Time bar (total: 10.2s)
| 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 |
| 0% | 0% | 50% | 0.1% | 0% | 50% | 0% | 3 |
| 0% | 0% | 50% | 0.1% | 0% | 50% | 0% | 4 |
| 25% | 12.5% | 37.5% | 0.1% | 0% | 50% | 0% | 5 |
| 26.7% | 12.5% | 34.3% | 0.1% | 0% | 53.1% | 0% | 6 |
| 37% | 15.6% | 26.5% | 0.1% | 1.6% | 54.6% | 1.6% | 7 |
| 40.8% | 15.6% | 22.6% | 0.1% | 2.3% | 57% | 2.3% | 8 |
| 49.4% | 17.2% | 17.6% | 0.1% | 3.5% | 58.1% | 3.5% | 9 |
| 53.3% | 17.2% | 15% | 0.1% | 4.1% | 59.5% | 4.1% | 10 |
| 59.5% | 18% | 12.2% | 0.1% | 4.8% | 60.2% | 4.8% | 11 |
| 62.5% | 18% | 10.8% | 0.1% | 5.1% | 60.9% | 5.1% | 12 |
Compiled 19 to 16 computations (15.8% saved)
| 1.3s | 8256× | body | 256 | valid |
| 708.0ms | 1324× | body | 1024 | invalid |
| 210.0ms | 639× | body | 512 | invalid |
| 187.0ms | 1526× | body | 256 | invalid |
| 83.0ms | 486× | body | 256 | infinite |
| 56.0ms | 232× | body | 256 | unsamplable |
| 2× | egg-herbie |
| 752× | *-commutative |
| 720× | associate-/l* |
| 718× | associate-/r* |
| 704× | neg-mul-1 |
| 660× | associate-*r* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 98 |
| 1 | 55 | 86 |
| 2 | 118 | 86 |
| 3 | 272 | 86 |
| 4 | 740 | 86 |
| 5 | 1771 | 78 |
| 6 | 3517 | 78 |
| 7 | 6184 | 78 |
| 0 | 2 | 2 |
| 1× | saturated |
| 1× | node limit |
| Inputs |
|---|
0 |
1 |
| Outputs |
|---|
0 |
1 |
| Inputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2))) |
| Outputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) |
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) k)) (-.f64 1/2 (/.f64 n 2)))) |
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 n 2))) (sqrt.f64 n)) |
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2)) (sqrt.f64 n)) |
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (+.f64 1/2 (/.f64 n -2))) (sqrt.f64 n)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 k (PI.f64))) (fma.f64 -1/2 n 1/2)) (sqrt.f64 n)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 k (PI.f64))) (fma.f64 n -1/2 1/2)) (sqrt.f64 n)) |
Compiled 20 to 17 computations (15% saved)
| 1× | egg-herbie |
| 1058× | associate-*r/ |
| 1052× | associate-/r* |
| 842× | distribute-frac-neg |
| 792× | associate-/l* |
| 672× | *-commutative |
Useful iterations: 5 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 49 |
| 1 | 35 | 43 |
| 2 | 69 | 43 |
| 3 | 151 | 43 |
| 4 | 399 | 43 |
| 5 | 948 | 39 |
| 6 | 1876 | 39 |
| 7 | 4291 | 39 |
| 8 | 7087 | 39 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| Outputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) |
Compiled 88 to 57 computations (35.2% saved)
3 alts after pruning (3 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 4 | 2 | 6 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 0 | 0 |
| Total | 4 | 3 | 7 |
| Status | Error | Program |
|---|---|---|
| ▶ | 0.3b | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| ▶ | 0.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
Compiled 34 to 28 computations (17.6% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.2b | (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) |
| ✓ | 0.2b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| ✓ | 0.2b | (*.f64 (*.f64 2 (PI.f64)) n) |
| ✓ | 0.3b | (/.f64 1 (sqrt.f64 k)) |
Compiled 56 to 38 computations (32.1% saved)
18 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 24.0ms | n | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 20.0ms | n | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 8.0ms | n | @ | inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 3.0ms | k | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 1.0ms | k | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 1× | batch-egg-rewrite |
| 1600× | associate-*l/ |
| 1006× | associate-/l* |
| 986× | associate-/r* |
| 366× | add-sqr-sqrt |
| 352× | *-un-lft-identity |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 102 |
| 1 | 363 | 98 |
| 2 | 4638 | 98 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 k))) (cbrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 -1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 k 1/4) -1) (pow.f64 (pow.f64 k 1/4) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 k) -1) (pow.f64 (cbrt.f64 (sqrt.f64 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 k) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1 (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (sqrt.f64 k)))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (neg.f64 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (sqrt.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 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| 1× | egg-herbie |
| 860× | associate-/l* |
| 686× | distribute-rgt-neg-out |
| 656× | distribute-lft-neg-out |
| 652× | associate-*r* |
| 576× | associate-/l/ |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 540 | 12603 |
| 1 | 1301 | 12271 |
| 2 | 5889 | 12217 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (sqrt.f64 k)))) 1) |
(*.f64 1 (/.f64 1 (sqrt.f64 k))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) 1) |
(*.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2)) |
(*.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 k))) (cbrt.f64 (/.f64 1 k))) |
(*.f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (/.f64 1 (sqrt.f64 k)))) |
(*.f64 -1 (/.f64 -1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -1) (pow.f64 (pow.f64 k 1/4) -1)) |
(*.f64 (pow.f64 (cbrt.f64 k) -1) (pow.f64 (cbrt.f64 (sqrt.f64 k)) -1)) |
(pow.f64 k -1/2) |
(pow.f64 (sqrt.f64 k) -1) |
(pow.f64 (/.f64 1 (sqrt.f64 k)) 1) |
(pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2) |
(pow.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 k))) 3) |
(pow.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) 1/3) |
(sqrt.f64 (/.f64 1 k)) |
(log.f64 (exp.f64 (/.f64 1 (sqrt.f64 k)))) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (sqrt.f64 k))))) |
(cbrt.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k)) |
(expm1.f64 (log1p.f64 (/.f64 1 (sqrt.f64 k)))) |
(exp.f64 (log.f64 (/.f64 1 (sqrt.f64 k)))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) -1)) |
(exp.f64 (*.f64 (log.f64 (/.f64 1 (sqrt.f64 k))) 1)) |
(log1p.f64 (expm1.f64 (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 1) |
(pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) |
(pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 3) |
(pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 3) 1/3) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 2)) |
(log.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64)))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 3)) |
(cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 3) (pow.f64 n 3))) |
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 2 (PI.f64)) 3))) |
(expm1.f64 (log1p.f64 (*.f64 (*.f64 2 (PI.f64)) n))) |
(exp.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 1)) |
(log1p.f64 (expm1.f64 (*.f64 (*.f64 2 (PI.f64)) n))) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) 1) |
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 1) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)))) |
(/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))))) |
(/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))))) |
(/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(/.f64 -1 (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (sqrt.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2))))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))))) |
(/.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))))) |
(/.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))) (/.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))))) |
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))))) |
(/.f64 (*.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))))) (/.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) -1) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 -1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 1) (sqrt.f64 k)) |
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (pow.f64 k 1/4)) |
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (pow.f64 n (/.f64 (+.f64 -1 k) -4)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (+.f64 -1 k) -4)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (/.f64 (-.f64 1 k) 2) 4)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (/.f64 (-.f64 1 k) 2) 4)))) |
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (+.f64 -1 k) -4)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (pow.f64 n (/.f64 (+.f64 -1 k) -4)))) |
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (+.f64 -1 k) -4)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (+.f64 -1 k) -4)))) |
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k)) |
(/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (pow.f64 1 (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 1 (/.f64 (+.f64 -1 k) -4)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 2 (/.f64 (+.f64 -1 k) -4)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (+.f64 -1 k) -4)))) |
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (+.f64 -1 k) -4)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (+.f64 -1 k) -4)))) |
(/.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (/.f64 (+.f64 -1 k) -4)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (+.f64 -1 k) -4)))) |
(/.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (pow.f64 (PI.f64) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (pow.f64 2 (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 (PI.f64) 2))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (*.f64 (cbrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 1 (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) 1) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)))) |
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))) 1) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) 1) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) -1) 1) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (*.f64 -1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 1) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 1) 1) (sqrt.f64 k)) |
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) 1) (pow.f64 k 1/4)) |
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) 1) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 1) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (pow.f64 k 1/4))) (pow.f64 k 1/4)) |
(/.f64 (*.f64 1 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4))) (pow.f64 k 1/4)) |
(/.f64 (*.f64 (sqrt.f64 -1) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))) k))) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (*.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k 1/2))) |
(/.f64 (*.f64 1 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 (sqrt.f64 k)))) (cbrt.f64 k)) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (sqrt.f64 k))) 1) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (cbrt.f64 (sqrt.f64 k)))) (cbrt.f64 k)) |
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))) 1) |
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (pow.f64 k 1/4))) (pow.f64 k 1/4)) |
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) (cbrt.f64 k)) |
(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) 1) |
(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4))) (pow.f64 k 1/4)) |
(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (cbrt.f64 (sqrt.f64 k)))) (cbrt.f64 k)) |
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (cbrt.f64 (*.f64 k k)))) (sqrt.f64 (cbrt.f64 k))) |
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 1 1/2)) (sqrt.f64 k)) |
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 (cbrt.f64 (*.f64 k k)) 1/2)) (pow.f64 (cbrt.f64 k) 1/2)) |
(/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) -1) 1) (neg.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) -1) (pow.f64 k 1/4)) (neg.f64 (pow.f64 k 1/4))) |
(/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) -1) (cbrt.f64 k)) (neg.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) -1) -1) (sqrt.f64 k)) |
(/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) -1) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) -1) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 k))) (cbrt.f64 (neg.f64 (sqrt.f64 k))))) (cbrt.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) -1) (neg.f64 (pow.f64 k 1/4))) (pow.f64 k 1/4)) |
(/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) -1) (neg.f64 (cbrt.f64 k))) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (*.f64 -1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 1) (neg.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (*.f64 -1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (pow.f64 k 1/4)) (neg.f64 (pow.f64 k 1/4))) |
(/.f64 (/.f64 (*.f64 -1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 k)) (neg.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (*.f64 -1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) -1) (sqrt.f64 k)) |
(/.f64 (/.f64 (*.f64 -1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (*.f64 -1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 k))) (cbrt.f64 (neg.f64 (sqrt.f64 k))))) (cbrt.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (*.f64 -1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (neg.f64 (pow.f64 k 1/4))) (pow.f64 k 1/4)) |
(/.f64 (/.f64 (*.f64 -1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (neg.f64 (cbrt.f64 k))) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 1) 1) (sqrt.f64 k)) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 1) (sqrt.f64 (cbrt.f64 (*.f64 k k)))) (sqrt.f64 (cbrt.f64 k))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 1) (pow.f64 1 1/2)) (sqrt.f64 k)) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 1) (pow.f64 (cbrt.f64 (*.f64 k k)) 1/2)) (pow.f64 (cbrt.f64 k) 1/2)) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) 1) (pow.f64 k 1/4)) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (pow.f64 k 1/4))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (sqrt.f64 (pow.f64 k 1/4))) (sqrt.f64 (pow.f64 k 1/4))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (sqrt.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) 1) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) (sqrt.f64 (cbrt.f64 (sqrt.f64 k)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) (cbrt.f64 (pow.f64 k 1/4))) (cbrt.f64 (pow.f64 k 1/4))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) (cbrt.f64 (cbrt.f64 k))) (cbrt.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (cbrt.f64 (sqrt.f64 k))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 1) (neg.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (pow.f64 k 1/4)) (neg.f64 (pow.f64 k 1/4))) |
(/.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 k)) (neg.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) -1) (sqrt.f64 k)) |
(/.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 k))) (cbrt.f64 (neg.f64 (sqrt.f64 k))))) (cbrt.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (neg.f64 (pow.f64 k 1/4))) (pow.f64 k 1/4)) |
(/.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (neg.f64 (cbrt.f64 k))) (cbrt.f64 (sqrt.f64 k))) |
(pow.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 1) |
(pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (pow.f64 k 1/4)) 2) |
(pow.f64 (cbrt.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) 3) |
(pow.f64 (pow.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 3) 1/3) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))) k)) |
(log.f64 (exp.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))))) |
(cbrt.f64 (pow.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 3)) |
(cbrt.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3))) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3) (/.f64 (/.f64 1 (sqrt.f64 k)) k))) |
(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(exp.f64 (log.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) 1)) |
(log1p.f64 (expm1.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) 1) |
(*.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 1) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) |
(*.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (pow.f64 1 (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (/.f64 (-.f64 1 k) 2)) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (-.f64 1 k) 2))) |
(/.f64 1 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2)) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(/.f64 (sqrt.f64 n) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2)) (sqrt.f64 (*.f64 2 (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2)) (sqrt.f64 n))) |
(/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2))) |
(/.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2)) (cbrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(/.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2)) (sqrt.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2)) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 1) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k 1/2))) |
(/.f64 (*.f64 (sqrt.f64 n) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (pow.f64 n (*.f64 k 1/2))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))) |
(log.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(exp.f64 (*.f64 (/.f64 (-.f64 1 k) 2) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
| Outputs |
|---|
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (*.f64 1/2 (-.f64 1 k))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (*.f64 1/2 (-.f64 1 k))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
