Migdal et al, Equation (51)
Time bar (total: 9.0s)
| 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)
| 1.3s | 8 256× | 0 | valid |
| 929.0ms | 3 391× | 1 | invalid |
| 455.0ms | 1 835× | 1 | exit |
| 217.0ms | 393× | 2 | invalid |
| 41.0ms | 488× | 0 | invalid |
| 25.0ms | 219× | 0 | exit |
ival-pow: 632.0ms (28.7% of total)ival-mult: 499.0ms (22.7% of total)ival-div: 365.0ms (16.6% of total)ival-sqrt: 223.0ms (10.1% of total)adjust: 178.0ms (8.1% of total)ival-sub: 148.0ms (6.7% of total)ival-pi: 123.0ms (5.6% of total)exact: 16.0ms (0.7% of total)ival-true: 12.0ms (0.5% of total)ival-assert: 6.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 4 | 87 | (1.3808789476236915e-236 5.345540054164014e+181) | 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 | 91 | 30 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 4 | 0 |
| - | 87 | 165 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 4 | 0 | 0 |
| - | 87 | 30 | 135 |
| number | freq |
|---|---|
| 0 | 165 |
| 1 | 91 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 67.0ms | 512× | 0 | valid |
Compiled 182 to 56 computations (69.2% saved)
ival-pow: 15.0ms (31.2% of total)ival-mult: 14.0ms (29.1% of total)ival-div: 7.0ms (14.6% of total)ival-sqrt: 6.0ms (12.5% of total)ival-sub: 3.0ms (6.2% of total)ival-pi: 2.0ms (4.2% of total)ival-true: 1.0ms (2.1% of total)exact: 1.0ms (2.1% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 88 |
| 1 | 91 | 74 |
| 2 | 263 | 74 |
| 3 | 682 | 74 |
| 4 | 1445 | 74 |
| 5 | 1814 | 74 |
| 6 | 1980 | 74 |
| 7 | 2061 | 74 |
| 8 | 2092 | 74 |
| 9 | 2092 | 74 |
| 0 | 13 | 16 |
| 0 | 22 | 16 |
| 1 | 46 | 14 |
| 2 | 109 | 14 |
| 3 | 280 | 14 |
| 4 | 576 | 14 |
| 5 | 786 | 14 |
| 6 | 880 | 14 |
| 7 | 975 | 14 |
| 8 | 1002 | 14 |
| 9 | 1011 | 14 |
| 0 | 1011 | 13 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) |
Compiled 16 to 13 computations (18.8% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.5% | (*.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)
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.1479960372449824 | (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) | |
| accuracy | 0.17578125 | (*.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 | 0.234375 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| accuracy | 0.265625 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 39.0ms | 256× | 0 | valid |
Compiled 110 to 28 computations (74.5% saved)
ival-sqrt: 9.0ms (36% of total)ival-pow: 5.0ms (20% of total)ival-mult: 4.0ms (16% of total)ival-div: 3.0ms (12% of total)ival-pi: 1.0ms (4% of total)ival-sub: 1.0ms (4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) |
| Outputs |
|---|
(sqrt (/ 1 k)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (* 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)))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(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 | |
|---|---|---|---|---|
| 30.0ms | n | @ | 0 | ((* (* 2 (PI)) n) (/ 1 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 24.0ms | n | @ | -inf | ((* (* 2 (PI)) n) (/ 1 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 10.0ms | n | @ | inf | ((* (* 2 (PI)) n) (/ 1 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 2.0ms | k | @ | 0 | ((* (* 2 (PI)) n) (/ 1 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 2.0ms | k | @ | -inf | ((* (* 2 (PI)) n) (/ 1 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 115 | 498 |
| 1 | 374 | 485 |
| 2 | 1477 | 449 |
| 3 | 5074 | 445 |
| 0 | 8334 | 433 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (/ 1 k)) |
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (* 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)))))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(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 (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(* (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 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(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 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (*.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 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #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 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 3 binary64))))) k (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) 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 #s(literal 2 binary64) (*.f64 (PI.f64) n))) 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 #s(literal 1/8 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (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 #s(literal 2 binary64) (*.f64 (PI.f64) n))) 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 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #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 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #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 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) |
(* 2 (* n (PI))) |
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 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)))) |
(pow.f64 (*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 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)))) |
(pow.f64 (*.f64 (pow.f64 n #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64))) (-.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))))) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 36 |
| 0 | 22 | 36 |
| 1 | 99 | 33 |
| 2 | 674 | 25 |
| 0 | 8051 | 25 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(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 (*.f64 n #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal -1 binary64)) (neg.f64 (PI.f64))) |
(*.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (PI.f64)) |
(*.f64 (*.f64 n (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))) |
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64))))) |
(*.f64 (exp.f64 (log.f64 #s(literal 0 binary64))) (exp.f64 (log.f64 n))) |
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 #s(literal 0 binary64)))) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64))) |
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) |
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n)) |
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)) |
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) n)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (PI.f64)) (fma.f64 (sqrt.f64 (PI.f64)) n (*.f64 (sqrt.f64 (PI.f64)) n))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n)) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 (cbrt.f64 (PI.f64)) n (*.f64 (cbrt.f64 (PI.f64)) n))) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)) n)) |
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 #s(literal 0 binary64) n) |
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) n)) |
(*.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 1 binary64)) |
(*.f64 n #s(literal 0 binary64)) |
(*.f64 (PI.f64) (*.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) |
(/.f64 (*.f64 (*.f64 (neg.f64 (PI.f64)) (PI.f64)) (*.f64 n #s(literal 2 binary64))) (neg.f64 (PI.f64))) |
(/.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (*.f64 n #s(literal 2 binary64))) (*.f64 (PI.f64) (PI.f64))) |
(/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) (PI.f64)) |
(/.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (*.f64 (neg.f64 (PI.f64)) (PI.f64))) (neg.f64 (PI.f64))) |
(/.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (*.f64 (PI.f64) (PI.f64))) |
(/.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64))) (PI.f64)) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64))) (pow.f64 (PI.f64) #s(literal -1 binary64))) |
(/.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (PI.f64) #s(literal -1 binary64))) |
(/.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (neg.f64 (PI.f64))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (neg.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) (*.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) (-.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) |
(/.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 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal -1 binary64))) |
(/.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 (PI.f64) (PI.f64))) |
(/.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 0 binary64)) |
(/.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 1 binary64)) |
(neg.f64 (fma.f64 (neg.f64 (PI.f64)) n (*.f64 (neg.f64 (PI.f64)) n))) |
(neg.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (neg.f64 (PI.f64)))) |
(neg.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 (PI.f64)) n))) |
(neg.f64 (*.f64 (*.f64 (neg.f64 (PI.f64)) n) #s(literal 2 binary64))) |
(neg.f64 (*.f64 (neg.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64)))) |
(neg.f64 (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal -1 binary64)) (neg.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal -1 binary64)) (neg.f64 (PI.f64)) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal -1 binary64)) (neg.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (PI.f64) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (PI.f64) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (PI.f64) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 n (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 n (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 n (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 n (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 n (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 n (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) n)) |
(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))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) n)) |
(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 n #s(literal -1 binary64)) (neg.f64 (PI.f64)) (*.f64 n (PI.f64))) |
(fma.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64)))) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (exp.f64 (log.f64 #s(literal 0 binary64))) (exp.f64 (log.f64 n)) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (exp.f64 (log.f64 #s(literal 0 binary64))) (exp.f64 (log.f64 n)) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (exp.f64 (log.f64 #s(literal 0 binary64))) (exp.f64 (log.f64 n)) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 #s(literal 0 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 #s(literal 0 binary64))) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 #s(literal 0 binary64))) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64)) (*.f64 n (PI.f64))) |
(fma.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) n)) |
(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 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 n #s(literal 2 binary64)))) |
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))) (*.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 0 binary64))) |
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) n)) |
(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)) #s(literal 1 binary64) (*.f64 n (PI.f64))) |
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(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(*.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(*.f64 (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))) |
(*.f64 (*.f64 (sqrt.f64 n) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (sqrt.f64 n) #s(literal 0 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) |
(*.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 #s(literal 0 binary64) n))) |
(pow.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (-.f64 k #s(literal 1 binary64))) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 1 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(pow.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) |
(pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (sqrt.f64 n) #s(literal 0 binary64)) (-.f64 #s(literal 1 binary64) k)) |
(pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 n) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k))) |
(/.f64 (*.f64 #s(literal 0 binary64) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) k))) |
(/.f64 (*.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 0 binary64)) (pow.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) k))) |
(/.f64 (*.f64 (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 n)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k))) |
(/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (-.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) |
(/.f64 (+.f64 (pow.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (-.f64 (*.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))))) |
(/.f64 (neg.f64 (*.f64 (sqrt.f64 n) #s(literal 0 binary64))) (neg.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 n) #s(literal 0 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 n) #s(literal 0 binary64))) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64))) |
