI.f64)) |
(PI.f64) |
n |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) |
#s(literal 2 binary64) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 k #s(literal -1/2 binary64)) |
k |
#s(literal -1/2 binary64) |
(pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
n |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
| Outputs |
|---|
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #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 k #s(literal -1/2 binary64)) |
k |
#s(literal -1/2 binary64) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #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 (PI.f64) (*.f64 n #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 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) n) |
(*.f64 n #s(literal 2 binary64)) |
#s(literal 2 binary64) |
n |
(PI.f64) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal 1/2 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 #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)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
(*.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))) |
#s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
(*.f64 n (PI.f64)) |
(*.f64 (PI.f64) n) |
n |
(PI.f64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
#s(literal 1 binary64) |
(sqrt.f64 k) |
k |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) n) |
(sqrt.f64 (PI.f64)) |
(PI.f64) |
n |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 n (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 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (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 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) |
(pow.f64 k #s(literal -1/2 binary64)) |
k |
#s(literal -1/2 binary64) |
(pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
n |
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.19988251953688402 | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) | |
| accuracy | 0.45703125 | (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) | |
| accuracy | 0.635097509768442 | (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) | |
| accuracy | 16.952712269370817 | (PI.f64) | |
| accuracy | 0.217128759768442 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| accuracy | 0.25 | (*.f64 (sqrt.f64 (PI.f64)) n) | |
| accuracy | 0.7265625 | (sqrt.f64 (PI.f64)) | |
| accuracy | 16.952712269370817 | (PI.f64) | |
| accuracy | 0.217128759768442 | (*.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))) | |
| accuracy | 0.31478500976844204 | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) | |
| accuracy | 16.285860469685268 | #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) | |
| accuracy | 16.952712269370817 | (PI.f64) | |
| accuracy | 0.1484375 | (*.f64 (PI.f64) n) | |
| accuracy | 8.284257329212148 | (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) | |
| accuracy | 16.21133387535574 | #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 | 16.952712269370817 | (PI.f64) | |
| accuracy | 0.11900044900415223 | (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 | 0.1484375 | (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) | |
| accuracy | 0.217128759768442 | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| accuracy | 16.952712269370817 | (PI.f64) |
| 259.0ms | 186× | 0 | valid |
| 59.0ms | 70× | 0 | exit |
Compiled 335 to 45 computations (86.6% saved)
ival-mult: 140.0ms (55.3% of total)ival-pow: 57.0ms (22.5% of total)ival-sqrt: 21.0ms (8.3% of total)ival-div: 15.0ms (5.9% of total)ival-sub: 13.0ms (5.1% of total)ival-pi: 3.0ms (1.2% of total)ival-add: 2.0ms (0.8% of total)exact: 1.0ms (0.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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) |
#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 #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))) |
#s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(PI.f64) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 (PI.f64) n) |
(sqrt.f64 (PI.f64)) |
(*.f64 (sqrt.f64 (PI.f64)) n) |
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(sqrt (/ 1 k)) |
(* (sqrt (* 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))) |
(* 2 (/ (* n (PI)) k)) |
(/ (* n (PI)) k) |
(sqrt k) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2))))))) k) |
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log n) (* (pow (log (* 2 (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log n) 2) (* (log (* 2 (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log n) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(sqrt (/ n k)) |
(/ (+ (sqrt (* k n)) (* -1/2 (* (sqrt (* (pow k 3) n)) (log n)))) k) |
(/ (+ (sqrt (* k n)) (* k (+ (* -1/2 (* (sqrt (* k n)) (log n))) (* 1/8 (* (sqrt (* (pow k 3) n)) (pow (log n) 2)))))) k) |
(/ (+ (sqrt (* k n)) (* k (+ (* -1/2 (* (sqrt (* k n)) (log n))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) n)) (pow (log n) 3))) (* 1/8 (* (sqrt (* k n)) (pow (log n) 2)))))))) k) |
(* (sqrt (PI)) (sqrt 2)) |
(+ (* -1/2 (* (* k (* (log (* 2 (PI))) (sqrt 2))) (sqrt (PI)))) (* (sqrt (PI)) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (PI))) 2) (sqrt 2))) (sqrt (PI)))))) (* (sqrt (PI)) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (PI))) 3) (sqrt 2))) (sqrt (PI)))) (* 1/8 (* (sqrt (PI)) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))))))) (* (sqrt (PI)) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (- 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log n) (- 1/2 (* 1/2 k))))) |
(exp (* (log (* 2 (PI))) (- 1/2 (* 1/2 k)))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* -1/2 k)))) (* (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* -1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log n) (+ 1/2 (* -1/2 k))))) |
(* n (PI)) |
(* n (sqrt (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)))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (* (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* -1/2 k))))) (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* -1/2 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)))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log -1) (* -1 (log (/ -1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log -1) (* -1 (log (/ -1 n))))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 177.0ms | n | @ | 0 | ((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (/ 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))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (sqrt (* n (PI))) (sqrt 2)) (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow n (+ (* -1/2 k) 1/2))) (pow (* (PI) 2) (+ (* -1/2 k) 1/2))) (* (pow k -1/2) (pow n (+ (* -1/2 k) 1/2))) (PI) (* (* 2 n) (PI)) (* (PI) n) (sqrt (PI)) (* (sqrt (PI)) n) (pow (* (PI) 2) (+ (* -1/2 k) 1/2))) |
| 95.0ms | n | @ | inf | ((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (/ 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))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (sqrt (* n (PI))) (sqrt 2)) (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow n (+ (* -1/2 k) 1/2))) (pow (* (PI) 2) (+ (* -1/2 k) 1/2))) (* (pow k -1/2) (pow n (+ (* -1/2 k) 1/2))) (PI) (* (* 2 n) (PI)) (* (PI) n) (sqrt (PI)) (* (sqrt (PI)) n) (pow (* (PI) 2) (+ (* -1/2 k) 1/2))) |
| 82.0ms | k | @ | 0 | ((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (/ 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))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (sqrt (* n (PI))) (sqrt 2)) (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow n (+ (* -1/2 k) 1/2))) (pow (* (PI) 2) (+ (* -1/2 k) 1/2))) (* (pow k -1/2) (pow n (+ (* -1/2 k) 1/2))) (PI) (* (* 2 n) (PI)) (* (PI) n) (sqrt (PI)) (* (sqrt (PI)) n) (pow (* (PI) 2) (+ (* -1/2 k) 1/2))) |
| 78.0ms | n | @ | -inf | ((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (/ 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))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (sqrt (* n (PI))) (sqrt 2)) (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow n (+ (* -1/2 k) 1/2))) (pow (* (PI) 2) (+ (* -1/2 k) 1/2))) (* (pow k -1/2) (pow n (+ (* -1/2 k) 1/2))) (PI) (* (* 2 n) (PI)) (* (PI) n) (sqrt (PI)) (* (sqrt (PI)) n) (pow (* (PI) 2) (+ (* -1/2 k) 1/2))) |