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(pow.f64 (/.f64 1 (sqrt.f64 k)) 1) |
(/.f64 1 (sqrt.f64 k)) |
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(/.f64 1 (sqrt.f64 k)) |
(pow.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 k))) 3) |
(/.f64 1 (sqrt.f64 k)) |
(pow.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) 1/3) |
(cbrt.f64 (/.f64 1 (*.f64 k (sqrt.f64 k)))) |
(cbrt.f64 (/.f64 (/.f64 1 k) (sqrt.f64 k))) |
(sqrt.f64 (/.f64 1 k)) |
(log.f64 (exp.f64 (/.f64 1 (sqrt.f64 k)))) |
(/.f64 1 (sqrt.f64 k)) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (sqrt.f64 k))))) |
(/.f64 1 (sqrt.f64 k)) |
(cbrt.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k)) |
(cbrt.f64 (/.f64 1 (*.f64 k (sqrt.f64 k)))) |
(cbrt.f64 (/.f64 (/.f64 1 k) (sqrt.f64 k))) |
(expm1.f64 (log1p.f64 (/.f64 1 (sqrt.f64 k)))) |
(/.f64 1 (sqrt.f64 k)) |
(exp.f64 (log.f64 (/.f64 1 (sqrt.f64 k)))) |
(/.f64 1 (sqrt.f64 k)) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) -1)) |
(/.f64 1 (sqrt.f64 k)) |
(exp.f64 (*.f64 (log.f64 (/.f64 1 (sqrt.f64 k))) 1)) |
(/.f64 1 (sqrt.f64 k)) |
(log1p.f64 (expm1.f64 (/.f64 1 (sqrt.f64 k)))) |
(/.f64 1 (sqrt.f64 k)) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1) |
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(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 1) |
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(pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 3) |
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(pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 3) 1/3) |
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(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 2)) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 2)) |
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(log.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64)))) |
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(log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
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(cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 3) (pow.f64 n 3))) |
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(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 2 (PI.f64)) 3))) |
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(expm1.f64 (log1p.f64 (*.f64 (*.f64 2 (PI.f64)) n))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(exp.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) |
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(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 1)) |
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(log1p.f64 (expm1.f64 (*.f64 (*.f64 2 (PI.f64)) n))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) 1) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
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(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (neg.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 1) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (/.f64 (+.f64 k -1) -4))) (sqrt.f64 k)) |
(/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (*.f64 2 (-.f64 1 k)) 2))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k))) |
(/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4))))) |
(/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (sqrt.f64 k) (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 k)) (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (*.f64 2 (-.f64 1 k)) 2))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k))) |
(/.f64 -1 (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4)))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4)))) |
(*.f64 (fabs.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -8))) (*.f64 (/.f64 (fabs.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -8))) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4)))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (sqrt.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2))))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4)))) (sqrt.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4)) (sqrt.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))))) |
(*.f64 (/.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (*.f64 2 (-.f64 1 k)) 2)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4)))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))))) (*.f64 (/.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (+.f64 k -1) -4)))) |
(/.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))) (/.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))))) |
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(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (*.f64 (/.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))))) |
(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (/.f64 (sqrt.f64 k) (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))))) |
(/.f64 (*.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))))) (/.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))))))) |
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(*.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (*.f64 (/.f64 (*.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))))) |
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(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
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(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (*.f64 (pow.f64 k 1/4) (pow.f64 k 1/4))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k 1/2)) |
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(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k 1/2))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k 1/2))) |
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k 1/2)) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k 1/2)) (sqrt.f64 (*.f64 2 (PI.f64))))) |
(/.f64 (*.f64 (sqrt.f64 n) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (pow.f64 n (*.f64 k 1/2))) |
(/.f64 (sqrt.f64 n) (/.f64 (pow.f64 n (*.f64 k 1/2)) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (*.f64 k 1/2))) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2)))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (*.f64 2 (-.f64 1 k)) 2))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(log.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(exp.f64 (*.f64 (/.f64 (-.f64 1 k) 2) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.2b | (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) |
| ✓ | 0.2b | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| ✓ | 0.2b | (*.f64 (PI.f64) (*.f64 2 n)) |
Compiled 50 to 34 computations (32% saved)
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | n | @ | 0 | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| 1.0ms | k | @ | -inf | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| 1.0ms | n | @ | inf | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| 1.0ms | n | @ | -inf | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| 1.0ms | k | @ | inf | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| 1× | batch-egg-rewrite |
| 1640× | associate-/r* |
| 1608× | associate-*l/ |
| 360× | add-sqr-sqrt |
| 348× | *-un-lft-identity |
| 346× | pow1 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 91 |
| 1 | 351 | 91 |
| 2 | 4655 | 91 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (PI.f64) (*.f64 2 n)) |
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (*.f64 2 n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 2 n) 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) 2) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))))))) 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(/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2))))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 (*.f64 k -1/2) -2))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 (*.f64 k -1/2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (PI.f64) (/.f64 k 2))) (pow.f64 (*.f64 2 n) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (*.f64 2 n) (/.f64 k 2))) (pow.f64 (PI.f64) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 1 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (*.f64 (PI.f64) 2) (/.f64 k 2))) (pow.f64 n (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))))))) |
| 1× | egg-herbie |
| 1792× | distribute-lft-in |
| 1364× | associate-*r/ |
| 1078× | associate-*l/ |
| 912× | associate-/r* |
| 730× | associate-/l/ |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 302 | 6630 |
| 1 | 714 | 6086 |
| 2 | 2860 | 6080 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1) |
(pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1) |
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 3) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3) 1/3) |
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) |
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 2)) |
(log.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3)) |
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (*.f64 2 n) 3))) |
(cbrt.f64 (*.f64 (pow.f64 (*.f64 2 n) 3) (pow.f64 (PI.f64) 3))) |
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1)) |
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) 1) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 1) |
(*.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 k -1/2))) |
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) k))) |
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) 2) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 k -1/2))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (/.f64 -1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))) (*.f64 (pow.f64 (*.f64 2 n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2))) |
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k 1/4))) |
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 k))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 k 1/4))) |
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(*.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))) 1) (/.f64 (pow.f64 (*.f64 2 n) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 2 n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k 1/4))) |
(*.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 n) (-.f64 1/2 (/.f64 k 2))) (cbrt.f64 (sqrt.f64 k)))) |
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 1) |
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) 2) |
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) 3) |
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 3) 1/3) |
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) -1) |
(neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (neg.f64 (sqrt.f64 k)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) k)) |
(log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))))) |
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 3)) |
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) 1)) |
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) 1) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) 1) |
(*.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) 2)) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) 2) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 k -1/2))) |
(*.f64 (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 2 n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(/.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1) (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)))) |
(/.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)))) |
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) 2)) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)))) |
(/.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 2 n) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (PI.f64) (/.f64 k 2))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 n)) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 2 n) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2))))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2)))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 (*.f64 k -1/2) -2))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 (*.f64 k -1/2) -2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (PI.f64) (/.f64 k 2))) (pow.f64 (*.f64 2 n) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (*.f64 2 n) (/.f64 k 2))) (pow.f64 (PI.f64) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 1 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (*.f64 (PI.f64) 2) (/.f64 k 2))) (pow.f64 n (/.f64 k 2))) |
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) |
(exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1)) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) |
| Outputs |
|---|
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (-.f64 1/2 (*.f64 k 1/2)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (*.f64 k (sqrt.f64 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 2)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 1/8 (sqrt.f64 2)) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 3)) (sqrt.f64 (*.f64 n (PI.f64))))))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (*.f64 -1/48 (*.f64 (sqrt.f64 2) (pow.f64 k 3))) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)) (*.f64 (*.f64 1/8 (sqrt.f64 2)) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (*.f64 k (sqrt.f64 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (sqrt.f64 2)))) (*.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (-.f64 1/2 (*.f64 k 1/2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 3) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3) 1/3) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 2)) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 2)) |
(fabs.f64 (*.f64 n (*.f64 2 (PI.f64)))) |
(fabs.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(log.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64))) |
(*.f64 (PI.f64) (log.f64 (pow.f64 (exp.f64 n) 2))) |
(*.f64 (PI.f64) (*.f64 2 (log.f64 (exp.f64 n)))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3)) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (*.f64 2 n) 3))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(cbrt.f64 (*.f64 (pow.f64 (*.f64 2 n) 3) (pow.f64 (PI.f64) 3))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1)) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) 1) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 1) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(*.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
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(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2)) (pow.f64 n (/.f64 k 2)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2)) (pow.f64 n (/.f64 k 2)))) |
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(fabs.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) |
(log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) 3)) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1)) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
Compiled 13509 to 9160 computations (32.2% saved)
17 alts after pruning (16 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 534 | 16 | 550 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 1 | 0 | 1 |
| Total | 535 | 17 | 552 |
| Status | Error | Program |
|---|---|---|
| 21.6b | (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 3) 1/3) | |
| 0.8b | (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (pow.f64 k 1/4)) 2) | |
| ✓ | 0.3b | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| 0.4b | (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (*.f64 (pow.f64 k 1/4) (pow.f64 k 1/4))) | |
| 0.7b | (/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k 1/2))) | |
| 22.0b | (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) | |
| ▶ | 0.3b | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) |
| ▶ | 3.3b | (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) |
| 3.5b | (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k)) | |
| 0.4b | (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) | |
| 17.0b | (*.f64 (pow.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) 1/3) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) | |
| ▶ | 0.3b | (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
| ▶ | 0.8b | (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
| ▶ | 3.9b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
| 0.3b | (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) | |
| 12.1b | (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))) k)) | |
| 3.3b | (exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
Compiled 622 to 513 computations (17.5% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.1b | (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
| ✓ | 0.1b | (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
| ✓ | 0.2b | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) |
| 0.2b | (*.f64 (*.f64 2 (PI.f64)) n) |
Compiled 76 to 56 computations (26.3% saved)
18 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | k | @ | -inf | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) |
| 2.0ms | n | @ | 0 | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) |
| 1.0ms | k | @ | 0 | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) |
| 1.0ms | k | @ | inf | (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
| 1.0ms | k | @ | 0 | (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
| 1× | batch-egg-rewrite |
| 1674× | associate-*l/ |
| 1546× | associate-/r* |
| 394× | add-sqr-sqrt |
| 382× | *-un-lft-identity |
| 378× | pow1 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 131 |
| 1 | 390 | 127 |