(/.f64 (fabs.f64 (*.f64 (sqrt.f64 n) #s(literal 0 binary64))) (fabs.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 2 binary64)) (*.f64 k #s(literal 1/4 binary64)))) |
(/.f64 (*.f64 (sqrt.f64 n) #s(literal 0 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) k) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 n) #s(literal 0 binary64)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))) |
(neg.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(fma.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64) (*.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) |
(sqrt.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (-.f64 #s(literal 1 binary64) k))) |
(fabs.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(fabs.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (*.f64 #s(literal 0 binary64) n)) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (*.f64 #s(literal 0 binary64) n))))) |
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (*.f64 #s(literal 0 binary64) n))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (*.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(+.f64 (*.f64 #s(literal 1 binary64) (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 #s(literal 1 binary64) (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) |
(+.f64 (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 0 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
Compiled 9 062 to 1 317 computations (85.5% saved)
19 alts after pruning (18 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 390 | 18 | 408 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 390 | 19 | 409 |
| Status | Accuracy | Program |
|---|---|---|
| 26.0% | (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| 74.9% | (*.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))) | |
| 99.5% | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| ▶ | 75.3% | (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
| 75.3% | (*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) | |
| ▶ | 99.5% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) (PI.f64)) (/.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)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 96.2% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64))))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| 75.2% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) | |
| 63.2% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) | |
| 99.5% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))) | |
| 53.6% | (*.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 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))) | |
| 53.2% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) | |
| ▶ | 75.3% | (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
| 96.1% | (*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) | |
| 58.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k)) | |
| ▶ | 99.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| ▶ | 43.0% | #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)))) |
Compiled 916 to 685 computations (25.2% saved)
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.2265625 | (*.f64 n (PI.f64)) | |
| accuracy | 0.22722626953688402 | (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) | |
| accuracy | 0.7578125 | (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) | |
| accuracy | 14.288714627041117 | (PI.f64) | |
| accuracy | 0.17578125 | (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| accuracy | 0.2265625 | (*.f64 n (PI.f64)) | |
| accuracy | 0.8287887695368842 | (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) | |
| accuracy | 14.288714627041117 | (PI.f64) | |
| accuracy | 0.18359375 | (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) | |
| accuracy | 0.2109375 | (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) (PI.f64)) | |
| accuracy | 0.30859375 | (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) | |
| accuracy | 14.288714627041117 | (PI.f64) | |
| accuracy | 0.33888627930532605 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) | |
| accuracy | 6.677570246884966 | (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) | |
| accuracy | 14.288714627041117 | (PI.f64) | |
| accuracy | 15.284758733647632 | #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 | 0.09346294491758643 | (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) | |
| accuracy | 0.17578125 | (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) | |
| accuracy | 0.2265625 | (*.f64 (PI.f64) n) | |
| accuracy | 14.288714627041117 | (PI.f64) |
| 77.0ms | 197× | 0 | valid |
| 24.0ms | 59× | 0 | exit |
Compiled 656 to 94 computations (85.7% saved)
ival-pow: 30.0ms (39.2% of total)ival-mult: 21.0ms (27.5% of total)ival-div: 11.0ms (14.4% of total)ival-sqrt: 9.0ms (11.8% of total)ival-pi: 2.0ms (2.6% of total)ival-add: 1.0ms (1.3% of total)ival-sub: 1.0ms (1.3% of total)exact: 1.0ms (1.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(PI.f64) |
(*.f64 (PI.f64) n) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.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)))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) |
(/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) (PI.f64)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 n (PI.f64)) |
(/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (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)) k)) |
(sqrt (/ 1 k)) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k) |
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* n (PI)))))) k) |
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 2)))))) k) |
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 3))) (* 1/8 (* (sqrt (* k (* n (PI)))) (pow (log (* n (PI))) 2)))))))) k) |
(* (sqrt (/ 1 k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (pow k 3)) (* (log 2) (sqrt 2)))) (* (sqrt k) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* 1/8 (* (sqrt (pow k 3)) (* (pow (log 2) 2) (sqrt 2)))))) (* (sqrt k) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (sqrt k) (* (pow (log 2) 2) (sqrt 2)))))))) (* (sqrt k) (sqrt 2))) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (exp (* (log (* n (PI))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log 2) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2))) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (log (* n (PI))) (+ 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* -1/2 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (* (exp (* (log (* n (PI))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(* n (PI)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* 2 (* n (pow (PI) 2))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (PI)))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -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 (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n))))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 73.0ms | n | @ | 0 | ((PI) (* (PI) n) (* (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt (/ 1 k))) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (PI) n) k)) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (* (* (PI) (PI)) (* n 2)) (/ (* (* (PI) (PI)) (* n 2)) (PI)) (/ 1 (sqrt k)) (* (pow 2 (+ (* k -1/2) 1/2)) (/ (pow (* n (PI)) (+ (* k -1/2) 1/2)) (sqrt k))) (* n (PI)) (/ (pow (* n (PI)) (+ (* k -1/2) 1/2)) (sqrt k)) (* (* (pow k -1/2) (pow 2 (+ (* k -1/2) 1/2))) (pow (* n (PI)) (+ (* k -1/2) 1/2))) (* (pow k -1/2) (pow 2 (+ (* k -1/2) 1/2)))) |
| 51.0ms | n | @ | -inf | ((PI) (* (PI) n) (* (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt (/ 1 k))) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (PI) n) k)) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (* (* (PI) (PI)) (* n 2)) (/ (* (* (PI) (PI)) (* n 2)) (PI)) (/ 1 (sqrt k)) (* (pow 2 (+ (* k -1/2) 1/2)) (/ (pow (* n (PI)) (+ (* k -1/2) 1/2)) (sqrt k))) (* n (PI)) (/ (pow (* n (PI)) (+ (* k -1/2) 1/2)) (sqrt k)) (* (* (pow k -1/2) (pow 2 (+ (* k -1/2) 1/2))) (pow (* n (PI)) (+ (* k -1/2) 1/2))) (* (pow k -1/2) (pow 2 (+ (* k -1/2) 1/2)))) |
| 40.0ms | n | @ | inf | ((PI) (* (PI) n) (* (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt (/ 1 k))) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (PI) n) k)) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (* (* (PI) (PI)) (* n 2)) (/ (* (* (PI) (PI)) (* n 2)) (PI)) (/ 1 (sqrt k)) (* (pow 2 (+ (* k -1/2) 1/2)) (/ (pow (* n (PI)) (+ (* k -1/2) 1/2)) (sqrt k))) (* n (PI)) (/ (pow (* n (PI)) (+ (* k -1/2) 1/2)) (sqrt k)) (* (* (pow k -1/2) (pow 2 (+ (* k -1/2) 1/2))) (pow (* n (PI)) (+ (* k -1/2) 1/2))) (* (pow k -1/2) (pow 2 (+ (* k -1/2) 1/2)))) |
| 6.0ms | k | @ | -inf | ((PI) (* (PI) n) (* (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt (/ 1 k))) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (PI) n) k)) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (* (* (PI) (PI)) (* n 2)) (/ (* (* (PI) (PI)) (* n 2)) (PI)) (/ 1 (sqrt k)) (* (pow 2 (+ (* k -1/2) 1/2)) (/ (pow (* n (PI)) (+ (* k -1/2) 1/2)) (sqrt k))) (* n (PI)) (/ (pow (* n (PI)) (+ (* k -1/2) 1/2)) (sqrt k)) (* (* (pow k -1/2) (pow 2 (+ (* k -1/2) 1/2))) (pow (* n (PI)) (+ (* k -1/2) 1/2))) (* (pow k -1/2) (pow 2 (+ (* k -1/2) 1/2)))) |
| 6.0ms | k | @ | 0 | ((PI) (* (PI) n) (* (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt (/ 1 k))) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (PI) n) k)) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (* (* (PI) (PI)) (* n 2)) (/ (* (* (PI) (PI)) (* n 2)) (PI)) (/ 1 (sqrt k)) (* (pow 2 (+ (* k -1/2) 1/2)) (/ (pow (* n (PI)) (+ (* k -1/2) 1/2)) (sqrt k))) (* n (PI)) (/ (pow (* n (PI)) (+ (* k -1/2) 1/2)) (sqrt k)) (* (* (pow k -1/2) (pow 2 (+ (* k -1/2) 1/2))) (pow (* n (PI)) (+ (* k -1/2) 1/2))) (* (pow k -1/2) (pow 2 (+ (* k -1/2) 1/2)))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 328 | 1644 |
| 0 | 1167 | 1579 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| Inputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (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)) k)) |
(sqrt (/ 1 k)) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k) |
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* n (PI)))))) k) |
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 2)))))) k) |
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 3))) (* 1/8 (* (sqrt (* k (* n (PI)))) (pow (log (* n (PI))) 2)))))))) k) |
(* (sqrt (/ 1 k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (pow k 3)) (* (log 2) (sqrt 2)))) (* (sqrt k) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* 1/8 (* (sqrt (pow k 3)) (* (pow (log 2) 2) (sqrt 2)))))) (* (sqrt k) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (sqrt k) (* (pow (log 2) 2) (sqrt 2)))))))) (* (sqrt k) (sqrt 2))) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (exp (* (log (* n (PI))) (- 1/2 (* 1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log 2) (- 1/2 (* 1/2 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2))) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (log (* n (PI))) (+ 1/2 (* -1/2 k)))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* -1/2 k))))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (* (exp (* (log (* n (PI))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(* n (PI)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(* 2 (* n (pow (PI) 2))) |
(* 2 (* n (PI))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (PI))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (PI)))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -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 (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n))))))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 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 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(sqrt (/ (* n (PI)) k)) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k) |
(/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (log.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)))))) (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (log.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))) (sqrt.f64 k))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/48 binary64) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (PI.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 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)))))) (sqrt.f64 k))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (log.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))) (sqrt.f64 k))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* n (PI)))))) k) |
(/.f64 (fma.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) k) |
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 2)))))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (log.f64 (*.f64 (PI.f64) n)))) k (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) k) |
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 3))) (* 1/8 (* (sqrt (* k (* n (PI)))) (pow (log (* n (PI))) 2)))))))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 3 binary64)) (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (log.f64 (*.f64 (PI.f64) n)))) k (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) k) |