| 19.0ms | k | @ | -inf | ((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (/ 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))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (sqrt (* n (PI))) (sqrt 2)) (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow n (+ (* -1/2 k) 1/2))) (pow (* (PI) 2) (+ (* -1/2 k) 1/2))) (* (pow k -1/2) (pow n (+ (* -1/2 k) 1/2))) (PI) (* (* 2 n) (PI)) (* (PI) n) (sqrt (PI)) (* (sqrt (PI)) n) (pow (* (PI) 2) (+ (* -1/2 k) 1/2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 293 | 1463 |
| 1 | 1047 | 1371 |
| 2 | 4308 | 1342 |
| 0 | 9068 | 1280 |
| 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 (* 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))) |
(* 2 (/ (* n (PI)) k)) |
(/ (* n (PI)) k) |
(sqrt k) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2))))))) k) |
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log n) (* (pow (log (* 2 (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log n) 2) (* (log (* 2 (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log n) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(sqrt (/ n k)) |
(/ (+ (sqrt (* k n)) (* -1/2 (* (sqrt (* (pow k 3) n)) (log n)))) k) |
(/ (+ (sqrt (* k n)) (* k (+ (* -1/2 (* (sqrt (* k n)) (log n))) (* 1/8 (* (sqrt (* (pow k 3) n)) (pow (log n) 2)))))) k) |
(/ (+ (sqrt (* k n)) (* k (+ (* -1/2 (* (sqrt (* k n)) (log n))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) n)) (pow (log n) 3))) (* 1/8 (* (sqrt (* k n)) (pow (log n) 2)))))))) k) |
(* (sqrt (PI)) (sqrt 2)) |
(+ (* -1/2 (* (* k (* (log (* 2 (PI))) (sqrt 2))) (sqrt (PI)))) (* (sqrt (PI)) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (PI))) 2) (sqrt 2))) (sqrt (PI)))))) (* (sqrt (PI)) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (PI))) 3) (sqrt 2))) (sqrt (PI)))) (* 1/8 (* (sqrt (PI)) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))))))) (* (sqrt (PI)) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (- 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log n) (- 1/2 (* 1/2 k))))) |
(exp (* (log (* 2 (PI))) (- 1/2 (* 1/2 k)))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* -1/2 k)))) (* (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* -1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log n) (+ 1/2 (* -1/2 k))))) |
(* n (PI)) |
(* n (sqrt (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)))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (* (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* -1/2 k))))) (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* -1/2 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)))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log -1) (* -1 (log (/ -1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log -1) (* -1 (log (/ -1 n))))))) |
| 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 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (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 (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 (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 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 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k)) (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 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 k #s(literal 1/8 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) k) (*.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 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 k k) (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 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 k) |
(sqrt.f64 k) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (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 n) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) #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 n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (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 n) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) #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 n) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) #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 (PI.f64) #s(literal 2 binary64))) (log.f64 n))) (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 n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log n) (* (pow (log (* 2 (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log n) 2) (* (log (* 2 (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log n) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (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 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (log.f64 n) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) #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 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 n) #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 n) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) #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 (PI.f64) #s(literal 2 binary64))) (log.f64 n))) (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 n) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 (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 k)) |
(sqrt.f64 (/.f64 n k)) |
(/ (+ (sqrt (* k n)) (* -1/2 (* (sqrt (* (pow k 3) n)) (log n)))) k) |
(/.f64 (fma.f64 (*.f64 (log.f64 n) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n)) (sqrt.f64 (*.f64 n k))) k) |
(/ (+ (sqrt (* k n)) (* k (+ (* -1/2 (* (sqrt (* k n)) (log n))) (* 1/8 (* (sqrt (* (pow k 3) n)) (pow (log n) 2)))))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 n) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n)) (*.f64 (*.f64 (log.f64 n) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n k)))) k (sqrt.f64 (*.f64 n k))) k) |
(/ (+ (sqrt (* k n)) (* k (+ (* -1/2 (* (sqrt (* k n)) (log n))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) n)) (pow (log n) 3))) (* 1/8 (* (sqrt (* k n)) (pow (log n) 2)))))))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 (log.f64 n) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n k)) (*.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 n) #s(literal 2 binary64))) (sqrt.f64 (*.f64 n k)) (*.f64 (*.f64 #s(literal -1/48 binary64) (pow.f64 (log.f64 n) #s(literal 3 binary64))) (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n)))) k)) k (sqrt.f64 (*.f64 n k))) k) |
(* (sqrt (PI)) (sqrt 2)) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* -1/2 (* (* k (* (log (* 2 (PI))) (sqrt 2))) (sqrt (PI)))) (* (sqrt (PI)) (sqrt 2))) |
(*.f64 (sqrt.f64 (PI.f64)) (fma.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (PI))) 2) (sqrt 2))) (sqrt (PI)))))) (* (sqrt (PI)) (sqrt 2))) |
(fma.f64 (sqrt.f64 (PI.f64)) (fma.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 k #s(literal 1/8 binary64)) (*.f64 (*.f64 k (sqrt.f64 (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) |
(+ (* k (+ (* -1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (PI))) 3) (sqrt 2))) (sqrt (PI)))) (* 1/8 (* (sqrt (PI)) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))))))) (* (sqrt (PI)) (sqrt 2))) |
(fma.f64 (sqrt.f64 (PI.f64)) (fma.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 k k) (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (PI.f64))) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (- 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (- 1/2 (* 1/2 k)))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (log n) (- 1/2 (* 1/2 k))))) |
(*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* 2 (PI))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))) |
(*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 k) #s(literal 1 binary64)) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* -1/2 k)))) (* (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))) |
(*.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(*.f64 (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* 2 (* n (PI))) |