| 2 | 5034 | 127 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1706× | associate-/l* |
| 1360× | associate-*r/ |
| 1166× | associate-*l/ |
| 694× | associate-/r* |
| 448× | associate-*r* |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 337 | 9470 |
| 1 | 850 | 8584 |
| 2 | 3279 | 8536 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1 (*.f64 (/.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 1/2 (*.f64 (/.f64 (*.f64 (pow.f64 k 2) (-.f64 (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))) (pow.f64 (*.f64 -1 (*.f64 (/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1 (*.f64 (/.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 1/2 (*.f64 (/.f64 (*.f64 (pow.f64 k 2) (-.f64 (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))) (pow.f64 (*.f64 -1 (*.f64 (/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1 (*.f64 (/.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/2 (*.f64 (/.f64 (*.f64 (pow.f64 k 3) (-.f64 (*.f64 -1/3 (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (PI.f64)))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))) (pow.f64 (*.f64 -1 (*.f64 (/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))) 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 (sqrt.f64 2) 2))))) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64))))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))) |
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 3) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))) |
(exp.f64 (*.f64 2 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 2 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 2 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 2 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 2 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)))) 1) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (pow.f64 k -1/2)) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) 1) |
(*.f64 1 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (*.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (pow.f64 k -1/2))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) k))) |
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) k)) (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (pow.f64 k -1/2))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (/.f64 -1 (sqrt.f64 k))) |
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (pow.f64 k 1/4))) |
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) 1) (/.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (sqrt.f64 k))) |
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (sqrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (pow.f64 k 1/4))) |
(pow.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) 1) |
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k))) 2) |
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k))) 3) |
(pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) k) 1/2) |
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) 3) 1/3) |
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) -1) |
(neg.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (neg.f64 (sqrt.f64 k)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) k)) |
(log.f64 (exp.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)))) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k))))) |
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) 3)) |
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)))) |
(exp.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k))) 1)) |
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)))) |
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) 1) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) 1) |
(*.f64 1 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 (pow.f64 n (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (pow.f64 n (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (pow.f64 n (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) |
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (pow.f64 2 (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) |
(*.f64 (pow.f64 1 (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) 2) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) 1/2)) |
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) 1/2) (pow.f64 (pow.f64 n (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) 1/2)) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) |
(pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) 1/2) |
(pow.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) 1) |
(pow.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) 2) |
(pow.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) 3) |
(pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) (*.f64 (-.f64 1/2 (/.f64 k 2)) 1/2)) |
(pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) (/.f64 (-.f64 1/2 (/.f64 k 2)) 2)) |
(pow.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) 3/2) 1/3) |
(fabs.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) |
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) 3/2)) |
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) |
(exp.f64 (*.f64 (/.f64 (-.f64 1/2 (/.f64 k 2)) 1) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) |
(exp.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1/2)) |
(exp.f64 (*.f64 (*.f64 (/.f64 (-.f64 1/2 (/.f64 k 2)) 1) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1)) |
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) 1) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) 1) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) |
(*.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)))) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) 2) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) 2)) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 n (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)))) |
(*.f64 (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) 1/2) (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) (*.f64 k -1/2))) |
(*.f64 (pow.f64 2 (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 1 (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) 1/2) (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) (/.f64 k 2))) |
(/.f64 (*.f64 (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) 1/2) 1) (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) (/.f64 k 2))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(log.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(exp.f64 (*.f64 (*.f64 2 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(exp.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1)) |
(exp.f64 (*.f64 (log.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2))) (-.f64 1/2 (/.f64 k 2)))) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
| Outputs |
|---|
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) k)) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))) |
(sqrt.f64 (exp.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))) |
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(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
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(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) 1) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) 1) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) 2) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) 2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 n (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1/2 (/.f64 k 2)) 1)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) 1/2) (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) (*.f64 k -1/2))) |
(*.f64 (sqrt.f64 (*.f64 4 (pow.f64 (*.f64 n (PI.f64)) 2))) (pow.f64 (*.f64 4 (pow.f64 (*.f64 n (PI.f64)) 2)) (*.f64 k -1/2))) |
(*.f64 (pow.f64 2 (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 2 (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 n (PI.f64)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 1 (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 4 (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 (-.f64 1/2 (/.f64 k 2)) 4)) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) 1/2) (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) (/.f64 k 2))) |
(/.f64 (sqrt.f64 (*.f64 4 (pow.f64 (*.f64 n (PI.f64)) 2))) (pow.f64 (*.f64 4 (pow.f64 (*.f64 n (PI.f64)) 2)) (/.f64 k 2))) |
(/.f64 (*.f64 (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) 1/2) 1) (pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)) (/.f64 k 2))) |
(/.f64 (sqrt.f64 (*.f64 4 (pow.f64 (*.f64 n (PI.f64)) 2))) (pow.f64 (*.f64 4 (pow.f64 (*.f64 n (PI.f64)) 2)) (/.f64 k 2))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 4 (-.f64 1/2 (/.f64 k 2))))) |
(fabs.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (-.f64 1/2 (/.f64 k 2)) 4))) |
(log.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) 3)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(exp.f64 (*.f64 (*.f64 2 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(exp.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2))) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 4 (pow.f64 (*.f64 n (PI.f64)) 2)) (-.f64 1/2 (/.f64 k 2))) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (pow.f64 k -1/2) |
| ✓ | 0.2b | (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) |
| ✓ | 0.2b | (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
| 0.2b | (*.f64 (*.f64 2 (PI.f64)) n) |
Compiled 53 to 38 computations (28.3% saved)
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 27.0ms | k | @ | -inf | (pow.f64 k -1/2) |
| 10.0ms | k | @ | 0 | (pow.f64 k -1/2) |
| 8.0ms | k | @ | inf | (pow.f64 k -1/2) |
| 1.0ms | n | @ | 0 | (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
| 1.0ms | k | @ | -inf | (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
| 1× | batch-egg-rewrite |
| 1370× | associate-*r/ |
| 992× | associate-*l/ |
| 424× | associate-/r* |
| 416× | associate-/l* |
| 362× | add-sqr-sqrt |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 85 |
| 1 | 354 | 85 |
| 2 | 4498 | 85 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 k -1/2) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 k -1/2) (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))))))) 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(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (pow.f64 k -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/2) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 k -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 k)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -1/2))))))) |
| 1× | egg-herbie |
| 1804× | distribute-lft-in |
| 1710× | associate-*r/ |
| 1370× | associate-/r/ |
| 1224× | associate-*l/ |
| 498× | associate-/l* |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 388 | 9290 |
| 1 | 883 | 8700 |
| 2 | 3487 | 8694 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) |
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) |
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) |
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)))) 1) |
(/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (pow.f64 k -1/2))) |
(/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (*.f64 (pow.f64 k -1/2) (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 1 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (*.f64 1 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (*.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (*.f64 1/4 k)))) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 2)) (cbrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 n)) (pow.f64 n (/.f64 k 2))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 k -1/2)) (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) 1) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (*.f64 1/4 k))) (pow.f64 k -1/2))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (*.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 1/4 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 1/4 k))) |
(/.f64 (/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) (pow.f64 n (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 n (/.f64 k 2))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 2 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 1 (/.f64 k 2))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) 1) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 1/4 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 1/4 k))) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) (pow.f64 n (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 n (/.f64 k 2))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 2 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 1 (/.f64 k 2))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) |
(pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) 1) |
(pow.f64 (*.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (*.f64 1/4 k)))) 2) |
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2))) 3) |
(pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) 3) 1/3) |
(sqrt.f64 (*.f64 (pow.f64 k -1) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2))))) |
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) 3)) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) 3) (pow.f64 (pow.f64 k -1/2) 3))) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) 3))) |
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)))) |
(exp.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2))) 1)) |
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 1) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) 1) |
(*.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2))) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (*.f64 1/4 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (*.f64 1/4 k)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 2)) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 2) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) |
(*.f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (-.f64 1/2 (/.f64 k 2)))) |
(/.f64 1 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (sqrt.f64 n))) |
(/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (pow.f64 (*.f64 (PI.f64) n) 1/2))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (sqrt.f64 n) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (sqrt.f64 (*.f64 2 (PI.f64))))) |
(/.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (cbrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(/.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (sqrt.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 1/4) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) 1/4))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (pow.f64 1 1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 1/2) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 1/2))) |
(/.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) 1/2) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 1/2))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 1) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (*.f64 1 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (*.f64 1/4 k))) (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 2) (cbrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 n)) (pow.f64 n (/.f64 k 2))) |
(/.f64 (*.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (*.f64 2 (PI.f64)))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) 1) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1) (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (*.f64 1/4 k)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 2)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) |
(/.f64 (*.f64 (sqrt.f64 n) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 1) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 1/4 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 1/4 k))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) (pow.f64 n (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 n (/.f64 k 2))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 2 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 1 (/.f64 k 2))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(log.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1)) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1) |
(*.f64 (pow.f64 k -1/2) 1) |
(*.f64 1 (pow.f64 k -1/2)) |
(*.f64 (pow.f64 k -1/4) (pow.f64 k -1/4)) |
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1))) |
(*.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2))) |
(*.f64 (pow.f64 1 -1/2) (pow.f64 k -1/2)) |
(*.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2)) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2)) |
(sqrt.f64 (pow.f64 k -1)) |
(log.f64 (exp.f64 (pow.f64 k -1/2))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2)))) |
(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 k -1/2))) |
(exp.f64 (*.f64 -1/2 (log.f64 k))) |
(exp.f64 (*.f64 (*.f64 -1/2 (log.f64 k)) 1)) |
(log1p.f64 (expm1.f64 (pow.f64 k -1/2))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (+.f64 1/2 (*.f64 k -1/2)))) |
(*.f64 (sqrt.f64 (pow.f64 k -1)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
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(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (/.f64 k 2)) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (/.f64 k 2)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 2 (/.f64 k 2)))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (/.f64 k 2))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (/.f64 k 2)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (/.f64 k 2)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (/.f64 k 2)) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (/.f64 k 2)))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) |