(* (sqrt (/ 1 k)) (sqrt 2)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64))) |
(/ (+ (* -1/2 (* (sqrt (pow k 3)) (* (log 2) (sqrt 2)))) (* (sqrt k) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (log.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* 1/8 (* (sqrt (pow k 3)) (* (pow (log 2) 2) (sqrt 2)))))) (* (sqrt k) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 k)) (*.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt k) (* (log 2) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (sqrt k) (* (pow (log 2) 2) (sqrt 2)))))))) (* (sqrt k) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/48 binary64) (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 k)) (*.f64 (log.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) |
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))) |
(pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (exp (* (log (* n (PI))) (- 1/2 (* 1/2 k)))))) |
(*.f64 (*.f64 (pow.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))) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* 1/2 k))))) |
(*.f64 (pow.f64 (*.f64 (PI.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 (* (log 2) (- 1/2 (* 1/2 k))))) |
(*.f64 (pow.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 (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2))) |
(*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) |
(pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (log (* n (PI))) (+ 1/2 (* -1/2 k)))))) |
(*.f64 (*.f64 (pow.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))) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* -1/2 k))))) |
(*.f64 (pow.f64 (*.f64 (PI.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 (* (log 2) (+ 1/2 (* -1/2 k)))) (* (exp (* (log (* n (PI))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))) |
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2))) |
(*.f64 (*.f64 (pow.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))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) |
(* n (PI)) |
(*.f64 (PI.f64) n) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* 2 (* n (pow (PI) 2))) |
(*.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) #s(literal 2 binary64)) |
(* 2 (* n (PI))) |
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (PI))))))) |
(*.f64 (*.f64 (pow.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))) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (PI)))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (PI.f64)) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))) |
(pow.f64 (exp.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))) |
(*.f64 (*.f64 (pow.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))) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (PI.f64))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n))))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(*.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))) |
(pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(neg.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal 2 binary64)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* -1/2 k)))) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))) |
(*.f64 (*.f64 (pow.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))) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (neg.f64 (PI.f64)))))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n))))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (neg.f64 (PI.f64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 44 | 151 |
| 0 | 72 | 141 |
| 1 | 263 | 128 |
| 2 | 1720 | 128 |
| 0 | 9183 | 128 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(PI.f64) |
(*.f64 (PI.f64) n) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.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)))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) |
(/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) (PI.f64)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 k)) |
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 n (PI.f64)) |
(/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
| Outputs |
|---|
(*.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 (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 (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 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64)))) |
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal -1 binary64))) (cbrt.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal -1 binary64)))) |
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(*.f64 (cbrt.f64 (neg.f64 (PI.f64))) (cbrt.f64 (*.f64 (neg.f64 (PI.f64)) (PI.f64)))) |
(*.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)))) |
(*.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)) (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))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (PI.f64))) |
(*.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (PI.f64)) |
(*.f64 (PI.f64) (log.f64 (E.f64))) |
(*.f64 (PI.f64) #s(literal 1 binary64)) |
(pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)) |
(pow.f64 (E.f64) (log.f64 (PI.f64))) |
(pow.f64 (pow.f64 (PI.f64) #s(literal -1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (PI.f64)) #s(literal 1 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 (cbrt.f64 (PI.f64)) #s(literal 3 binary64)) |
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)) |
(pow.f64 (PI.f64) #s(literal 1 binary64)) |
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(*.f64 (*.f64 n #s(literal 1 binary64)) (PI.f64)) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n)) |
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(*.f64 (PI.f64) n) |
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(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (neg.f64 k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (neg.f64 k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))) |
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)))) |
(/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)) |
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 n (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)))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)) |
(/.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal -1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))) |
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))) (neg.f64 (sqrt.f64 k)))) |
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))))) |
(/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) |
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))) (neg.f64 (neg.f64 (sqrt.f64 k))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))) (sqrt.f64 k))) |
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k) (neg.f64 (neg.f64 (sqrt.f64 k))))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))) |
(fabs.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (sqrt.f64 k)))) |
(exp.f64 (-.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (log.f64 (sqrt.f64 k)))) |
(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (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 (+.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (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 (+.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) |
(exp.f64 (+.f64 (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (*.f64 (log.f64 (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (*.f64 (log.f64 (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64) (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (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) (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (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) (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (-.f64 #s(literal 1 binary64) k) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (-.f64 #s(literal 1 binary64) k) (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (-.f64 #s(literal 1 binary64) k) (*.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 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (neg.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))) (neg.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))) |
(*.f64 (neg.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) (neg.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))) |
(*.f64 (fabs.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))) (fabs.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))) |
(*.f64 (fabs.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) (fabs.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) |
(*.f64 (pow.f64 (*.f64 k (pow.f64 #s(literal 2 binary64) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))) |
(*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 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 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) |
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 2 binary64)) |
(fabs.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 #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 (sqrt.f64 k)) #s(literal -1 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (*.f64 (log.f64 #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 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) |
(+.f64 (cosh.f64 (fma.f64 (log.f64 k) #s(literal -1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) (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 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) |
(+.f64 (cosh.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64)))) (sinh.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64))))) |
Compiled 45 076 to 6 398 computations (85.8% saved)
20 alts after pruning (19 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 461 | 17 | 1 478 |
| Fresh | 11 | 2 | 13 |
| Picked | 4 | 1 | 5 |
| Done | 1 | 0 | 1 |
| Total | 1 477 | 20 | 1 497 |
| Status | Accuracy | Program |
|---|---|---|
| 26.0% | (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| 53.2% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) | |
| 99.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))) | |
| 75.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))) | |
| 78.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))) | |
| 53.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) | |
| 43.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) | |
| 75.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)) k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))) | |
| ▶ | 99.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 99.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| ▶ | 99.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 53.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))) | |
| 42.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) | |
| 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))) | |
| 43.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))) | |
| 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) | |
| ▶ | 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
| ✓ | 43.0% | #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)))) |
| ▶ | 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| ▶ | 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
Compiled 1 144 to 893 computations (21.9% saved)
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.09765625 | (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) | |
| accuracy | 0.1479960372449824 | (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) | |
| accuracy | 0.17578125 | (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 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 | 0.265625 | (*.f64 n (PI.f64)) | |
| accuracy | 0.17578125 | (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) | |
| accuracy | 0.265625 | (*.f64 (PI.f64) n) | |
| accuracy | 0.4277725586106521 | (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) | |
| accuracy | 29.720417483970163 | #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) | |
| accuracy | 0.25 | (/.f64 (PI.f64) k) | |
| accuracy | 0.359375 | (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) | |
| accuracy | 0.4567375488422101 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))) | |
| accuracy | 29.708445791475217 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) | |
| accuracy | 0.1796875 | (/.f64 (*.f64 n (PI.f64)) k) | |
| accuracy | 0.265625 | (*.f64 n (PI.f64)) | |
| accuracy | 13.825403888616698 | (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) | |
| accuracy | 29.708445791475217 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) | |
| accuracy | 0.09765625 | (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) | |
| accuracy | 0.12109375 | (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) | |
| accuracy | 0.17578125 | (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) | |
| accuracy | 0.265625 | (*.f64 n (PI.f64)) |
| 91.0ms | 256× | 0 | valid |
Compiled 741 to 98 computations (86.8% saved)