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) |
(* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* -1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (log n) (+ 1/2 (* -1/2 k))))) |
(*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* n (PI)) |
(*.f64 n (PI.f64)) |
(* n (sqrt (PI))) |
(*.f64 (sqrt.f64 (PI.f64)) n) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (* (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* -1/2 k))))) (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* -1/2 k)))))) |
(*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.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))) |
(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 (* -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)) (* (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)) (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))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (PI))) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log -1) (* -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 (PI.f64) #s(literal 2 binary64))) (-.f64 (log.f64 #s(literal -1 binary64)) (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 -1) (* -1 (log (/ -1 n))))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 328 |
| 0 | 88 | 314 |
| 1 | 264 | 294 |
| 2 | 1258 | 294 |
| 0 | 8377 | 294 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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) |
#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 #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))) |
#s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(sqrt.f64 k) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(PI.f64) |
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) |
(*.f64 (PI.f64) n) |
(sqrt.f64 (PI.f64)) |
(*.f64 (sqrt.f64 (PI.f64)) n) |
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
| Outputs |
|---|
(*.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #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 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))) |
(/.f64 (neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #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 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(neg.f64 (/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))) |
(neg.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))) |
(neg.f64 (*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #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)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(fma.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(fma.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(+.f64 (*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))))) |
(*.f64 (pow.f64 (fabs.f64 k) #s(literal -1/4 binary64)) (pow.f64 (fabs.f64 k) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (neg.f64 k) #s(literal -1/4 binary64)) (pow.f64 (neg.f64 k) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) |
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 k)) |
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64)) |
(pow.f64 (*.f64 (pow.f64 k #s(literal -1 binary64)) (pow.f64 k #s(literal -1 binary64))) #s(literal 1/4 binary64)) |
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) #s(literal 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 (sqrt.f64 k) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 k #s(literal -1/2 binary64)) |
(/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) (-.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(/.f64 (+.f64 (pow.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (-.f64 (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))))) |
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (neg.f64 k)))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 k))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 k)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(neg.f64 (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) |
(neg.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 k #s(literal -1/4 binary64))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) |
(sqrt.f64 (pow.f64 k #s(literal -1 binary64))) |
(fabs.f64 (pow.f64 k #s(literal -1/2 binary64))) |
(exp.f64 (neg.f64 (log.f64 (sqrt.f64 k)))) |
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(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #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 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #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 (PI.f64) (*.f64 n #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 (PI.f64) (*.f64 n #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 (*.f64 (cosh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #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 (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #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 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (cosh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(+.f64 (*.f64 (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(+.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(+.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (neg.f64 (sqrt.f64 (pow.f64 n (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 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64))))) |
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(*.f64 (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (sqrt.f64 (pow.f64 n (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 n (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 n (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 n (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 n (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 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))) |
(*.f64 (neg.f64 (*.f64 (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64)))) (neg.f64 (*.f64 (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))) |
(*.f64 (neg.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) (neg.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))) |
(*.f64 (fabs.f64 (*.f64 (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64)))) (fabs.f64 (*.f64 (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))) |
(*.f64 (fabs.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) (fabs.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))) |
(*.f64 (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 (*.f64 k (pow.f64 n k)) #s(literal -1/2 binary64)) (sqrt.f64 n)) |
(*.f64 (*.f64 (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(*.f64 (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 n (*.f64 #s(literal -1/2 binary64) k)) (*.f64 (sqrt.f64 n) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal 2 binary64)) |
(neg.f64 (*.f64 (pow.f64 n (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 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(fma.f64 (cosh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sinh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) |
(fma.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(fma.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(fma.f64 (pow.f64 k #s(literal -1/2 binary64)) (cosh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sinh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(exp.f64 (fma.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 n) (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 (sqrt.f64 k)) #s(literal -1 binary64) (*.f64 (log.f64 n) (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 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) (*.f64 (sinh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) |
(+.f64 (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cosh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sinh.f64 (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(+.f64 (cosh.f64 (fma.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (sinh.f64 (fma.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(+.f64 (cosh.f64 (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sinh.f64 (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.f64 (log.f64 n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(*.f64 (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64))))) |