(fabs.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(log.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) 3)) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) |
(exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1)) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1) |
(pow.f64 k -1/2) |
(*.f64 (pow.f64 k -1/2) 1) |
(pow.f64 k -1/2) |
(*.f64 1 (pow.f64 k -1/2)) |
(pow.f64 k -1/2) |
(*.f64 (pow.f64 k -1/4) (pow.f64 k -1/4)) |
(pow.f64 k -1/2) |
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1))) |
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k))) |
(*.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2))) |
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k))) |
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1))) |
(*.f64 (pow.f64 1 -1/2) (pow.f64 k -1/2)) |
(pow.f64 k -1/2) |
(*.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2)) |
(pow.f64 (sqrt.f64 k) -1) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2)) |
(sqrt.f64 (pow.f64 k -1)) |
(sqrt.f64 (/.f64 1 k)) |
(log.f64 (exp.f64 (pow.f64 k -1/2))) |
(pow.f64 k -1/2) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2)))) |
(pow.f64 k -1/2) |
(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3)) |
(pow.f64 k -1/2) |
(expm1.f64 (log1p.f64 (pow.f64 k -1/2))) |
(pow.f64 k -1/2) |
(exp.f64 (*.f64 -1/2 (log.f64 k))) |
(pow.f64 k -1/2) |
(exp.f64 (*.f64 (*.f64 -1/2 (log.f64 k)) 1)) |
(pow.f64 k -1/2) |
(log1p.f64 (expm1.f64 (pow.f64 k -1/2))) |
(pow.f64 k -1/2) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.2b | (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) |
| 0.2b | (*.f64 (PI.f64) (*.f64 2 n)) | |
| ✓ | 0.2b | (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
| ✓ | 3.1b | (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
Compiled 72 to 51 computations (29.2% saved)
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | k | @ | 0 | (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) |
| 0.0ms | n | @ | -inf | (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
| 0.0ms | n | @ | inf | (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
| 0.0ms | n | @ | 0 | (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
| 0.0ms | k | @ | 0 | (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
| 1× | batch-egg-rewrite |
| 1828× | associate-*r/ |
| 1476× | associate-*l/ |
| 378× | add-sqr-sqrt |
| 366× | pow1 |
| 366× | *-un-lft-identity |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 111 |
| 1 | 376 | 95 |
| 2 | 4720 | 95 |
| 1× | node limit |
| Inputs |
|---|
(exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(log.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) |
| Outputs |
|---|
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 2 n)) (log.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 2) (+.f64 (log.f64 n) (log.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 n) (+.f64 (log.f64 2) (log.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 2 n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (*.f64 2 n))) (+.f64 (log.f64 (sqrt.f64 (*.f64 2 n))) (log.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (log.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) 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| 1× | egg-herbie |
| 1372× | associate-*r/ |
| 1168× | associate-+r+ |
| 1144× | associate-+l+ |
| 1090× | associate-*l/ |
| 934× | associate-/r* |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 331 | 7270 |
| 1 | 765 | 6308 |
| 2 | 3553 | 6308 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
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(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
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(log.f64 (exp.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)))) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k))))) |
(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) 3)) |
(cbrt.f64 (/.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) 3) (pow.f64 k 3/2))) |
(expm1.f64 (log1p.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)))) |
(exp.f64 (log.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k))) 1)) |
(log1p.f64 (expm1.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 1/8 (sqrt.f64 2)) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (sqrt.f64 (*.f64 n (PI.f64))))))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (*.f64 1/8 (sqrt.f64 2)) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 (*.f64 -1/48 (sqrt.f64 2)) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k)))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 -1/2 k 1/2)) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))) |
(-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))) |
(-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))) |
(-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))) |
(-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 (/.f64 1 k))) |
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(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(pow.f64 (cbrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k))) 3) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(pow.f64 (pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) 3) 1/3) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(pow.f64 (/.f64 (sqrt.f64 k) (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) -1) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(neg.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) 2) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 2) k)) |
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) 2) k)) |
(log.f64 (exp.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)))) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k))))) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) 3)) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(cbrt.f64 (/.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) 3) (pow.f64 k 3/2))) |
(cbrt.f64 (/.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 3) (pow.f64 k 3/2))) |
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) 3) (pow.f64 k 3/2))) |
(expm1.f64 (log1p.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)))) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(exp.f64 (log.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)))) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(exp.f64 (*.f64 (log.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k))) 1)) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(log1p.f64 (expm1.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)))) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.1b | (pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
| ✓ | 0.3b | (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
| ✓ | 0.4b | (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| ✓ | 0.6b | (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) |
Compiled 68 to 48 computations (29.4% saved)
18 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 16.0ms | n | @ | 0 | (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
| 9.0ms | n | @ | inf | (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
| 9.0ms | n | @ | -inf | (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
| 3.0ms | k | @ | 0 | (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
| 2.0ms | k | @ | -inf | (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| 1× | batch-egg-rewrite |
| 1798× | associate-/l* |
| 574× | distribute-lft-in |
| 388× | add-sqr-sqrt |
| 386× | associate-/r/ |
| 376× | *-un-lft-identity |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 144 |
| 1 | 377 | 126 |
| 2 | 5110 | 126 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) |
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 836× | associate-*r* |
| 590× | associate-/l* |
| 582× | associate-*l* |
| 552× | *-commutative |
| 518× | sqr-pow |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 546 | 12969 |
| 1 | 1336 | 12303 |
| 2 | 5645 | 12215 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64)))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (+.f64 (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3))) (sqrt.f64 (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64))))))) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
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(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) 1)) |
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))) 1) |
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(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 n)) (*.f64 (sqrt.f64 k) (pow.f64 n (/.f64 k 2)))) |
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 n (/.f64 k 2))) |
(/.f64 (*.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (neg.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2)))) |
(/.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (neg.f64 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 n) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) (pow.f64 n (/.f64 k 2))) |
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k 1/4)) (pow.f64 k 1/4)) |
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) |
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(/.f64 (pow.f64 n 1/4) (/.f64 (*.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (/.f64 k 2))) (pow.f64 n 1/4))) |
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(/.f64 (*.f64 (sqrt.f64 n) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (*.f64 (pow.f64 n (/.f64 k 2)) (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 n) 1) (*.f64 (pow.f64 n (/.f64 k 2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 (*.f64 (sqrt.f64 n) (neg.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))) (*.f64 (pow.f64 n (/.f64 k 2)) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) (neg.f64 (sqrt.f64 k))) |
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(/.f64 (pow.f64 1 1/2) (/.f64 (*.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (/.f64 k 2))) (sqrt.f64 n))) |
(/.f64 (pow.f64 (sqrt.f64 n) 1/2) (/.f64 (*.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (/.f64 k 2))) (pow.f64 (sqrt.f64 n) 1/2))) |
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(/.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))))) |
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(pow.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) 1) |
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(pow.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) 3) |
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(sqrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) 2)) |
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(*.f64 (/.f64 1 (pow.f64 n (/.f64 k 2))) (sqrt.f64 n)) |
(*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (sqrt.f64 n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 n) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 n) (-.f64 1/2 (/.f64 k 2)))) |
(/.f64 1 (/.f64 (pow.f64 n (/.f64 k 2)) (sqrt.f64 n))) |
(/.f64 (cbrt.f64 n) (/.f64 (pow.f64 n (/.f64 k 2)) (cbrt.f64 (sqrt.f64 n)))) |
(/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) |
(/.f64 (sqrt.f64 (sqrt.f64 n)) (/.f64 (pow.f64 n (/.f64 k 2)) (sqrt.f64 (sqrt.f64 n)))) |
(/.f64 (sqrt.f64 (pow.f64 (cbrt.f64 n) 2)) (/.f64 (pow.f64 n (/.f64 k 2)) (sqrt.f64 (cbrt.f64 n)))) |
(/.f64 (pow.f64 n 1/4) (/.f64 (pow.f64 n (/.f64 k 2)) (pow.f64 n 1/4))) |
(/.f64 (neg.f64 (sqrt.f64 n)) (neg.f64 (pow.f64 n (/.f64 k 2)))) |
(/.f64 (pow.f64 1 1/2) (/.f64 (pow.f64 n (/.f64 k 2)) (sqrt.f64 n))) |
(/.f64 (pow.f64 (sqrt.f64 n) 1/2) (/.f64 (pow.f64 n (/.f64 k 2)) (pow.f64 (sqrt.f64 n) 1/2))) |
(/.f64 (pow.f64 (pow.f64 (cbrt.f64 n) 2) 1/2) (/.f64 (pow.f64 n (/.f64 k 2)) (pow.f64 (cbrt.f64 n) 1/2))) |
(sqrt.f64 (pow.f64 n (+.f64 1 (*.f64 2 (*.f64 k -1/2))))) |
(log.f64 (exp.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))) |
(cbrt.f64 (pow.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
(exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 n))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 n)) 1)) |
(log1p.f64 (expm1.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64))))) |
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (*.f64 -1/2 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (PI.f64)))) k)))) |
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (+.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) 1) (sqrt.f64 2))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64)))))) |
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (fma.f64 -1/2 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (PI.f64))))) (*.f64 1/8 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2)))))) |
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (PI.f64)))) k)) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k))))))) |
(*.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/8 (*.f64 k (*.f64 k (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2)))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (PI.f64))))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (+.f64 (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3))) (sqrt.f64 (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64))))))) |
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (fma.f64 -1/2 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (PI.f64))))) (fma.f64 -1/48 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3))) (*.f64 1/8 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))))))) |
(+.f64 (*.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (PI.f64)))) k)))) (*.f64 (sqrt.f64 (PI.f64)) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k))))))) |
(*.f64 (sqrt.f64 (PI.f64)) (+.f64 (*.f64 (+.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) 1) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3))) (*.f64 1/8 (*.f64 k (*.f64 k (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2)))))))) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))))))) |
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
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(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) |
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1))) |
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n)))) |
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) |
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1))) |
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n)))) |
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) |
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(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n)))) |
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(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n)))) |
(sqrt.f64 n) |
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(fma.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 n) k) (log.f64 n)) (sqrt.f64 n)) |
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(pow.f64 n (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
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(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 n (fma.f64 -1/2 k 1/2)) |
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(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) |
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) 1) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) |
(/.f64 1 (/.f64 1 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) |
(/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2)) (sqrt.f64 (PI.f64)))) |
(*.f64 (/.f64 (sqrt.f64 2) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2)))) |
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(pow.f64 (*.f64 2 (PI.f64)) (*.f64 2 (+.f64 1/4 (*.f64 -1/4 k)))) |
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 (*.f64 k -1/4) 2))) |
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(*.f64 (/.f64 (sqrt.f64 2) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2)))) |
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(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) (cbrt.f64 (sqrt.f64 (*.f64 2 (PI.f64))))) |
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(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (/.f64 1 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) 2))) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) |
(/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) 2) (/.f64 1 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))))) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) |
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(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) 1) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) |
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 1 (/.f64 1 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) 1) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) |
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) |
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)))) |
(*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 -1/2 k))) |
(/.f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (/.f64 1 (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2)))) |
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(*.f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2)))) |
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(*.f64 (/.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) 2)) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) (sqrt.f64 (cbrt.f64 (*.f64 2 (PI.f64))))) |