ival-mult: 22.0ms (32.7% of total)ival-pow: 17.0ms (25.3% of total)ival-sqrt: 14.0ms (20.8% of total)ival-div: 8.0ms (11.9% of total)ival-add: 2.0ms (3% of total)ival-pi: 1.0ms (1.5% of total)ival-sub: 1.0ms (1.5% of total)exact: 1.0ms (1.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 n (PI.f64)) |
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) |
(/.f64 (*.f64 n (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 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) |
(/.f64 (PI.f64) k) |
#s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (PI.f64) n) |
(*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 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 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(sqrt (/ 1 k)) |
(/ (* n (PI)) k) |
(sqrt (/ (* n (PI)) k)) |
(/ (PI) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(+ (* -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)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))) |
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2))) |
(* (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)))) |
(* n (PI)) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(* (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)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -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)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -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)))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 20.0ms | n | @ | -inf | ((* n (PI)) (* (* (pow (* 2 (* n (PI))) (* -1/2 k)) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))) (sqrt (* 2 (* n (PI)))) (sqrt (/ 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (/ (* n (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (* (sqrt n) (sqrt (/ (PI) k))) (/ (PI) k) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (* (sqrt (* (PI) n)) (sqrt 2)) (* (PI) n) (* (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt (/ 1 k))) (* (pow (* 2 (* n (PI))) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* 2 (* n (PI))) (+ (* -1/2 k) 1/2))) |
| 19.0ms | n | @ | inf | ((* n (PI)) (* (* (pow (* 2 (* n (PI))) (* -1/2 k)) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))) (sqrt (* 2 (* n (PI)))) (sqrt (/ 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (/ (* n (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (* (sqrt n) (sqrt (/ (PI) k))) (/ (PI) k) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (* (sqrt (* (PI) n)) (sqrt 2)) (* (PI) n) (* (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt (/ 1 k))) (* (pow (* 2 (* n (PI))) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* 2 (* n (PI))) (+ (* -1/2 k) 1/2))) |
| 17.0ms | n | @ | 0 | ((* n (PI)) (* (* (pow (* 2 (* n (PI))) (* -1/2 k)) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))) (sqrt (* 2 (* n (PI)))) (sqrt (/ 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (/ (* n (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (* (sqrt n) (sqrt (/ (PI) k))) (/ (PI) k) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (* (sqrt (* (PI) n)) (sqrt 2)) (* (PI) n) (* (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt (/ 1 k))) (* (pow (* 2 (* n (PI))) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* 2 (* n (PI))) (+ (* -1/2 k) 1/2))) |
| 8.0ms | k | @ | -inf | ((* n (PI)) (* (* (pow (* 2 (* n (PI))) (* -1/2 k)) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))) (sqrt (* 2 (* n (PI)))) (sqrt (/ 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (/ (* n (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (* (sqrt n) (sqrt (/ (PI) k))) (/ (PI) k) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (* (sqrt (* (PI) n)) (sqrt 2)) (* (PI) n) (* (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt (/ 1 k))) (* (pow (* 2 (* n (PI))) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* 2 (* n (PI))) (+ (* -1/2 k) 1/2))) |
| 3.0ms | k | @ | inf | ((* n (PI)) (* (* (pow (* 2 (* n (PI))) (* -1/2 k)) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))) (sqrt (* 2 (* n (PI)))) (sqrt (/ 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (/ (* n (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (* (sqrt n) (sqrt (/ (PI) k))) (/ (PI) k) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (* (sqrt (* (PI) n)) (sqrt 2)) (* (PI) n) (* (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt (/ 1 k))) (* (pow (* 2 (* n (PI))) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* 2 (* n (PI))) (+ (* -1/2 k) 1/2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 247 | 1314 |
| 0 | 874 | 1280 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| 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)) |
(/ (* n (PI)) k) |
(sqrt (/ (* n (PI)) k)) |
(/ (PI) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(+ (* -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)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))) |
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2))) |
(* (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)))) |
(* n (PI)) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(* (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)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -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)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -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)))))) |
| 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 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 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 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(sqrt (/ 1 k)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
(/ (* n (PI)) k) |
(/.f64 (*.f64 (PI.f64) n) k) |
(sqrt (/ (* n (PI)) k)) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(/ (PI) k) |
(/.f64 (PI.f64) k) |
(* (sqrt (* n (PI))) (sqrt 2)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/6 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (log.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (fma.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 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 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))) |
(pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) |
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (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 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(*.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) |
(*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #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 (PI.f64) n) k)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) |
(pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (* (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))) (pow (sqrt -1) 2))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 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 (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* n (PI)) |
(*.f64 (PI.f64) n) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (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 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))) (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 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))) |
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) k))) (sqrt.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 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))) |
(pow.f64 (exp.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 #s(literal 1 binary64) k)) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (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))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1))))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) k))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1)))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(neg.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))) (-.f64 #s(literal 1 binary64) k)) |
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))) |
(*.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) (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))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 48 | 195 |
| 0 | 75 | 179 |
| 1 | 258 | 168 |
| 2 | 1528 | 168 |
| 0 | 8846 | 168 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 n (PI.f64)) |
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) |
(/.f64 (*.f64 n (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 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) |
(/.f64 (PI.f64) k) |
#s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (PI.f64) n) |
(*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 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 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
| Outputs |
|---|
(*.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 (*.f64 n #s(literal 1 binary64)) (PI.f64)) |
(*.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 #s(literal 1 binary64) (*.f64 (PI.f64) n)) |
(*.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)) |
(*.f64 (PI.f64) (*.f64 #s(literal 1 binary64) n)) |
(*.f64 (PI.f64) n) |
(*.f64 n (PI.f64)) |
(/.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)) |
(neg.f64 (*.f64 (neg.f64 n) (PI.f64))) |
(fma.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 0 binary64))) |
(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 0 binary64))) |
(fma.f64 (*.f64 n #s(literal 1 binary64)) (PI.f64) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 n #s(literal 1 binary64)) (PI.f64) (*.f64 n #s(literal 0 binary64))) |
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n) (*.f64 n #s(literal 0 binary64))) |
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) n) (*.f64 n #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) n (*.f64 (PI.f64) n)) |
(fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n) (*.f64 n #s(literal 0 binary64))) |
(fma.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64) (*.f64 n #s(literal 0 binary64))) |
(fma.f64 (PI.f64) (*.f64 #s(literal 1 binary64) n) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (PI.f64) (*.f64 #s(literal 1 binary64) n) (*.f64 n #s(literal 0 binary64))) |
(fma.f64 (PI.f64) n (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (PI.f64) n (*.f64 n #s(literal 0 binary64))) |
(fma.f64 n #s(literal 0 binary64) (*.f64 (PI.f64) n)) |
(fma.f64 n (PI.f64) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 n (PI.f64) (*.f64 n #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 (PI.f64) n)) |
(+.f64 (*.f64 n #s(literal 0 binary64)) (*.f64 (PI.f64) n)) |
(+.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal 0 binary64) n)) |
(+.f64 (*.f64 (PI.f64) n) (*.f64 n #s(literal 0 binary64))) |
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (*.f64 n #s(literal 1 binary64)))) |
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) #s(literal 1 binary64))) |
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n)) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) |
(*.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/4 binary64)) (*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/4 binary64)) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) k) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (pow.f64 k #s(literal -1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) (sqrt.f64 (neg.f64 k)))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64)) (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)) (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) (neg.f64 (neg.f64 (sqrt.f64 k))))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)) (*.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) (sqrt.f64 k))) |
(/.f64 (*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) (sqrt.f64 (neg.f64 k)))) |
(/.f64 (*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) (neg.f64 (neg.f64 (sqrt.f64 k))))) |
(/.f64 (*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) |
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(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) |
(*.f64 (sqrt.f64 n) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) #s(literal 1/2 binary64))) |
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(pow.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) |
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) |
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(pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
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(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) |
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(fabs.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
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(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))) |
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(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k)) |
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(*.f64 n (/.f64 (PI.f64) k)) |
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(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1 binary64)) |