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))) |
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))) |
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(*.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 (PI.f64)))) |
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(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
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(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
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(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64)) #s(literal 1/2 binary64)) (cbrt.f64 (PI.f64))) |
(*.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
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(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (*.f64 (sqrt.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 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 #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 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (PI.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)))) |
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (PI.f64)) #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)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal -1/2 binary64)) k)) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal -1/2 binary64)) k) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(pow.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (PI.f64) (PI.f64))) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))) |
(pow.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (/.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 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) |
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.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))) |
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) (-.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(/.f64 (+.f64 (pow.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (-.f64 (*.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))))) |
(/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) k))) |
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(neg.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))) |
(fabs.f64 (pow.f64 (*.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 (PI.f64) #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.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))) |
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 4 binary64) (*.f64 (PI.f64) (PI.f64)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 2 binary64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.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)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
Compiled 40 452 to 4 649 computations (88.5% saved)
19 alts after pruning (15 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 019 | 12 | 1 031 |
| Fresh | 15 | 3 | 18 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 2 | 2 |
| Total | 1 037 | 19 | 1 056 |
| Status | Accuracy | Program |
|---|---|---|
| 99.6% | (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) | |
| ▶ | 99.7% | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
| 29.6% | (*.f64 (/.f64 (/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))))) (-.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| ✓ | 99.4% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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))))) |
| 48.0% | (*.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))))) | |
| ▶ | 5.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
| 47.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))) | |
| 71.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) | |
| 47.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) | |
| ▶ | 34.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
| ✓ | 34.9% | #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)))) |
| ▶ | 47.5% | #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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 47.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 21.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 k (*.f64 (PI.f64) n))) (*.f64 k k)))) | |
| ✓ | 35.0% | #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)))) |
| 34.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) | |
| 35.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k)))) | |
| ▶ | 34.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
Compiled 1 055 to 791 computations (25% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) | |
| cost-diff | 0 | #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) | |
| cost-diff | 0 | (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) | |
| cost-diff | 0 | #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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| cost-diff | 0 | (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) | |
| cost-diff | 0 | (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) | |
| cost-diff | 3 | (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (PI.f64) | |
| cost-diff | 0 | (sqrt.f64 (PI.f64)) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)))) | |
| cost-diff | 0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) | |
| cost-diff | 0 | (*.f64 n (/.f64 (PI.f64) k)) | |
| cost-diff | 0 | (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (sqrt.f64 (*.f64 (*.f64 n (/.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 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) | |
| cost-diff | 0 | #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k)))) | |
| cost-diff | 0 | (pow.f64 k #s(literal -1/2 binary64)) | |
| cost-diff | 0 | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 55 | 384 |
| 0 | 85 | 384 |
| 1 | 123 | 376 |
| 2 | 154 | 376 |
| 3 | 217 | 376 |
| 4 | 335 | 376 |
| 5 | 478 | 376 |
| 6 | 705 | 376 |
| 7 | 838 | 376 |
| 8 | 906 | 376 |
| 9 | 930 | 376 |
| 10 | 956 | 376 |
| 0 | 956 | 364 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
k |
#s(literal -1/2 binary64) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k)))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(PI.f64) |
(*.f64 n #s(literal 2 binary64)) |
n |
#s(literal 2 binary64) |
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k)) |
(*.f64 #s(literal 1/2 binary64) k) |
#s(literal 1/2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))) |
(*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) |
(*.f64 n (/.f64 (PI.f64) k)) |
n |
(/.f64 (PI.f64) k) |
(PI.f64) |
k |
#s(literal 2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)))) |
(sqrt.f64 (PI.f64)) |
(PI.f64) |
(sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) |
(*.f64 (/.f64 n k) #s(literal 2 binary64)) |
(/.f64 n k) |
n |
k |
#s(literal 2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) |
(PI.f64) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 k) |
k |
#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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
#s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(sqrt.f64 n) |
n |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
| Outputs |
|---|
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
(*.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k)))) (pow.f64 k #s(literal -1/2 binary64))) |
(pow.f64 k #s(literal -1/2 binary64)) |
k |
#s(literal -1/2 binary64) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k)))) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k)))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) |
(PI.f64) |
(*.f64 n #s(literal 2 binary64)) |
n |
#s(literal 2 binary64) |
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k)) |
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k)) |