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(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/4) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) (pow.f64 (*.f64 2 (PI.f64)) 1/4)) |
(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/4) (pow.f64 (*.f64 2 (PI.f64)) 1/4)) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) |
(/.f64 (pow.f64 1 1/2) (/.f64 1 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) |
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(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (PI.f64)))) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 (*.f64 2 (PI.f64))))) |
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(/.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) 2) 1/2) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k 2)) (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) 1/2))) |
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(sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1 (*.f64 2 (*.f64 -1/2 k))))) |
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(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(pow.f64 (sqrt.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) 2) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) 3) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(pow.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) 3) 1/3) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) 2)) |
(fabs.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(log.f64 (exp.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) 3)) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 3) (pow.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) 3))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) 3) (pow.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 3))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(exp.f64 (log.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) 1)) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) 1) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
(*.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) 1) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
(*.f64 1 (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
(*.f64 (pow.f64 n (-.f64 1/4 (*.f64 1/4 k))) (pow.f64 n (-.f64 1/4 (*.f64 1/4 k)))) |
(pow.f64 n (*.f64 2 (+.f64 1/4 (*.f64 -1/4 k)))) |
(pow.f64 n (+.f64 1/2 (*.f64 (*.f64 k -1/4) 2))) |
(*.f64 (cbrt.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (cbrt.f64 (pow.f64 n (+.f64 1 (*.f64 2 (*.f64 k -1/2)))))) |
(*.f64 (cbrt.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (cbrt.f64 (pow.f64 n (+.f64 1 (*.f64 2 (*.f64 -1/2 k)))))) |
(*.f64 (cbrt.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (cbrt.f64 (pow.f64 n (+.f64 1 (*.f64 k -1))))) |
(*.f64 (cbrt.f64 (pow.f64 n (+.f64 1 (*.f64 2 (*.f64 k -1/2))))) (cbrt.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (cbrt.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (cbrt.f64 (pow.f64 n (+.f64 1 (*.f64 2 (*.f64 -1/2 k)))))) |
(*.f64 (cbrt.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (cbrt.f64 (pow.f64 n (+.f64 1 (*.f64 k -1))))) |
(*.f64 (sqrt.f64 n) (/.f64 1 (pow.f64 n (/.f64 k 2)))) |
(/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) |
(*.f64 (sqrt.f64 n) (pow.f64 n (*.f64 k -1/2))) |
(*.f64 (sqrt.f64 n) (pow.f64 n (*.f64 -1/2 k))) |
(*.f64 (/.f64 1 (pow.f64 n (/.f64 k 2))) (sqrt.f64 n)) |
(/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) |
(*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
(*.f64 (pow.f64 (sqrt.f64 n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (sqrt.f64 n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 n) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 n) (-.f64 1/2 (/.f64 k 2)))) |
(/.f64 1 (/.f64 (pow.f64 n (/.f64 k 2)) (sqrt.f64 n))) |
(/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) |
(/.f64 (cbrt.f64 n) (/.f64 (pow.f64 n (/.f64 k 2)) (cbrt.f64 (sqrt.f64 n)))) |
(*.f64 (cbrt.f64 (sqrt.f64 n)) (/.f64 (cbrt.f64 n) (pow.f64 n (/.f64 k 2)))) |
(/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) |
(/.f64 (sqrt.f64 (sqrt.f64 n)) (/.f64 (pow.f64 n (/.f64 k 2)) (sqrt.f64 (sqrt.f64 n)))) |
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 n)) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 n))) |
(*.f64 (sqrt.f64 (sqrt.f64 n)) (/.f64 (sqrt.f64 (sqrt.f64 n)) (pow.f64 n (/.f64 k 2)))) |
(/.f64 (sqrt.f64 (pow.f64 (cbrt.f64 n) 2)) (/.f64 (pow.f64 n (/.f64 k 2)) (sqrt.f64 (cbrt.f64 n)))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (cbrt.f64 n) 2)) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (cbrt.f64 n))) |
(*.f64 (sqrt.f64 (cbrt.f64 n)) (/.f64 (fabs.f64 (cbrt.f64 n)) (pow.f64 n (/.f64 k 2)))) |
(/.f64 (pow.f64 n 1/4) (/.f64 (pow.f64 n (/.f64 k 2)) (pow.f64 n 1/4))) |
(*.f64 (/.f64 (pow.f64 n 1/4) (pow.f64 n (/.f64 k 2))) (pow.f64 n 1/4)) |
(*.f64 (pow.f64 n 1/4) (/.f64 (pow.f64 n 1/4) (pow.f64 n (/.f64 k 2)))) |
(/.f64 (neg.f64 (sqrt.f64 n)) (neg.f64 (pow.f64 n (/.f64 k 2)))) |
(/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) |
(/.f64 (pow.f64 1 1/2) (/.f64 (pow.f64 n (/.f64 k 2)) (sqrt.f64 n))) |
(/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) |
(/.f64 (pow.f64 (sqrt.f64 n) 1/2) (/.f64 (pow.f64 n (/.f64 k 2)) (pow.f64 (sqrt.f64 n) 1/2))) |
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 n)) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 n))) |
(*.f64 (sqrt.f64 (sqrt.f64 n)) (/.f64 (sqrt.f64 (sqrt.f64 n)) (pow.f64 n (/.f64 k 2)))) |
(/.f64 (pow.f64 (pow.f64 (cbrt.f64 n) 2) 1/2) (/.f64 (pow.f64 n (/.f64 k 2)) (pow.f64 (cbrt.f64 n) 1/2))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (cbrt.f64 n) 2)) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (cbrt.f64 n))) |
(*.f64 (sqrt.f64 (cbrt.f64 n)) (/.f64 (fabs.f64 (cbrt.f64 n)) (pow.f64 n (/.f64 k 2)))) |
(sqrt.f64 (pow.f64 n (+.f64 1 (*.f64 2 (*.f64 k -1/2))))) |
(sqrt.f64 (pow.f64 n (+.f64 1 (*.f64 2 (*.f64 -1/2 k))))) |
(sqrt.f64 (pow.f64 n (+.f64 1 (*.f64 k -1)))) |
(log.f64 (exp.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
(cbrt.f64 (pow.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) 3)) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
(expm1.f64 (log1p.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
(exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 n))) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 n)) 1)) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
(log1p.f64 (expm1.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
(pow.f64 n (-.f64 1/2 (/.f64 k 2))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.2b | (*.f64 n (PI.f64)) |
| ✓ | 0.2b | (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
| 0.3b | (/.f64 1 (sqrt.f64 k)) | |
| ✓ | 3.6b | (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
Compiled 74 to 46 computations (37.8% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 13.0ms | n | @ | 0 | (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
| 1.0ms | n | @ | inf | (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
| 1.0ms | n | @ | -inf | (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
| 0.0ms | k | @ | 0 | (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
| 0.0ms | n | @ | -inf | (*.f64 n (PI.f64)) |
| 1× | batch-egg-rewrite |
| 954× | distribute-rgt-in |
| 904× | distribute-lft-in |
| 830× | associate-*r/ |
| 636× | associate-*l/ |
| 342× | add-sqr-sqrt |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 69 |
| 1 | 342 | 59 |
| 2 | 4075 | 59 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(*.f64 n (PI.f64)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (-.f64 1 k)) (log.f64 2)) (pow.f64 (pow.f64 (exp.f64 1/2) (-.f64 1 k)) (log.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (exp.f64 1/2)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (pow.f64 (sqrt.f64 (exp.f64 1/2)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (E.f64)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (pow.f64 (cbrt.f64 (exp.f64 1/2)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 1/2) (-.f64 1 k))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))))) |
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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 n (PI.f64)))))))) |
| 1× | egg-herbie |
| 1444× | fma-def |
| 1330× | unswap-sqr |
| 1202× | associate-+l+ |
| 1200× | associate-+r+ |
| 404× | +-commutative |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 287 | 4511 |
| 1 | 647 | 4029 |
| 2 | 2652 | 3743 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) 1) |
(*.f64 1 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1) |
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(*.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(*.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (-.f64 1 k)) (log.f64 2)) (pow.f64 (pow.f64 (exp.f64 1/2) (-.f64 1 k)) (log.f64 (*.f64 n (PI.f64))))) |
(*.f64 (pow.f64 1 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 1/2)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (pow.f64 (sqrt.f64 (exp.f64 1/2)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (pow.f64 (cbrt.f64 (E.f64)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (pow.f64 (cbrt.f64 (exp.f64 1/2)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(log.f64 (exp.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) |
(cbrt.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(exp.f64 (log.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 1/2) (-.f64 1 k))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(log1p.f64 (expm1.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(+.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 0) |
(+.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 2 n))) |
(+.f64 (log.f64 (PI.f64)) (+.f64 (log.f64 n) (log.f64 2))) |
(+.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64)))) |
(+.f64 0 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(+.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 2)) |
(+.f64 (log.f64 n) (+.f64 (log.f64 (PI.f64)) (log.f64 2))) |
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) |
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2)) (+.f64 (log.f64 (cbrt.f64 (*.f64 n (PI.f64)))) (log.f64 2))) |
(+.f64 (log.f64 (*.f64 2 n)) (log.f64 (PI.f64))) |
(+.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (log.f64 2))) |
(+.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 (log.f64 2) 1) (*.f64 (log.f64 (*.f64 n (PI.f64))) 1)) |
(+.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1) (*.f64 (log.f64 2) 1)) |
(+.f64 (+.f64 (log.f64 2) (log.f64 (PI.f64))) (log.f64 n)) |
(+.f64 (+.f64 (log.f64 2) 0) (log.f64 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 (log.f64 2) (log.f64 n)) (log.f64 (PI.f64))) |
(+.f64 (+.f64 (log.f64 2) (log.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2))) (log.f64 (cbrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (+.f64 (log.f64 2) (log.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (log.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (+.f64 0 (log.f64 2)) (log.f64 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 0 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (+.f64 0 (log.f64 (*.f64 2 n))) (log.f64 (PI.f64))) |
(+.f64 (+.f64 0 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (+.f64 0 (*.f64 (log.f64 2) 1)) (*.f64 (log.f64 (*.f64 n (PI.f64))) 1)) |
(+.f64 (+.f64 (log.f64 (*.f64 2 n)) 0) (log.f64 (PI.f64))) |
(+.f64 (+.f64 (log.f64 (*.f64 2 n)) (log.f64 (sqrt.f64 (PI.f64)))) (log.f64 (sqrt.f64 (PI.f64)))) |
(+.f64 (+.f64 (log.f64 (*.f64 2 n)) (log.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2))) (log.f64 (cbrt.f64 (PI.f64)))) |
(+.f64 (*.f64 1 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 1 (log.f64 (*.f64 2 n))) (log.f64 (PI.f64))) |
(+.f64 (*.f64 1 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 1 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 1 (*.f64 (log.f64 2) 1)) (*.f64 1 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1))) |
(+.f64 (*.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) 1) (*.f64 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)) |
(+.f64 (*.f64 (log.f64 (*.f64 2 n)) 1) (*.f64 (log.f64 (PI.f64)) 1)) |
(+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)) |
(+.f64 (*.f64 (*.f64 (log.f64 2) 1) 1) (*.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1) 1)) |
(-.f64 (exp.f64 (log1p.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1) |
(-.f64 (+.f64 0 (exp.f64 (log1p.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1) |
(*.f64 1 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 2 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(*.f64 (sqrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (cbrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 (cbrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 2)) |
(*.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 2) (cbrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(/.f64 (-.f64 (*.f64 (log.f64 2) (log.f64 2)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64))))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) |
(/.f64 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) (+.f64 (*.f64 (log.f64 2) (log.f64 2)) (-.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (*.f64 1 (-.f64 (*.f64 (log.f64 2) (log.f64 2)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64)))))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 1 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3))) (+.f64 (*.f64 (log.f64 2) (log.f64 2)) (-.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (log.f64 2) (log.f64 2)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64))))) 1) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) 1) (+.f64 (*.f64 (log.f64 2) (log.f64 2)) (-.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))))) |
(pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(pow.f64 (sqrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 2) |
(pow.f64 (cbrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3) |
(pow.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) 1/3) |
(sqrt.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) |
(cbrt.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) |
(expm1.f64 (log1p.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(exp.f64 (log.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(exp.f64 (*.f64 (log.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)) |
(log1p.f64 (-.f64 (*.f64 2 (*.f64 n (PI.f64))) 1)) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1) |
(pow.f64 (*.f64 n (PI.f64)) 1) |
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 2) |
(pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3) |
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3) |
(sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 2)) |
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n)) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 n (PI.f64))))) |
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3)) |
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) |
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3))) |
(expm1.f64 (log1p.f64 (*.f64 n (PI.f64)))) |
(exp.f64 (log.f64 (*.f64 n (PI.f64)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1)) |
(log1p.f64 (expm1.f64 (*.f64 n (PI.f64)))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 -1/2 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 2))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (fma.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k))) (sqrt.f64 2)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (sqrt.f64 (*.f64 n (PI.f64))))))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 (*.f64 -1/48 (*.f64 (sqrt.f64 2) (pow.f64 k 3))) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (fma.f64 -1/2 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (*.f64 1/8 (*.f64 k (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(pow.f64 (exp.f64 1/2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 1/2 (-.f64 1 k))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(pow.f64 (exp.f64 1/2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 1/2 (-.f64 1 k))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
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(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
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(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
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(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
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(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
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(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
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(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))) |
(-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))) |
(-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))) |
(-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) |
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) |
(fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))) |
(-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) 1) |
(pow.f64 (exp.f64 1/2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 1/2 (-.f64 1 k))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(*.f64 1 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(pow.f64 (exp.f64 1/2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 1/2 (-.f64 1 k))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(*.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1) |