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(/.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) n) (*.f64 (*.f64 (PI.f64) (PI.f64)) k)) |
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(/.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -1 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 k))) |
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(/.f64 (*.f64 (PI.f64) n) k) |
(/.f64 n (/.f64 k (PI.f64))) |
(neg.f64 (/.f64 (*.f64 (neg.f64 n) (PI.f64)) k)) |
(exp.f64 (*.f64 (log.f64 (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1 binary64))) |
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) (pow.f64 k #s(literal -1 binary64)))) |
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(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) |
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(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) |
(*.f64 (sqrt.f64 n) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) |
(pow.f64 (exp.f64 (log.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) |
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (pow.f64 k #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
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(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (PI.f64)))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (sqrt.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k))) |
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(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) |
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(sqrt.f64 (*.f64 (pow.f64 k #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) |
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) |
(fabs.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) |
(exp.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (log.f64 (sqrt.f64 k)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #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) (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))) |
(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
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(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n (pow.f64 k #s(literal -1 binary64))))) |
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 n (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (/.f64 n k) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -1 binary64))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 n #s(literal 1 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 k (*.f64 (PI.f64) n))))) |
(/.f64 (sqrt.f64 (*.f64 (neg.f64 n) (PI.f64))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (neg.f64 (neg.f64 k)))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(exp.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (log.f64 (sqrt.f64 k)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1/2 binary64) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 (PI.f64) n)) #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) k)) #s(literal 1/2 binary64) (*.f64 (log.f64 n) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 n) #s(literal 1/2 binary64) (*.f64 (log.f64 (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64))) |
(*.f64 (neg.f64 (PI.f64)) (pow.f64 (neg.f64 k) #s(literal -1 binary64))) |
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) k)) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (PI.f64)) k)) |
(*.f64 (/.f64 (PI.f64) k) #s(literal 1 binary64)) |
(*.f64 (pow.f64 k #s(literal -1 binary64)) (PI.f64)) |
(*.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k)) |
(*.f64 (PI.f64) (pow.f64 k #s(literal -1 binary64))) |
(pow.f64 (/.f64 k (PI.f64)) #s(literal -1 binary64)) |
(/.f64 (-.f64 (*.f64 (neg.f64 (PI.f64)) k) (*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 0 binary64))) (*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 k)) k)) |
(/.f64 (-.f64 (*.f64 (neg.f64 (PI.f64)) k) (*.f64 (neg.f64 k) #s(literal 0 binary64))) (*.f64 (neg.f64 k) k)) |
(/.f64 (-.f64 (neg.f64 k) (*.f64 (neg.f64 (/.f64 k (PI.f64))) #s(literal 0 binary64))) (*.f64 (neg.f64 (/.f64 k (PI.f64))) k)) |
(/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) k) k) #s(literal 0 binary64)) k) |
(/.f64 (-.f64 k (*.f64 (/.f64 k (PI.f64)) #s(literal 0 binary64))) (*.f64 (/.f64 k (PI.f64)) k)) |
(/.f64 (-.f64 (*.f64 (PI.f64) k) (*.f64 (neg.f64 (neg.f64 k)) #s(literal 0 binary64))) (*.f64 (neg.f64 (neg.f64 k)) k)) |
(/.f64 (-.f64 (*.f64 (PI.f64) k) (*.f64 k #s(literal 0 binary64))) (*.f64 k k)) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (PI.f64))) #s(literal -1 binary64)) (*.f64 (neg.f64 (PI.f64)) (neg.f64 k))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64)) (*.f64 (neg.f64 (PI.f64)) (neg.f64 (neg.f64 k)))) |
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(pow.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) (*.f64 k k))) (pow.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -1 binary64))) |
(pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 (*.f64 k k) #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64))) (pow.f64 (fma.f64 (*.f64 k k) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal -1/4 binary64)))) #s(literal -1 binary64))) |
(pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 k #s(literal 1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))) |
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) k))) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) |
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 k #s(literal -1/4 binary64))))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal -1/4 binary64) (*.f64 k #s(literal -1/4 binary64))))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 #s(literal 2 binary64) (*.f64 k #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (fma.f64 k #s(literal -1/4 binary64) (*.f64 k #s(literal -1/4 binary64))) #s(literal 1/2 binary64))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(/.f64 (fabs.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (fabs.f64 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))) |
(/.f64 (fabs.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) |
(/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -1 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 (*.f64 k k) (+.f64 #s(literal 1 binary64) k)))) |
(/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 1/4 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (neg.f64 k) #s(literal -1/2 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) |
(/.f64 #s(literal 1 binary64) (fabs.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 k #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -2 binary64)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 k #s(literal 1 binary64)))) |
(sqrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) |
(fabs.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(fabs.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(exp.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) k))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
Compiled 30 025 to 3 398 computations (88.7% saved)
31 alts after pruning (25 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 766 | 21 | 787 |
| Fresh | 10 | 4 | 14 |
| Picked | 0 | 5 | 5 |
| Done | 0 | 1 | 1 |
| Total | 776 | 31 | 807 |
| Status | Accuracy | Program |
|---|---|---|
| 26.0% | (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| 53.2% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) | |
| ▶ | 99.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
| 78.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))) | |
| 53.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) | |
| 43.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) | |
| ✓ | 99.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 99.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 k #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 99.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 99.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| ✓ | 99.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))) | |
| ▶ | 53.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
| 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) | |
| 42.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) | |
| ▶ | 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
| 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) | |
| 43.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))) | |
| 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) | |
| 42.8% | #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 (fma.f64 (PI.f64) k (*.f64 k #s(literal 0 binary64))) (*.f64 k k)))))) | |
| ▶ | 42.8% | #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 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))))))) |
| ✓ | 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
| ✓ | 43.0% | #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)))) |
| ✓ | 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 53.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) | |
| 42.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) | |
| ✓ | 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
| 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) | |
| 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) | |
| ▶ | 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
Compiled 1 624 to 1 273 computations (21.6% saved)
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.359375 | (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))))) | |
| accuracy | 0.4567375488422101 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64))))))) | |
| accuracy | 26.246512591540508 | (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))) | |
| accuracy | 29.708445791475217 | #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 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))))))) | |
| accuracy | 0.265625 | (*.f64 (PI.f64) n) | |
| accuracy | 0.34765625 | (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) | |
| accuracy | 0.4567375488422101 | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) | |
| accuracy | 29.708445791475217 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) | |
| accuracy | 0.13671875 | (sqrt.f64 (*.f64 (PI.f64) n)) | |
| accuracy | 0.265625 | (*.f64 (PI.f64) n) | |
| accuracy | 0.28125 | (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) | |
| accuracy | 29.708445791475217 | #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)))) | |
| accuracy | 0.0234375 | (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) | |
| accuracy | 0.293632519536884 | (*.f64 (PI.f64) (/.f64 n k)) | |
| accuracy | 13.825403888616698 | (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) | |
| accuracy | 29.708445791475217 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) | |
| accuracy | 0.0 | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) | |
| accuracy | 0.1479960372449824 | (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) | |
| accuracy | 0.203125 | (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| accuracy | 0.265625 | (*.f64 (PI.f64) n) |
| 82.0ms | 256× | 0 | valid |
Compiled 658 to 92 computations (86% saved)
ival-mult: 20.0ms (33.8% of total)ival-div: 12.0ms (20.3% of total)ival-sqrt: 11.0ms (18.6% of total)ival-pow: 10.0ms (16.9% of total)ival-add: 2.0ms (3.4% of total)ival-pi: 1.0ms (1.7% of total)ival-sub: 1.0ms (1.7% of total)exact: 1.0ms (1.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (PI.f64) n) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) |
(*.f64 (PI.f64) (/.f64 n k)) |
(*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) |
(/.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 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))))))) |
(/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64))))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (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))) |
(/ (* n (PI)) k) |
(* 2 (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(/ (PI) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(* n (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)))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(sqrt (* n (PI))) |
(* (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))))) |
(* (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))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 25.0ms | k | @ | inf | ((* (PI) n) (/ (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (sqrt k)) (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (PI) (/ n k)) (* (* (PI) (/ n k)) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) n)) (sqrt (/ 2 k))) (sqrt (* (PI) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI)))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI))))))) (* (sqrt n) (sqrt (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI))))))) |