(*.f64 #s(literal 1/2 binary64) k) |
#s(literal 1/2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.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 (PI.f64) k) n) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))) |
(*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)) |
(*.f64 n (/.f64 (PI.f64) k)) |
(*.f64 (/.f64 (PI.f64) k) n) |
n |
(/.f64 (PI.f64) k) |
(PI.f64) |
k |
#s(literal 2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) |
(sqrt.f64 (PI.f64)) |
(PI.f64) |
(sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) |
(*.f64 (/.f64 n k) #s(literal 2 binary64)) |
(/.f64 n k) |
n |
k |
#s(literal 2 binary64) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (hypot.f64 (PI.f64) (PI.f64)) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(/.f64 (hypot.f64 (PI.f64) (PI.f64)) (sqrt.f64 k)) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(hypot.f64 (PI.f64) (PI.f64)) |
(*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) |
(PI.f64) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 k) |
k |
#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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (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)) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))) |
(*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) |
#s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(PI.f64) |
#s(literal 2 binary64) |
(sqrt.f64 n) |
n |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/.f64 #s(literal 1 binary64) k) |
#s(literal 1 binary64) |
k |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.33203125 | (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) | |
| accuracy | 0.72265625 | (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) | |
| accuracy | 16.042343116287817 | #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) | |
| accuracy | 17.194893873218973 | (PI.f64) | |
| accuracy | 0.0 | (sqrt.f64 k) | |
| accuracy | 0.24609375 | (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) | |
| accuracy | 17.194893873218973 | (PI.f64) | |
| accuracy | 43.545829549723905 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) | |
| accuracy | 0.72265625 | (sqrt.f64 (PI.f64)) | |
| accuracy | 8.281227117467964 | (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) | |
| accuracy | 15.967759226035254 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) | |
| accuracy | 17.194893873218973 | (PI.f64) | |
| accuracy | 0.1640625 | (/.f64 (PI.f64) k) | |
| accuracy | 8.284257329212148 | (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))) | |
| accuracy | 15.967759226035254 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) | |
| accuracy | 17.194893873218973 | (PI.f64) | |
| accuracy | 0.05859375 | (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) | |
| accuracy | 0.1484375 | (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) | |
| accuracy | 0.217128759768442 | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) | |
| accuracy | 17.194893873218973 | (PI.f64) |
| 852.0ms | 185× | 0 | valid |
| 94.0ms | 71× | 0 | exit |
Compiled 282 to 49 computations (82.6% saved)
ival-sqrt: 691.0ms (79% of total)ival-mult: 113.0ms (12.9% of total)ival-pow: 33.0ms (3.8% of total)ival-div: 29.0ms (3.3% of total)ival-sub: 3.0ms (0.3% of total)ival-pi: 2.0ms (0.2% of total)ival-add: 2.0ms (0.2% of total)exact: 1.0ms (0.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k)))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))) |
(*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) |
(*.f64 n (/.f64 (PI.f64) k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)))) |
(sqrt.f64 (PI.f64)) |
(PI.f64) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(*.f64 (PI.f64) (*.f64 (PI.f64) #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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
#s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(/.f64 (PI.f64) k) |
(sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) |
(sqrt.f64 k) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(sqrt (/ 1 k)) |
(* (sqrt (* 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))) |
(+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -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 (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(* 2 (/ (* n (PI)) k)) |
(/ (* n (PI)) k) |
(* (sqrt (/ 1 k)) (* (PI) (sqrt 2))) |
(/ (PI) k) |
(* (sqrt (/ n k)) (sqrt 2)) |
(sqrt k) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))) |
(* (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 (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (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 k)) (* (sqrt -2) (sqrt -1))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) |
(* (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 (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* (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))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 82.0ms | k | @ | 0 | ((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt (* (PI) (* n 2))) (pow (* (PI) (* n 2)) (* 1/2 k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (PI)) (sqrt (* (/ n k) 2))) (sqrt (PI)) (PI) (sqrt (* (PI) (* (PI) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (* (PI) (* (PI) 2)) (* (/ 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)) (* (sqrt (* (PI) 2)) (sqrt n)) (* (PI) (* n 2)) (sqrt (* (PI) (* n 2))) (/ (PI) k) (sqrt (* (/ n k) 2)) (sqrt k) (sqrt (* (PI) 2))) |
| 62.0ms | n | @ | 0 | ((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt (* (PI) (* n 2))) (pow (* (PI) (* n 2)) (* 1/2 k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (PI)) (sqrt (* (/ n k) 2))) (sqrt (PI)) (PI) (sqrt (* (PI) (* (PI) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (* (PI) (* (PI) 2)) (* (/ 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)) (* (sqrt (* (PI) 2)) (sqrt n)) (* (PI) (* n 2)) (sqrt (* (PI) (* n 2))) (/ (PI) k) (sqrt (* (/ n k) 2)) (sqrt k) (sqrt (* (PI) 2))) |
| 61.0ms | n | @ | inf | ((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt (* (PI) (* n 2))) (pow (* (PI) (* n 2)) (* 1/2 k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (PI)) (sqrt (* (/ n k) 2))) (sqrt (PI)) (PI) (sqrt (* (PI) (* (PI) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (* (PI) (* (PI) 2)) (* (/ 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)) (* (sqrt (* (PI) 2)) (sqrt n)) (* (PI) (* n 2)) (sqrt (* (PI) (* n 2))) (/ (PI) k) (sqrt (* (/ n k) 2)) (sqrt k) (sqrt (* (PI) 2))) |
| 34.0ms | n | @ | -inf | ((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt (* (PI) (* n 2))) (pow (* (PI) (* n 2)) (* 1/2 k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (PI)) (sqrt (* (/ n k) 2))) (sqrt (PI)) (PI) (sqrt (* (PI) (* (PI) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (* (PI) (* (PI) 2)) (* (/ 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)) (* (sqrt (* (PI) 2)) (sqrt n)) (* (PI) (* n 2)) (sqrt (* (PI) (* n 2))) (/ (PI) k) (sqrt (* (/ n k) 2)) (sqrt k) (sqrt (* (PI) 2))) |
| 14.0ms | k | @ | -inf | ((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt (* (PI) (* n 2))) (pow (* (PI) (* n 2)) (* 1/2 k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (PI)) (sqrt (* (/ n k) 2))) (sqrt (PI)) (PI) (sqrt (* (PI) (* (PI) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (* (PI) (* (PI) 2)) (* (/ 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)) (* (sqrt (* (PI) 2)) (sqrt n)) (* (PI) (* n 2)) (sqrt (* (PI) (* n 2))) (/ (PI) k) (sqrt (* (/ n k) 2)) (sqrt k) (sqrt (* (PI) 2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 210 | 1029 |
| 1 | 736 | 983 |
| 2 | 2962 | 913 |
| 3 | 7945 | 913 |
| 0 | 8156 | 896 |
| 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 (* 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))) |
(+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -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 (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(* 2 (/ (* n (PI)) k)) |
(/ (* n (PI)) k) |
(* (sqrt (/ 1 k)) (* (PI) (sqrt 2))) |
(/ (PI) k) |