(pow.f64 (exp.f64 1/2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 1/2 (-.f64 1 k))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
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(pow.f64 (exp.f64 1/2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 1/2 (-.f64 1 k))) |
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(*.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
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(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(*.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 1/2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (-.f64 1 k)) (log.f64 2)) (pow.f64 (pow.f64 (exp.f64 1/2) (-.f64 1 k)) (log.f64 (*.f64 n (PI.f64))))) |
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(pow.f64 (exp.f64 1/2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 1/2 (-.f64 1 k))) |
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(*.f64 (pow.f64 (sqrt.f64 (exp.f64 1/2)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (pow.f64 (sqrt.f64 (exp.f64 1/2)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(pow.f64 (sqrt.f64 (exp.f64 1/2)) (*.f64 2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))) |
(*.f64 (pow.f64 (cbrt.f64 (E.f64)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (pow.f64 (cbrt.f64 (exp.f64 1/2)) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
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(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 1/2 (-.f64 1 k))) |
(log.f64 (exp.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
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(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(log1p.f64 (expm1.f64 (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(pow.f64 (exp.f64 1/2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 1/2 (-.f64 1 k))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(+.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 0) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 (PI.f64)) (log.f64 (*.f64 2 n))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 (PI.f64)) (+.f64 (log.f64 n) (log.f64 2))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 0 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 2)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 n) (+.f64 (log.f64 (PI.f64)) (log.f64 2))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 3 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) |
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 3 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2)) (+.f64 (log.f64 (cbrt.f64 (*.f64 n (PI.f64)))) (log.f64 2))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 (*.f64 2 n)) (log.f64 (PI.f64))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (log.f64 2))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 2 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 (log.f64 2) 1) (*.f64 (log.f64 (*.f64 n (PI.f64))) 1)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1) (*.f64 (log.f64 2) 1)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 (log.f64 2) (log.f64 (PI.f64))) (log.f64 n)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 (log.f64 2) 0) (log.f64 (*.f64 n (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 (log.f64 2) (log.f64 n)) (log.f64 (PI.f64))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 (log.f64 2) (log.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2))) (log.f64 (cbrt.f64 (*.f64 n (PI.f64))))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 (log.f64 2) (log.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (log.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 0 (log.f64 2)) (log.f64 (*.f64 n (PI.f64)))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 0 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 3 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (+.f64 0 (log.f64 (*.f64 2 n))) (log.f64 (PI.f64))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 0 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 2 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (+.f64 0 (*.f64 (log.f64 2) 1)) (*.f64 (log.f64 (*.f64 n (PI.f64))) 1)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 (log.f64 (*.f64 2 n)) 0) (log.f64 (PI.f64))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (+.f64 (log.f64 (*.f64 2 n)) (log.f64 (sqrt.f64 (PI.f64)))) (log.f64 (sqrt.f64 (PI.f64)))) |
(+.f64 (log.f64 (sqrt.f64 (PI.f64))) (+.f64 (log.f64 (*.f64 2 n)) (log.f64 (sqrt.f64 (PI.f64))))) |
(+.f64 (log.f64 (*.f64 2 n)) (*.f64 2 (log.f64 (sqrt.f64 (PI.f64))))) |
(fma.f64 2 (log.f64 (sqrt.f64 (PI.f64))) (log.f64 (*.f64 2 n))) |
(+.f64 (+.f64 (log.f64 (*.f64 2 n)) (log.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2))) (log.f64 (cbrt.f64 (PI.f64)))) |
(+.f64 (log.f64 (*.f64 2 n)) (+.f64 (*.f64 2 (log.f64 (cbrt.f64 (PI.f64)))) (log.f64 (cbrt.f64 (PI.f64))))) |
(+.f64 (log.f64 (*.f64 2 n)) (*.f64 3 (log.f64 (cbrt.f64 (PI.f64))))) |
(fma.f64 3 (log.f64 (cbrt.f64 (PI.f64))) (log.f64 (*.f64 2 n))) |
(+.f64 (*.f64 1 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 3 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 1 (log.f64 (*.f64 2 n))) (log.f64 (PI.f64))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 1 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 1 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 2 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 1 (*.f64 (log.f64 2) 1)) (*.f64 1 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) 1) (*.f64 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)) |
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 3 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 (log.f64 (*.f64 2 n)) 1) (*.f64 (log.f64 (PI.f64)) 1)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)) |
(*.f64 2 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 (*.f64 (log.f64 2) 1) 1) (*.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1) 1)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(-.f64 (exp.f64 (log1p.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(-.f64 (+.f64 0 (exp.f64 (log1p.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(*.f64 1 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(*.f64 2 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(*.f64 (cbrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 (cbrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 2)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(*.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 2) (cbrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(/.f64 (-.f64 (*.f64 (log.f64 2) (log.f64 2)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64))))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) |
(/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64)))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64)))))) |
(/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(/.f64 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) (+.f64 (*.f64 (log.f64 2) (log.f64 2)) (-.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) (fma.f64 (log.f64 2) (log.f64 2) (*.f64 (log.f64 (*.f64 n (PI.f64))) (-.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 2))))) |
(/.f64 (+.f64 (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3) (pow.f64 (log.f64 2) 3)) (fma.f64 (log.f64 2) (log.f64 2) (*.f64 (log.f64 (*.f64 n (PI.f64))) (-.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 2))))) |
(/.f64 (*.f64 1 (-.f64 (*.f64 (log.f64 2) (log.f64 2)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64)))))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) |
(/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64)))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64)))))) |
(/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(/.f64 (*.f64 1 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3))) (+.f64 (*.f64 (log.f64 2) (log.f64 2)) (-.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) (fma.f64 (log.f64 2) (log.f64 2) (*.f64 (log.f64 (*.f64 n (PI.f64))) (-.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 2))))) |
(/.f64 (+.f64 (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3) (pow.f64 (log.f64 2) 3)) (fma.f64 (log.f64 2) (log.f64 2) (*.f64 (log.f64 (*.f64 n (PI.f64))) (-.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 2))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (log.f64 2) (log.f64 2)) (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64))))) 1) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))) |
(/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64)))) (-.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64)))))) |
(/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(/.f64 (*.f64 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) 1) (+.f64 (*.f64 (log.f64 2) (log.f64 2)) (-.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 2) (log.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) (fma.f64 (log.f64 2) (log.f64 2) (*.f64 (log.f64 (*.f64 n (PI.f64))) (-.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 2))))) |
(/.f64 (+.f64 (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3) (pow.f64 (log.f64 2) 3)) (fma.f64 (log.f64 2) (log.f64 2) (*.f64 (log.f64 (*.f64 n (PI.f64))) (-.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 2))))) |
(pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(pow.f64 (sqrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 2) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(pow.f64 (cbrt.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(pow.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) 1/3) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(cbrt.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(expm1.f64 (log1p.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(exp.f64 (log.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(exp.f64 (*.f64 (log.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)) |
(log.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(log1p.f64 (-.f64 (*.f64 2 (*.f64 n (PI.f64))) 1)) |
(log1p.f64 (fma.f64 2 (*.f64 n (PI.f64)) -1)) |
(log1p.f64 (fma.f64 (PI.f64) (*.f64 2 n) -1)) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1) |
(*.f64 n (PI.f64)) |
(pow.f64 (*.f64 n (PI.f64)) 1) |
(*.f64 n (PI.f64)) |
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 2) |
(*.f64 n (PI.f64)) |
(pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3) |
(*.f64 n (PI.f64)) |
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3) |
(*.f64 n (PI.f64)) |
(sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 2)) |
(*.f64 n (PI.f64)) |
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n)) |
(*.f64 n (PI.f64)) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 n (PI.f64))))) |
(*.f64 n (PI.f64)) |
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3)) |
(*.f64 n (PI.f64)) |
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3))) |
(*.f64 n (PI.f64)) |
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3))) |
(*.f64 n (PI.f64)) |
(expm1.f64 (log1p.f64 (*.f64 n (PI.f64)))) |
(*.f64 n (PI.f64)) |
(exp.f64 (log.f64 (*.f64 n (PI.f64)))) |
(*.f64 n (PI.f64)) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1)) |
(*.f64 n (PI.f64)) |
(log1p.f64 (expm1.f64 (*.f64 n (PI.f64)))) |
(*.f64 n (PI.f64)) |
Compiled 31279 to 21711 computations (30.6% saved)
20 alts after pruning (15 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1211 | 8 | 1219 |
| Fresh | 4 | 7 | 11 |
| Picked | 0 | 1 | 1 |
| Done | 1 | 4 | 5 |
| Total | 1216 | 20 | 1236 |
| Status | Error | Program |
|---|---|---|
| 21.6b | (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 3) 1/3) | |
| ✓ | 0.3b | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| ▶ | 3.9b | (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) |
| ▶ | 0.3b | (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
| 0.7b | (/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k 1/2))) | |
| 22.0b | (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) | |
| ▶ | 21.9b | (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| 3.5b | (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 k)) | |
| ✓ | 3.3b | (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) |
| ▶ | 0.4b | (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 17.0b | (*.f64 (pow.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) 1/3) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) | |
| ✓ | 0.3b | (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
| 0.3b | (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (/.f64 1 k))) | |
| 3.9b | (*.f64 (pow.f64 k -1/2) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) | |
| ✓ | 0.8b | (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
| 1.6b | (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (sqrt.f64 n)) | |
| ✓ | 3.9b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
| ▶ | 0.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
| 12.1b | (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))) k)) | |
| 3.3b | (exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
Compiled 629 to 519 computations (17.5% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.1b | (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
| ✓ | 0.2b | (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
| 0.2b | (*.f64 n (PI.f64)) | |
| 0.3b | (/.f64 1 (sqrt.f64 k)) |
Compiled 58 to 33 computations (43.1% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | k | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
| 1.0ms | k | @ | -inf | (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
| 1.0ms | k | @ | inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
| 1.0ms | n | @ | inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
| 1.0ms | n | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
| 1× | batch-egg-rewrite |
| 1404× | associate-*r/ |
| 1090× | associate-*l/ |
| 846× | associate-/r* |
| 354× | add-sqr-sqrt |
| 342× | *-un-lft-identity |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 72 |
| 1 | 354 | 68 |
| 2 | 4405 | 68 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1168× | distribute-lft-in |
| 1160× | distribute-rgt-in |
| 1144× | associate-/l* |
| 648× | times-frac |
| 556× | associate-/l/ |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 430 | 9857 |
| 1 | 1018 | 9139 |
| 2 | 5080 | 9139 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
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(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 1) (pow.f64 1 1/2)) (sqrt.f64 k)) |
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 1) (pow.f64 (cbrt.f64 (*.f64 k k)) 1/2)) (pow.f64 (cbrt.f64 k) 1/2)) |
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)) 1) (pow.f64 k 1/4)) |
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (pow.f64 k 1/4))) |
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)) (sqrt.f64 (pow.f64 k 1/4))) (sqrt.f64 (pow.f64 k 1/4))) |
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 k 1/4)) (sqrt.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) 1) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) (sqrt.f64 (cbrt.f64 (sqrt.f64 k)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (cbrt.f64 (sqrt.f64 k))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (pow.f64 k 1/4))) (cbrt.f64 (pow.f64 k 1/4))) |
(/.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (cbrt.f64 k))) (cbrt.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 1) (neg.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (pow.f64 k 1/4)) (neg.f64 (pow.f64 k 1/4))) |
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (cbrt.f64 k)) (neg.f64 (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) -1) (sqrt.f64 k)) |
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) (sqrt.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 k))) (cbrt.f64 (neg.f64 (sqrt.f64 k))))) (cbrt.f64 (neg.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (neg.f64 (pow.f64 k 1/4))) (pow.f64 k 1/4)) |
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (neg.f64 (cbrt.f64 k))) (cbrt.f64 (sqrt.f64 k))) |
(pow.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 1) |
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) 2) |
(pow.f64 (cbrt.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) 3) |
(pow.f64 (pow.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 3) 1/3) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)) |
(log.f64 (exp.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))))) |
(cbrt.f64 (pow.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 3)) |
(cbrt.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2))) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2) (/.f64 (/.f64 1 (sqrt.f64 k)) k))) |
(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) |
(exp.f64 (log.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) 1)) |
(log1p.f64 (expm1.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) |
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) 1) |
(*.f64 1 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 1) |
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/4) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/4)) |
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 2 (pow.f64 2 k))) (sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) (-.f64 1 k)))) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 n (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 2) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 1/2)) |