| 12.0ms | n | @ | -inf | ((* (PI) n) (/ (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (sqrt k)) (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (PI) (/ n k)) (* (* (PI) (/ n k)) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) n)) (sqrt (/ 2 k))) (sqrt (* (PI) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI)))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI))))))) (* (sqrt n) (sqrt (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI))))))) |
| 10.0ms | n | @ | inf | ((* (PI) n) (/ (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (sqrt k)) (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (PI) (/ n k)) (* (* (PI) (/ n k)) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) n)) (sqrt (/ 2 k))) (sqrt (* (PI) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI)))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI))))))) (* (sqrt n) (sqrt (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI))))))) |
| 9.0ms | n | @ | 0 | ((* (PI) n) (/ (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (sqrt k)) (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (PI) (/ n k)) (* (* (PI) (/ n k)) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) n)) (sqrt (/ 2 k))) (sqrt (* (PI) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI)))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI))))))) (* (sqrt n) (sqrt (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI))))))) |
| 5.0ms | k | @ | -inf | ((* (PI) n) (/ (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (sqrt k)) (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (PI) (/ n k)) (* (* (PI) (/ n k)) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) n)) (sqrt (/ 2 k))) (sqrt (* (PI) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI)))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI))))))) (* (sqrt n) (sqrt (/ (+ (* 0 (/ k (PI))) k) (* k (/ k (PI))))))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 149 | 698 |
| 0 | 496 | 676 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| 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))) |
(/ (* n (PI)) k) |
(* 2 (/ (* n (PI)) k)) |
(sqrt (/ (* n (PI)) k)) |
(/ (PI) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(* n (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)))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(sqrt (* n (PI))) |
(* (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))))) |
(* (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))))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
| Outputs |
|---|
(* (sqrt (/ (* n (PI)) k)) (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 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 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k) |
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) |
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) 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))) |
(fma.f64 (*.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) |
(fma.f64 (fma.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 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 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) |
(/ (* n (PI)) k) |
(/.f64 (*.f64 (PI.f64) n) k) |
(* 2 (/ (* n (PI)) k)) |
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) |
(sqrt (/ (* n (PI)) k)) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) |
(/ (PI) k) |
(/.f64 (PI.f64) k) |
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (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 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) |
(pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) n) #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 (PI.f64) n) k)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))) |
(*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)) |
(*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) |
(* n (PI)) |
(*.f64 (PI.f64) n) |
(* (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 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))) (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 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(sqrt (* n (PI))) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
(* (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))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (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))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (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 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) (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))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) |
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) |
(neg.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2))) |
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) |
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 47 | 267 |
| 0 | 75 | 225 |
| 1 | 273 | 213 |
| 2 | 1782 | 204 |
| 0 | 9105 | 204 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (PI.f64) n) |
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) |
(*.f64 (PI.f64) (/.f64 n k)) |
(*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) |
(sqrt.f64 (*.f64 (PI.f64) n)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))) |
(/.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 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))))))) |
(/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64))))))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))))) |
| Outputs |
|---|
(*.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 (*.f64 n #s(literal 1 binary64)) (PI.f64)) |
(*.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 #s(literal 1 binary64) (*.f64 n (PI.f64))) |
(*.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64)) |
(*.f64 n (PI.f64)) |
(*.f64 (PI.f64) (*.f64 #s(literal 1 binary64) n)) |
(*.f64 (PI.f64) n) |
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 3 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 0 binary64) n) (-.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 n (PI.f64)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 n #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64))) (fma.f64 (*.f64 n #s(literal 0 binary64)) (*.f64 n #s(literal 0 binary64)) (-.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 n #s(literal 0 binary64)) (*.f64 n (PI.f64)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 #s(literal 0 binary64) n) (*.f64 #s(literal 0 binary64) n)) (*.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 #s(literal 0 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 n #s(literal 0 binary64)) (*.f64 n #s(literal 0 binary64))) (*.f64 (*.f64 n (PI.f64)) (*.f64 n #s(literal 0 binary64)))))) |
(/.f64 (neg.f64 (*.f64 n (PI.f64))) #s(literal -1 binary64)) |
(/.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64)) |
(neg.f64 (*.f64 n (neg.f64 (PI.f64)))) |
(neg.f64 (*.f64 (neg.f64 (PI.f64)) n)) |
(fma.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (/.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 1 binary64))) |
(fma.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (/.f64 (*.f64 n #s(literal 0 binary64)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (*.f64 #s(literal 0 binary64) n)) |
(fma.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 0 binary64))) |
(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (/.f64 (*.f64 #s(literal 0 binary64) n) #s(literal 1 binary64))) |
(fma.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)) (/.f64 (*.f64 n #s(literal 0 binary64)) #s(literal 1 binary64))) |
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(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) k))) (neg.f64 (/.f64 (fabs.f64 k) (sqrt.f64 (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal -2 binary64))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) k)) (/.f64 (fabs.f64 k) (sqrt.f64 (PI.f64)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) |
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))) |
(sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) |
(fabs.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 1/2 binary64)) (log.f64 (sqrt.f64 k)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 1/2 binary64) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64) (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
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(*.f64 (sqrt.f64 (*.f64 n #s(literal 1 binary64))) (sqrt.f64 (PI.f64))) |
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(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) n))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 1/2 binary64))) |
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) |
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(pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) |
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1 binary64)) |
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(exp.f64 (fma.f64 (log.f64 n) #s(literal 1/2 binary64) (log.f64 (sqrt.f64 (PI.f64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64))) |
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(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))) |
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 1 binary64) (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
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(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (/.f64 n k) #s(literal 2 binary64))))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) |
(*.f64 (sqrt.f64 n) (pow.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
(pow.f64 (exp.f64 (log.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) k))) (neg.f64 (/.f64 (fabs.f64 k) (sqrt.f64 (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal -2 binary64))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) k)) (/.f64 (fabs.f64 k) (sqrt.f64 (PI.f64)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) |
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))) |
(sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) |
(fabs.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 1/2 binary64)) (log.f64 (sqrt.f64 k)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 1/2 binary64) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64) (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64)))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 1 binary64))) (sqrt.f64 (PI.f64))) |
(*.f64 (pow.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (*.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) |
(*.f64 (pow.f64 (*.f64 (/.f64 n k) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))) |
(*.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 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) |
(*.f64 (sqrt.f64 (*.f64 n k)) (/.f64 (sqrt.f64 (PI.f64)) (fabs.f64 k))) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) |
(*.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))) |
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (pow.f64 k #s(literal -1 binary64)) (PI.f64)))) |
(*.f64 (sqrt.f64 n) (pow.f64 (*.f64 (pow.f64 k #s(literal -1 binary64)) (PI.f64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) |
(pow.f64 (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) |
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 1/2 binary64)) |
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(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k) (/.f64 #s(literal 0 binary64) (*.f64 (fma.f64 k k #s(literal 0 binary64)) (*.f64 (/.f64 k (PI.f64)) k)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k) (/.f64 #s(literal 0 binary64) k)) |
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k) #s(literal 0 binary64)) |
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(fma.f64 k (/.f64 (/.f64 (PI.f64) k) k) (/.f64 #s(literal 0 binary64) k)) |
(fma.f64 k (/.f64 (/.f64 (PI.f64) k) k) #s(literal 0 binary64)) |
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(fma.f64 (PI.f64) (pow.f64 k #s(literal -1 binary64)) (/.f64 #s(literal 0 binary64) k)) |
(fma.f64 (PI.f64) (pow.f64 k #s(literal -1 binary64)) #s(literal 0 binary64)) |
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(-.f64 (/.f64 #s(literal 0 binary64) k) (/.f64 (neg.f64 (PI.f64)) k)) |
(-.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 0 binary64) k)) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) k))) |
(exp.f64 (*.f64 (log.f64 (/.f64 k (PI.f64))) #s(literal -1 binary64))) |
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(pow.f64 (*.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) |
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
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(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) k))) (neg.f64 (/.f64 (fabs.f64 k) (sqrt.f64 (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal -2 binary64))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) k)) (/.f64 (fabs.f64 k) (sqrt.f64 (PI.f64)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) |
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))) |
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))) |
(sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) |