(* (sqrt (/ n k)) (sqrt 2)) |
(sqrt k) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))) |
(* (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 (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (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 k)) (* (sqrt -2) (sqrt -1))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) |
(* (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 (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* (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))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))) |
| 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 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.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 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.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)))))) 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 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 #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))))) 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 (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 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))) (*.f64 (fma.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) k)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (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 (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (fma.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) k)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (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 (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -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 (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 k k) (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (fma.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 (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 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) k (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (fma.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 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 (/ 1 k)) (* (PI) (sqrt 2))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(/ (PI) k) |
(/.f64 (PI.f64) k) |
(* (sqrt (/ n k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt k) |
(sqrt.f64 k) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))) |
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2))) |
(*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) |
(* -1 (* (sqrt k) (pow (sqrt -1) 2))) |
(sqrt.f64 k) |
(* (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 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) (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 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) |
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) |
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(* 2 (* n (PI))) |
(*.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 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) (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 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) |
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(* (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 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) (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 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(* (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)))) |
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 (pow.f64 (exp.f64 k) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) |
(* -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)) (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))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(* -1 (* (sqrt (/ n k)) (* (sqrt -2) (sqrt -1)))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 n k)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 55 | 325 |
| 0 | 85 | 314 |
| 1 | 254 | 288 |
| 2 | 1182 | 286 |
| 0 | 8272 | 273 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
(pow.f64 k #s(literal -1/2 binary64)) |
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k)))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))) |
(*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) |
(*.f64 n (/.f64 (PI.f64) k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)))) |
(sqrt.f64 (PI.f64)) |
(PI.f64) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)) |
(*.f64 (PI.f64) (*.f64 (PI.f64) #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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
#s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) |
(/.f64 (PI.f64) k) |
(sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) |
(sqrt.f64 k) |
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(neg.f64 (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (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)) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(fma.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(fma.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(+.f64 (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))))) |
(*.f64 (pow.f64 (fabs.f64 k) #s(literal -1/4 binary64)) (pow.f64 (fabs.f64 k) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (neg.f64 k) #s(literal -1/4 binary64)) (pow.f64 (neg.f64 k) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (neg.f64 (pow.f64 k #s(literal -1/4 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) |
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 k)) |
(pow.f64 (*.f64 (pow.f64 k #s(literal -1 binary64)) (pow.f64 k #s(literal -1 binary64))) #s(literal 1/4 binary64)) |
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64)) |
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) #s(literal 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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) |
(pow.f64 k #s(literal -1/2 binary64)) |
(/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) (-.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(/.f64 (+.f64 (pow.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (-.f64 (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))))) |
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (neg.f64 k)))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 k))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 k)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(neg.f64 (*.f64 (neg.f64 (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) |
(neg.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (neg.f64 (pow.f64 k #s(literal -1/4 binary64))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) |
(sqrt.f64 (pow.f64 k #s(literal -1 binary64))) |
(fabs.f64 (pow.f64 k #s(literal -1/2 binary64))) |
(exp.f64 (neg.f64 (log.f64 (sqrt.f64 k)))) |
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(pow.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)) |
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(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
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(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (cbrt.f64 (PI.f64))) |
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(pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/6 binary64)) |
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) |
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3/2 binary64)) |
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) |
(pow.f64 (PI.f64) #s(literal 1/2 binary64)) |
(sqrt.f64 (PI.f64)) |
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(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(exp.f64 (log.f64 (sqrt.f64 (PI.f64)))) |
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(*.f64 (sqrt.f64 k) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))) |
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(hypot.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (sqrt.f64 (neg.f64 (PI.f64)))) |
(hypot.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(hypot.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))) |