(*.f64 (pow.f64 (/.f64 2 (pow.f64 2 k)) 1/2) (pow.f64 (pow.f64 (*.f64 n (PI.f64)) (-.f64 1 k)) 1/2)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) |
(pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 1) |
(pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/4) 2) |
(pow.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 3) |
(pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2) 1/3) |
(fabs.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2)) |
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1/2)) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 1)) |
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
| Outputs |
|---|
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
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(log.f64 (exp.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) |
(cbrt.f64 (pow.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 3)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) |
(cbrt.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2))) |
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 k (sqrt.f64 k))) (pow.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) 3/2))) |
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 k (sqrt.f64 k))) (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 3/2))) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2) (/.f64 (/.f64 1 (sqrt.f64 k)) k))) |
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 k (sqrt.f64 k))) (pow.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) 3/2))) |
(cbrt.f64 (*.f64 (/.f64 1 (*.f64 k (sqrt.f64 k))) (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 3/2))) |
(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) |
(exp.f64 (log.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) 1)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) |
(log1p.f64 (expm1.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) |
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) 1) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(*.f64 1 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 1) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/4) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/4)) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 2 (pow.f64 2 k))) (sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) (-.f64 1 k)))) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) |
(*.f64 (fabs.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) |
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 n (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 n 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 2) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 1/2)) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) |
(*.f64 (fabs.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) |
(*.f64 (pow.f64 (/.f64 2 (pow.f64 2 k)) 1/2) (pow.f64 (pow.f64 (*.f64 n (PI.f64)) (-.f64 1 k)) 1/2)) |
(*.f64 (sqrt.f64 (/.f64 2 (pow.f64 2 k))) (sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) (-.f64 1 k)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k))) |
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k))) (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) |
(/.f64 (*.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k))) |
(/.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k))) (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/2) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 1) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 1/4) 2) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(pow.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 3) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2) 1/3) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) 3/2)) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 3/2)) |
(fabs.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) 3/2)) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) 3/2)) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 3/2)) |
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1/2)) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 1)) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) |
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.2b | (*.f64 n (PI.f64)) | |
| ✓ | 0.3b | (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| ✓ | 0.4b | (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
Compiled 31 to 15 computations (51.6% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | n | @ | inf | (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| 1.0ms | n | @ | 0 | (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| 1.0ms | k | @ | -inf | (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| 1.0ms | k | @ | 0 | (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| 1.0ms | n | @ | 0 | (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
| 1× | batch-egg-rewrite |
| 1552× | associate-/l* |
| 1416× | associate-/r* |
| 674× | associate-*r/ |
| 584× | associate-*l/ |
| 276× | distribute-rgt-in |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 44 |
| 1 | 263 | 44 |
| 2 | 3282 | 44 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 n)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 n) 1/2) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (cbrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (neg.f64 (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (neg.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 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egg-rr> (2) ((x *.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 1) (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 n (PI.f64))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))))))) |
| 1× | egg-herbie |
| 1620× | associate-*r/ |
| 1016× | associate-/r* |
| 962× | unswap-sqr |
| 830× | *-commutative |
| 630× | distribute-lft-in |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 187 | 2493 |
| 1 | 420 | 2463 |
| 2 | 1853 | 2463 |
| 1× | node limit |
| Inputs |
|---|
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1) |
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(*.f64 1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (*.f64 2 n)) (sqrt.f64 (PI.f64))) |
(*.f64 -1 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(*.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (neg.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/2)) |
(*.f64 (pow.f64 (*.f64 2 n) 1/2) (sqrt.f64 (PI.f64))) |
(*.f64 (neg.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (neg.f64 (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (cbrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (neg.f64 (neg.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/2) |
(pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) |
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3) |
(pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) 1/3) |
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(fabs.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)) |
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/2)) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)) |
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) 1) |
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2)) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 1) |
(*.f64 1 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 k -1/2))) |
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k -1/2))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (cbrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64))))) |
(*.f64 (cbrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k -1/2))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 -1 (sqrt.f64 k))) |
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4))) |
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 1) (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(*.f64 (/.f64 (sqrt.f64 2) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k 1/4))) |
(*.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k 1/4))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 1) |
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 2) |
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 3) |
(pow.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64))) 1/2) |
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 3) 1/3) |
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 n (PI.f64))))) -1) |
(neg.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 k)))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(log.f64 (exp.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))) |
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 3)) |
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(exp.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 1)) |
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
| Outputs |
|---|
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(*.f64 1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (fabs.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(*.f64 (fabs.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (*.f64 2 n)) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 2 n))) |
(*.f64 -1 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(*.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) |
(*.f64 (neg.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/2)) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (fabs.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(*.f64 (fabs.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (pow.f64 (*.f64 2 n) 1/2) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 2 n))) |
(*.f64 (neg.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(*.f64 (neg.f64 (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (cbrt.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(*.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) |
(*.f64 (neg.f64 (neg.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/2) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) 1/3) |
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)) |
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3/2)) |
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(fabs.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)) |
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3/2)) |
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/2)) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) 1) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k -1/2)) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 1) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(*.f64 1 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 k -1/2))) |
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k -1/2))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 k -1/2))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (cbrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64))))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (cbrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 2 k)))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k))) (cbrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k)))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(*.f64 (cbrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (cbrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 2 k)))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k))) (cbrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k)))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k -1/2))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k -1/2))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k -1/2)) |
(*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 -1 (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k 1/4)) (pow.f64 k 1/4)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 (pow.f64 k 1/4) (pow.f64 k 1/4))) |
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 1) (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))) |
(*.f64 (/.f64 (sqrt.f64 2) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k 1/4))) |
(*.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k 1/4))) |
(/.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k 1/4))) (pow.f64 k 1/4)) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (pow.f64 k 1/4))) |
(/.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4)) (/.f64 (pow.f64 k 1/4) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 k))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k))) (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (cbrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k))) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))) |
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k))) |
(pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 1) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 2) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 3) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(pow.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64))) 1/2) |
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 2 k))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 3) 1/3) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 n (PI.f64))))) -1) |
(/.f64 1 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 n (PI.f64)))))) |
(/.f64 1 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 2 n))))) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
(neg.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 2 k))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(log.f64 (exp.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 3)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(exp.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 1)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (sqrt.f64 k)) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.2b | (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) | |
| ✓ | 0.2b | (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
| 0.2b | (*.f64 (*.f64 2 (PI.f64)) n) | |
| ✓ | 0.3b | (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
Compiled 69 to 51 computations (26.1% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | n | @ | 0 | (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
| 2.0ms | k | @ | 0 | (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
| 1.0ms | n | @ | inf | (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
| 1.0ms | n | @ | -inf | (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
| 1.0ms | k | @ | 0 | (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
| 1× | batch-egg-rewrite |
| 1810× | associate-/r* |
| 1434× | associate-/l* |
| 408× | add-sqr-sqrt |
| 386× | *-un-lft-identity |
| 382× | pow1 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 86 |
| 1 | 403 | 82 |
| 2 | 5279 | 78 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
| Outputs |
|---|
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(*.f64 (*.f64 2 (PI.f64)) n))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (+.f64 -1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))))))) |
| 1× | egg-herbie |
| 922× | fma-def |
| 562× | associate-*r* |
| 538× | associate-/l/ |
| 462× | associate-*l* |
| 440× | distribute-lft-neg-in |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 279 | 6174 |
| 1 | 775 | 5612 |
| 2 | 3517 | 5258 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 -1 (*.f64 (pow.f64 k 2) (+.f64 (*.f64 -1/4 (*.f64 (*.f64 (pow.f64 (sqrt.f64 2) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64))))))))) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 -1 (*.f64 (pow.f64 k 3) (+.f64 (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (*.f64 -1/4 (*.f64 (*.f64 (pow.f64 (sqrt.f64 2) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64))))))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 1/16 (*.f64 (*.f64 (pow.f64 (sqrt.f64 2) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))))))) (+.f64 (*.f64 -1 (*.f64 (pow.f64 k 2) (+.f64 (*.f64 -1/4 (*.f64 (*.f64 (pow.f64 (sqrt.f64 2) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64))))))))) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))))) |
(/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))) |
(/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))) |
(/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))) |
(/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))) |
(/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) 1) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 1 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
(*.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 1) |
(*.f64 (*.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4)))) (*.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4))))) |
(*.f64 (pow.f64 k -1/4) (*.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (cbrt.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) 2)) |
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) 2) (cbrt.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (cbrt.f64 (pow.f64 k -1)) (*.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 -1 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 2)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4)))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4)))) |