(fabs.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 1/2 binary64)) (log.f64 (sqrt.f64 k)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 1/2 binary64) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64) (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
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(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 1 binary64))) (sqrt.f64 (PI.f64))) |
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(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) |
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(neg.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 k)))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64)) (log.f64 (sqrt.f64 k)))) |
(exp.f64 (fma.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64) (*.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (/.f64 (PI.f64) k)) #s(literal 1/2 binary64) (*.f64 (log.f64 n) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 n) #s(literal 1/2 binary64) (*.f64 (log.f64 (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))) #s(literal 1/2 binary64))) |
Compiled 38 611 to 4 815 computations (87.5% saved)
47 alts after pruning (37 fresh and 10 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 093 | 24 | 1 117 |
| Fresh | 7 | 13 | 20 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 6 | 6 |
| Total | 1 101 | 47 | 1 148 |
| Status | Accuracy | Program |
|---|---|---|
| 26.0% | (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) | |
| 53.2% | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) | |
| ✓ | 99.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
| 78.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))) | |
| 53.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))) | |
| 53.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) | |
| 43.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) | |
| 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) | |
| ✓ | 99.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 99.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 k #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 99.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 99.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| ✓ | 99.7% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 53.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) | |
| 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) | |
| 42.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) | |
| 42.9% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) | |
| 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) | |
| 53.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) | |
| ✓ | 53.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) |
| ✓ | 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
| 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) | |
| 43.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))) | |
| 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) | |
| 43.5% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n k)) (/.f64 (sqrt.f64 (PI.f64)) (fabs.f64 k))))) | |
| 42.8% | #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 (fma.f64 (PI.f64) k #s(literal 0 binary64)) (*.f64 k k)))))) | |
| 26.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (neg.f64 (*.f64 k k)) (*.f64 (neg.f64 k) (*.f64 (/.f64 k (PI.f64)) k))))))) | |
| ✓ | 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
| 42.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (*.f64 (/.f64 k (PI.f64)) k)))))) | |
| 42.8% | #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 (/.f64 k (*.f64 k k)) (PI.f64)))))) | |
| 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))) | |
| ✓ | 43.0% | #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)))) |
| ✓ | 53.2% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| 53.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) | |
| 28.6% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) | |
| 31.4% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 k n) (*.f64 (/.f64 k n) (PI.f64))) (*.f64 (/.f64 k n) (/.f64 k n))))) | |
| 31.3% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))) (*.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal 1 binary64))) (*.f64 (/.f64 k (*.f64 n (PI.f64))) (/.f64 k (*.f64 n (PI.f64))))))) | |
| 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) | |
| 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) | |
| ✓ | 43.0% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
| 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) | |
| 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) | |
| 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) | |
| 42.8% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))) | |
| ✓ | 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
| 43.1% | #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
Compiled 3 713 to 1 467 computations (60.5% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#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 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (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 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 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 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.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 #s(approx (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n k)) (/.f64 (sqrt.f64 (PI.f64)) (fabs.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k #s(literal 0 binary64)) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) 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 k (*.f64 (/.f64 k (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 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k (*.f64 k #s(literal 0 binary64))) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 k n) (*.f64 (/.f64 k n) (PI.f64))) (*.f64 (/.f64 k n) (/.f64 k n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (neg.f64 (*.f64 k k)) (*.f64 (neg.f64 k) (*.f64 (/.f64 k (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 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))) (*.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal 1 binary64))) (*.f64 (/.f64 k (*.f64 n (PI.f64))) (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (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 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 k #s(literal 1 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 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.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)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (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 (*.f64 (fma.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) 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)) (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 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) k)))) k)) |
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64)) k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 #s(literal 1/8 binary64) k) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64))))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
4 calls:
| 22.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 21.0ms | n |
| 20.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 20.0ms | k |
| 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))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#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 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (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 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 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 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.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 #s(approx (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n k)) (/.f64 (sqrt.f64 (PI.f64)) (fabs.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k #s(literal 0 binary64)) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) 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 k (*.f64 (/.f64 k (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 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k (*.f64 k #s(literal 0 binary64))) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 k n) (*.f64 (/.f64 k n) (PI.f64))) (*.f64 (/.f64 k n) (/.f64 k n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (neg.f64 (*.f64 k k)) (*.f64 (neg.f64 k) (*.f64 (/.f64 k (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 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))) (*.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal 1 binary64))) (*.f64 (/.f64 k (*.f64 n (PI.f64))) (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (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 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 k #s(literal 1 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 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
4 calls:
| 20.0ms | n |
| 18.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 16.0ms | k |
| 16.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | k |
| 99.6% | 1 | n |
| 99.6% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 99.6% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#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 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (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 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 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 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.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 #s(approx (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n k)) (/.f64 (sqrt.f64 (PI.f64)) (fabs.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k #s(literal 0 binary64)) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) 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 k (*.f64 (/.f64 k (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 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k (*.f64 k #s(literal 0 binary64))) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 k n) (*.f64 (/.f64 k n) (PI.f64))) (*.f64 (/.f64 k n) (/.f64 k n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (neg.f64 (*.f64 k k)) (*.f64 (neg.f64 k) (*.f64 (/.f64 k (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 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))) (*.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal 1 binary64))) (*.f64 (/.f64 k (*.f64 n (PI.f64))) (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (*.f64 (/.f64 k (PI.f64)) k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) |
4 calls:
| 20.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 18.0ms | n |
| 13.0ms | k |
| 12.0ms | (*.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 |
|---|---|---|
| 78.5% | 3 | k |
| 59.1% | 2 | n |
| 86.8% | 3 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 59.1% | 2 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#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 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (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 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 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 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.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 #s(approx (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n k)) (/.f64 (sqrt.f64 (PI.f64)) (fabs.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k #s(literal 0 binary64)) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) 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 k (*.f64 (/.f64 k (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 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k (*.f64 k #s(literal 0 binary64))) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 k n) (*.f64 (/.f64 k n) (PI.f64))) (*.f64 (/.f64 k n) (/.f64 k n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (neg.f64 (*.f64 k k)) (*.f64 (neg.f64 k) (*.f64 (/.f64 k (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 n) (sqrt.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 k (PI.f64)) k) (*.f64 k (/.f64 k (PI.f64)))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))) (*.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal 1 binary64))) (*.f64 (/.f64 k (*.f64 n (PI.f64))) (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (neg.f64 (*.f64 k k)) (*.f64 (neg.f64 k) (*.f64 (/.f64 k (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 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))) |
2 calls:
| 157.0ms | k |
| 12.0ms | (*.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 |
|---|---|---|
| 65.7% | 3 | k |