(hypot.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(hypot.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(hypot.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(hypot.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (neg.f64 (sqrt.f64 (PI.f64)))) |
(hypot.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (sqrt.f64 (PI.f64))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 (neg.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (neg.f64 (sqrt.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 (PI.f64))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (neg.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 (neg.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (neg.f64 (sqrt.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 (PI.f64))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (neg.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (PI.f64)))) |
(hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64))))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (neg.f64 (PI.f64)))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64)))) |
(hypot.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64))))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64))))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (neg.f64 (PI.f64)))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 (PI.f64)))) |
(hypot.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
Compiled 49 558 to 5 892 computations (88.1% saved)
26 alts after pruning (20 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 298 | 15 | 1 313 |
| Fresh | 5 | 5 | 10 |
| Picked | 2 | 3 | 5 |
| Done | 1 | 3 | 4 |
| Total | 1 306 | 26 | 1 332 |
| Status | Accuracy | Program |
|---|---|---|
| 99.6% | (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) | |
| 99.6% | (*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) | |
| ✓ | 99.4% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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))))) |
| 99.7% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) | |
| 48.0% | (*.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))))) | |
| 99.7% | (*.f64 #s(approx (pow k -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) | |
| 5.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 k))) | |
| 5.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 k))) | |
| 47.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) | |
| 16.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 binary64)))) | |
| 47.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) | |
| 47.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) | |
| 5.0% | #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 (PI.f64) k)))) | |
| 47.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))) | |
| 4.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) | |
| ✓ | 34.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
| 5.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) | |
| ✓ | 47.5% | #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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 21.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 k (*.f64 (PI.f64) n))) (*.f64 k k)))) | |
| 4.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) k))) | |
| ✓ | 35.0% | #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)))) |
| 35.0% | #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))))) | |
| 34.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) | |
| ✓ | 34.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
| 5.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) |
Compiled 2 464 to 873 computations (64.6% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) 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 2 binary64)) (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 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 (*.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 (*.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n 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 (PI.f64) 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 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.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 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #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 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 k (*.f64 (PI.f64) n))) (*.f64 k 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 (PI.f64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 k))) |
#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)))) |
#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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (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 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 binary64)))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 #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)))) |
(*.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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 #s(approx (pow k -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) 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))))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
(*.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 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
(*.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 (pow.f64 k #s(literal -1/8 binary64)) #s(literal 4 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 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 -1/4 binary64)) (pow.f64 k #s(literal 1/4 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 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (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))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (exp.f64 (log.f64 n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (pow.f64 k #s(literal 1/4 binary64)) (cosh.f64 (*.f64 (log.f64 k) #s(literal 1/4 binary64)))) (*.f64 (pow.f64 k #s(literal 1/4 binary64)) (sinh.f64 (*.f64 (log.f64 k) #s(literal 1/4 binary64)))))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) (-.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 (/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))) (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))))) (-.f64 (cosh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))) (sinh.f64 (*.f64 (log.f64 k) #s(literal -1/4 binary64))))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Outputs |
|---|
(*.f64 #s(approx (pow k -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
4 calls:
| 80.0ms | k |
| 71.0ms | (*.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)))) |
| 63.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 43.0ms | n |
| 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))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) 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 2 binary64)) (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 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 (*.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 (*.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n 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 (PI.f64) 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 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.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 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #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 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 k (*.f64 (PI.f64) n))) (*.f64 k 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 (PI.f64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 k))) |
#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)))) |
#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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (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 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 binary64)))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 #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)))) |
(*.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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
| Outputs |
|---|
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
4 calls:
| 82.0ms | k |
| 44.0ms | (*.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)))) |
| 21.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 21.0ms | n |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | k |
| 99.6% | 1 | n |
| 99.6% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 99.6% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) 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 2 binary64)) (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 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 (*.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 (*.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n 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 (PI.f64) 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 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.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 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #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 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 k (*.f64 (PI.f64) n))) (*.f64 k 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 (PI.f64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 k))) |
#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)))) |
#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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (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 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 binary64)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 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)))) |
4 calls:
| 35.0ms | (*.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)))) |
| 20.0ms | k |
| 17.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 17.0ms | n |
| Accuracy | Segments | Branch |
|---|---|---|
| 60.2% | 2 | k |
| 47.7% | 1 | n |
| 60.2% | 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)))) |
| 47.7% | 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))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) 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 2 binary64)) (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 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 (*.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 (*.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n 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 (PI.f64) 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 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.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 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #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 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 k (*.f64 (PI.f64) n))) (*.f64 k 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 (PI.f64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 k))) |
#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)))) |
#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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (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)))) |
| Outputs |
|---|
#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)))) |
2 calls:
| 24.0ms | k |
| 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)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 47.7% | 1 | k |
| 47.7% | 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)))) |
Compiled 17 to 15 computations (11.8% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) 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 2 binary64)) (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 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 (*.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 (*.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (* (PI) (* (PI) 2))) (sqrt k)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n 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 (PI.f64) k)))) |
| Outputs |
|---|
#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)))) |
4 calls:
| 37.0ms | n |
| 9.0ms | k |
| 9.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) 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 |
|---|---|---|
| 35.0% | 1 | n |
| 35.0% | 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)))) |
| 35.0% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 35.0% | 1 | k |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) 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 2 binary64)) (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k)))) |
4 calls:
| 8.0ms | k |
| 6.0ms | n |
| 5.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 4.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| Accuracy | Segments | Branch |
|---|---|---|
| 35.0% | 1 | k |
| 35.0% | 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)))) |
| 35.0% | 1 | n |
| 35.0% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
4 calls:
| 36.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 4.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 3.0ms | k |
| 3.0ms | n |
| Accuracy | Segments | Branch |
|---|---|---|
| 34.9% | 1 | k |
| 34.9% | 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)))) |
| 34.9% | 1 | n |
| 34.9% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
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))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
4 calls:
| 3.0ms | n |
| 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)))) |
| 3.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 3.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 5.0% | 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)))) |
| 5.0% | 1 | k |
| 5.0% | 1 | n |
| 5.0% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 8.421866120149475e-151 |
Compiled 19 to 18 computations (5.3% saved)
| 1× | egg-herbie |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 72 | 260 |
| 1 | 90 | 246 |
| 2 | 106 | 246 |
| 3 | 127 | 246 |
| 4 | 144 | 246 |
| 5 | 163 | 246 |
| 6 | 197 | 246 |
| 7 | 268 | 246 |
| 8 | 299 | 246 |
| 9 | 332 | 246 |
| 10 | 342 | 246 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 #s(approx (pow k -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 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))))) |
#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))) (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 2 binary64)) (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
| Outputs |
|---|
(*.f64 #s(approx (pow k -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
(*.f64 #s(approx (pow k -1/2) (sqrt.f64 (pow.f64 k #s(literal -1 binary64)))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) k))))) |
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 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))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (*.f64 k k) #s(literal 1/4 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))))) |
#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))) (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 2 binary64)) (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (PI.f64) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 55 | 325 |
| 0 | 85 | 314 |
| 1 | 254 | 288 |
| 2 | 1182 | 286 |
| 0 | 8272 | 273 |
| 0 | 120 | 502 |
| 1 | 378 | 489 |
| 2 | 1377 | 453 |
| 3 | 4131 | 453 |
| 0 | 8166 | 441 |
| 0 | 210 | 1029 |
| 1 | 736 | 983 |
| 2 | 2962 | 913 |
| 3 | 7945 | 913 |
| 0 | 8156 | 896 |
| 0 | 57 | 328 |
| 0 | 88 | 314 |
| 1 | 264 | 294 |
| 2 | 1258 | 294 |
| 0 | 8377 | 294 |
| 0 | 47 | 234 |
| 0 | 76 | 226 |
| 1 | 216 | 212 |
| 2 | 1033 | 210 |
| 0 | 8741 | 210 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 822 to 507 computations (38.3% saved)
Compiled 552 to 178 computations (67.8% saved)
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