| 63.1% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 17 to 15 computations (11.8% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#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 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (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 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 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 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.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 #s(approx (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n k)) (/.f64 (sqrt.f64 (PI.f64)) (fabs.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k #s(literal 0 binary64)) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) 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 k (*.f64 (/.f64 k (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 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k (*.f64 k #s(literal 0 binary64))) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 k n) (*.f64 (/.f64 k n) (PI.f64))) (*.f64 (/.f64 k n) (/.f64 k n))))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (*.f64 (/.f64 k (PI.f64)) k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
2 calls:
| 16.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 12.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 63.1% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 63.0% | 2 | k |
Compiled 17 to 15 computations (11.8% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#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 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (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 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 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 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.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 #s(approx (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n k)) (/.f64 (sqrt.f64 (PI.f64)) (fabs.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) k #s(literal 0 binary64)) (*.f64 k k)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.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 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
1 calls:
| 20.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 63.1% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 16 to 13 computations (18.8% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#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 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (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 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 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 k (*.f64 (PI.f64) n))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (PI.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 #s(approx (pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n k)) (/.f64 (sqrt.f64 (PI.f64)) (fabs.f64 k))))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
4 calls:
| 15.0ms | n |
| 14.0ms | k |
| 11.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 10.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 53.3% | 1 | n |
| 53.3% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 53.3% | 1 | k |
| 54.9% | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#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 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 #s(approx (pow (sqrt (* 2 (* (PI) n))) (- 1 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
1 calls:
| 6.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 53.3% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 16 to 13 computations (18.8% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#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 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))) |
| 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)))) |
4 calls:
| 10.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 6.0ms | n |
| 6.0ms | k |
| 5.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 53.3% | 1 | k |
| 53.3% | 1 | n |
| 53.3% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 53.3% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
4 calls:
| 4.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 4.0ms | k |
| 4.0ms | 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)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 53.2% | 1 | n |
| 53.2% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 53.2% | 1 | k |
| 53.2% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) n) (*.f64 (PI.f64) k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
4 calls:
| 7.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 4.0ms | n |
| 4.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 4.0ms | k |
| Accuracy | Segments | Branch |
|---|---|---|
| 43.1% | 1 | k |
| 43.1% | 1 | n |
| 43.1% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 43.1% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
Compiled 23 to 23 computations (0% saved)
Total -0.1b remaining (-0.2%)
Threshold costs -0.1b (-0.2%)
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
4 calls:
| 3.0ms | n |
| 2.0ms | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
| 2.0ms | k |
| 2.0ms | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 43.1% | 1 | k |
| 43.1% | 1 | n |
| 43.1% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) |
| 43.1% | 1 | (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) |
Compiled 23 to 23 computations (0% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 8.519510637697356e+273 | +inf |
| 0.0ms | 2.1468021822266086e-100 | 8.638335299548821e-84 |
Compiled 19 to 18 computations (5.3% saved)
| 2× | binary-search |
| 1× | narrow-enough |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 25.0ms | 2.9661829790610777e+147 | 4.912419908060719e+162 |
| 17.0ms | 8.295131286967e+104 | 1.2817905380843305e+109 |
| 30.0ms | 288× | 0 | valid |
Compiled 1 203 to 966 computations (19.7% saved)
ival-div: 7.0ms (31% of total)ival-mult: 5.0ms (22.1% of total)ival-pow: 5.0ms (22.1% of total)ival-sqrt: 2.0ms (8.9% of total)ival-pi: 1.0ms (4.4% of total)ival-sub: 1.0ms (4.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 2.1468021822266086e-100 | 8.638335299548821e-84 |
Compiled 19 to 18 computations (5.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 2.1468021822266086e-100 | 8.638335299548821e-84 |
Compiled 19 to 18 computations (5.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 1.24092758342061e-118 |
Compiled 19 to 18 computations (5.3% saved)
| 1× | egg-herbie |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 109 | 633 |
| 1 | 150 | 633 |
| 2 | 172 | 631 |
| 3 | 228 | 631 |
| 4 | 296 | 631 |
| 5 | 382 | 631 |
| 6 | 497 | 631 |
| 7 | 635 | 631 |
| 8 | 815 | 631 |
| 9 | 945 | 631 |
| 10 | 1029 | 631 |
| 11 | 1068 | 631 |
| 12 | 1080 | 631 |
| 13 | 1082 | 631 |
| 1× | saturated |
| Inputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
(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 492525077454931/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (*.f64 (/.f64 k (PI.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 9999999999999999213782878444176341486712719163258207029349796604673073768736360688744211624391338142173265718425108901184740478000812045911233791501695173449709921389782217629235579129702792695009666351450002856415308090320884466574359759805482716570229159677380024223137792 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))) |
(if (<=.f64 k #s(literal 849999999999999985713980257761295876811329917477146326265286161894345467478543181985946818940885257945088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (if (<=.f64 k #s(literal 13199999999999999773196063550815192655340841269168371305534464478777571651222204465790151517816444445650545021209011632002935604597533337723926189038370816 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (neg.f64 (*.f64 k k)) (*.f64 (neg.f64 k) (*.f64 (/.f64 k (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 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 492525077454931/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (*.f64 (/.f64 k (PI.f64)) k)))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (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 492525077454931/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (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))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.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 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
| Outputs |
|---|
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (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 (/.f64 #s(literal 1 binary64) k)) (*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 (PI.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))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #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 492525077454931/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (*.f64 (/.f64 k (PI.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 9999999999999999213782878444176341486712719163258207029349796604673073768736360688744211624391338142173265718425108901184740478000812045911233791501695173449709921389782217629235579129702792695009666351450002856415308090320884466574359759805482716570229159677380024223137792 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))) |
(if (<=.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 492525077454931/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 k (*.f64 (/.f64 k (PI.f64)) k))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))) (if (<=.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 9999999999999999213782878444176341486712719163258207029349796604673073768736360688744211624391338142173265718425108901184740478000812045911233791501695173449709921389782217629235579129702792695009666351450002856415308090320884466574359759805482716570229159677380024223137792 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))) |
(if (<=.f64 k #s(literal 849999999999999985713980257761295876811329917477146326265286161894345467478543181985946818940885257945088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) (if (<=.f64 k #s(literal 13199999999999999773196063550815192655340841269168371305534464478777571651222204465790151517816444445650545021209011632002935604597533337723926189038370816 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (neg.f64 (*.f64 k k)) (*.f64 (neg.f64 k) (*.f64 (/.f64 k (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 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))))) |
(if (<=.f64 k #s(literal 849999999999999985713980257761295876811329917477146326265286161894345467478543181985946818940885257945088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))) (if (<=.f64 k #s(literal 13199999999999999773196063550815192655340841269168371305534464478777571651222204465790151517816444445650545021209011632002935604597533337723926189038370816 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 k k) (*.f64 (*.f64 (/.f64 k (PI.f64)) k) k))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))))) |
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 492525077454931/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (*.f64 (/.f64 k (PI.f64)) k)))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(if (<=.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 492525077454931/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (/.f64 k (*.f64 (/.f64 k (PI.f64)) k))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 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 492525077454931/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64)))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(if (<=.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 492525077454931/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 k (*.f64 k k)) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 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))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 n (PI.f64)) k (*.f64 k (*.f64 n (PI.f64)))) (*.f64 k k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(if (<=.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) n) k (*.f64 (*.f64 (PI.f64) n) k)) (*.f64 k k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.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 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.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) 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 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))) |
#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))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) |
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 47 | 267 |
| 0 | 75 | 225 |
| 1 | 273 | 213 |
| 2 | 1782 | 204 |
| 0 | 9105 | 204 |
| 0 | 48 | 195 |
| 0 | 75 | 179 |
| 1 | 258 | 168 |
| 2 | 1528 | 168 |
| 0 | 8846 | 168 |
| 0 | 44 | 151 |
| 0 | 72 | 141 |
| 1 | 263 | 128 |
| 2 | 1720 | 128 |
| 0 | 9183 | 128 |
| 0 | 115 | 498 |
| 1 | 374 | 485 |
| 2 | 1477 | 449 |
| 3 | 5074 | 445 |
| 0 | 8334 | 433 |
| 0 | 13 | 36 |
| 0 | 22 | 36 |
| 1 | 99 | 33 |
| 2 | 674 | 25 |
| 0 | 8051 | 25 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 1 805 to 1 057 computations (41.4% saved)
Compiled 1 294 to 240 computations (81.5% saved)
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