(*.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (/.f64 1 (sqrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 2)) (/.f64 (pow.f64 k -1/2) (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (/.f64 (pow.f64 k -1/2) -1) (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (/.f64 (pow.f64 k -1/4) 1) (/.f64 (pow.f64 k -1/4) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 2)) (/.f64 (pow.f64 k -1/4) (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) 1) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (sqrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (sqrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (pow.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 2)) (cbrt.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(pow.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 1) |
(pow.f64 (*.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4)))) 2) |
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) 3) |
(pow.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 3) 1/3) |
(pow.f64 (/.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 k -1/2)) -1) |
(neg.f64 (/.f64 (pow.f64 k -1/2) (neg.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(sqrt.f64 (*.f64 (pow.f64 k -1) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))))) |
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))))) |
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 3)) |
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 3))) |
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(exp.f64 (log.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) 1)) |
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) 1) |
(*.f64 1 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 1) |
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) (pow.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 2)) |
(*.f64 (pow.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 2) (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 -1 (neg.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(*.f64 (pow.f64 1 (+.f64 -1/2 (/.f64 k 2))) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 2 (+.f64 -1/2 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) n) (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 -1/2 (/.f64 k 2))) (pow.f64 n (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 n (+.f64 -1/2 (/.f64 k 2))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (+.f64 -1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (+.f64 -1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4))) -1) (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4))) -1)) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 2) -1) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) -1)) |
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) -1) (pow.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) -1)) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (+.f64 -1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 (-.f64 1/2 (/.f64 k 2)) -1)) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 (+.f64 -1/2 (/.f64 k 2)) 1)) |
(pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) -1) |
(pow.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 1) |
(pow.f64 (sqrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 2) |
(pow.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 3) |
(pow.f64 (pow.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 3) 1/3) |
(sqrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) -2)) |
(log.f64 (exp.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(cbrt.f64 (pow.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 3)) |
(expm1.f64 (log1p.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(exp.f64 (*.f64 (+.f64 -1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (+.f64 -1/2 (/.f64 k 2)))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) -1)) |
(exp.f64 (*.f64 (*.f64 (+.f64 -1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1)) |
(log1p.f64 (expm1.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 k -1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(*.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
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(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(exp.f64 (log.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) 1)) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) 1) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 1 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 1) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) (pow.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 2)) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 2) (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 -1 (neg.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2))) |
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 k 2)) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) |
(*.f64 (pow.f64 1 (+.f64 -1/2 (/.f64 k 2))) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 2 (+.f64 -1/2 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) n) (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 -1/2 (/.f64 k 2))) (pow.f64 n (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 n (+.f64 -1/2 (/.f64 k 2))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 -1/2 (/.f64 k 2))) (pow.f64 n (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (+.f64 -1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (+.f64 -1/2 (/.f64 k 2)))) |
(pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 2 (+.f64 -1/2 (/.f64 k 2)))) |
(pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (+.f64 -1 (*.f64 2 (/.f64 k 2)))) |
(pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (fma.f64 2 (/.f64 k 2) -1)) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) 2) (+.f64 -1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (+.f64 -1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (+.f64 -1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4))) -1) (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4))) -1)) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 2) -1) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) -1)) |
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 2)) (/.f64 1 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) 2)) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) -1) (pow.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) -1)) |
(*.f64 (/.f64 1 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) (/.f64 1 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) |
(/.f64 (*.f64 1 (/.f64 1 (pow.f64 n (-.f64 1/2 (/.f64 k 2))))) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) |
(/.f64 (/.f64 1 (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (+.f64 -1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 -1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 (-.f64 1/2 (/.f64 k 2)) -1)) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 (+.f64 -1/2 (/.f64 k 2)) 1)) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (+.f64 -1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 -1/2 (/.f64 k 2))) |
(pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) -1) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 1) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (sqrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 2) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (cbrt.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) 3) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (pow.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 3) 1/3) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) -2)) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(log.f64 (exp.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))))) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(cbrt.f64 (pow.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) 3)) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(expm1.f64 (log1p.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(exp.f64 (*.f64 (+.f64 -1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (+.f64 -1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 -1/2 (/.f64 k 2))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (+.f64 -1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (+.f64 -1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 -1/2 (/.f64 k 2))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) -1)) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
(exp.f64 (*.f64 (*.f64 (+.f64 -1/2 (/.f64 k 2)) (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))) 1)) |
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (+.f64 -1/2 (/.f64 k 2))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 -1/2 (/.f64 k 2))) |
(log1p.f64 (expm1.f64 (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))))) |
(/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (-.f64 1/2 (/.f64 k 2)))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.2b | (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) | |
| ✓ | 0.2b | (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 0.2b | (*.f64 (*.f64 2 (PI.f64)) n) | |
| ✓ | 0.5b | (pow.f64 (pow.f64 k 1/4) -2) |
Compiled 61 to 45 computations (26.2% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | k | @ | -inf | (pow.f64 (pow.f64 k 1/4) -2) |
| 1.0ms | k | @ | 0 | (pow.f64 (pow.f64 k 1/4) -2) |
| 1.0ms | k | @ | inf | (pow.f64 (pow.f64 k 1/4) -2) |
| 1.0ms | k | @ | -inf | (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 0.0ms | k | @ | 0 | (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 1× | batch-egg-rewrite |
| 1328× | associate-*r/ |
| 984× | associate-*l/ |
| 388× | add-sqr-sqrt |
| 382× | associate-/l* |
| 378× | associate-/r* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 52 |
| 1 | 393 | 52 |
| 2 | 4792 | 52 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (pow.f64 k 1/4) -2) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (pow.f64 k 1/4) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 k 1/4) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (pow.f64 k 1/4) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (pow.f64 k -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (pow.f64 k 1/4) -2)) (cbrt.f64 (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 (pow.f64 k 1/4) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/2) (pow.f64 (pow.f64 k 1/4) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 k 1/8) -2) (pow.f64 (pow.f64 k 1/8) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sqrt.f64 k)) -2) (pow.f64 (cbrt.f64 (pow.f64 k 1/4)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 k -1/4) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 k -1/4) 1) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 k -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (pow.f64 k 1/4) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (pow.f64 k 1/4) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (pow.f64 k 1/4) -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (pow.f64 k 1/4) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (pow.f64 k 1/4) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (pow.f64 k 1/4) -2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (pow.f64 k 1/4) -2))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 n)) (pow.f64 n (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k -1/4)) 1) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (pow.f64 k 1/4) -2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k -1/4))) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (*.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (pow.f64 (pow.f64 k 1/4) -2))) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (pow.f64 (pow.f64 k 1/4) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (pow.f64 k 1/4) -2) 3) (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3) (pow.f64 (pow.f64 (pow.f64 k 1/4) -2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))))))) |
| 1× | egg-herbie |
| 708× | unswap-sqr |
| 658× | +-commutative |
| 608× | *-commutative |
| 576× | distribute-lft-in |
| 534× | distribute-rgt-in |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 172 | 2417 |
| 1 | 403 | 2409 |
| 2 | 1424 | 2197 |
| 3 | 5505 | 1951 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(sqrt.f64 (/.f64 1 k)) |
(/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) 2)) |
(/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) 2)) |
(/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) 2)) |
(/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) 2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (pow.f64 k 1/4) -2))) 1) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) 1) |
(*.f64 1 (pow.f64 (pow.f64 k 1/4) -2)) |
(*.f64 (pow.f64 k -1/4) (pow.f64 k -1/4)) |
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 k 1/4) -2)) (cbrt.f64 (pow.f64 k -1))) |
(*.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 (pow.f64 k 1/4) -2))) |
(*.f64 (pow.f64 1 -1/2) (pow.f64 (pow.f64 k 1/4) -2)) |
(*.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2)) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2)) |
(*.f64 (pow.f64 (pow.f64 k 1/8) -2) (pow.f64 (pow.f64 k 1/8) -2)) |
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 k)) -2) (pow.f64 (cbrt.f64 (pow.f64 k 1/4)) -2)) |
(/.f64 (pow.f64 k -1/4) (pow.f64 k 1/4)) |
(/.f64 (*.f64 (pow.f64 k -1/4) 1) (pow.f64 k 1/4)) |
(sqrt.f64 (pow.f64 k -1)) |
(log.f64 (exp.f64 (pow.f64 (pow.f64 k 1/4) -2))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (pow.f64 k 1/4) -2)))) |
(cbrt.f64 (pow.f64 (pow.f64 (pow.f64 k 1/4) -2) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 k 1/4) -2))) |
(exp.f64 (log.f64 (pow.f64 (pow.f64 k 1/4) -2))) |
(exp.f64 (*.f64 (log.f64 k) -1/2)) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (pow.f64 k 1/4) -2)) 1)) |
(log1p.f64 (expm1.f64 (pow.f64 (pow.f64 k 1/4) -2))) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) 1) |
(/.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2))) |
(/.f64 (*.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 n)) (pow.f64 n (*.f64 k 1/2))) |
(/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k -1/4)) 1) (pow.f64 k 1/4)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 (pow.f64 k 1/4) -2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k 1/2))) |
(/.f64 (*.f64 1 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k -1/4))) (pow.f64 k 1/4)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (*.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (pow.f64 (pow.f64 k 1/4) -2))) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k 1/2))) |
(pow.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 1) |
(pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k -1/4)) 2) |
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) 3) |
(pow.f64 (pow.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 3) 1/3) |
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))) (pow.f64 k -1))) |
(log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) (pow.f64 (pow.f64 k 1/4) -2))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))))) |
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 3)) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (pow.f64 k 1/4) -2) 3) (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3))) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3) (pow.f64 (pow.f64 (pow.f64 k 1/4) -2) 3))) |
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(exp.f64 (log.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) 1)) |
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
| Outputs |
|---|
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) 2)) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) 2)) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) 2)) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k)))))) 2)) |
(sqrt.f64 (/.f64 1 k)) |
(pow.f64 k -1/2) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (-.f64 1 k))) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (-.f64 1 k))) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (-.f64 1 k))) (pow.f64 k -1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
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(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) 3)) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (pow.f64 k 1/4) -2) 3) (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3) (pow.f64 (pow.f64 (pow.f64 k 1/4) -2) 3))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
(exp.f64 (log.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) 1)) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.2b | (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) |
| 0.2b | (*.f64 (PI.f64) (*.f64 2 n)) | |
| 0.2b | (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) | |
| ✓ | 3.6b | (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
Compiled 66 to 47 computations (28.8% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 53.0ms | k | @ | -inf | (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
| 26.0ms | k | @ | inf | (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
| 13.0ms | n | @ | 0 | (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
| 1.0ms | k | @ | 0 | (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) |
| 1.0ms | k | @ | 0 | (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
| 1× | batch-egg-rewrite |
| 1732× | associate-*r/ |
| 1434× | associate-*l/ |
| 384× | add-sqr-sqrt |
| 372× | *-un-lft-identity |
| 370× | pow1 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 92 |
| 1 | 380 | 92 |
| 2 | 4824 | 92 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) |
| Outputs |
|---|
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(*.f64 (PI.f64) (*.f64 2 n))))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (log.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (log.f64 (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))))))) |
| 1× | egg-herbie |
| 848× | distribute-lft-in |
| 832× | associate-/l* |
| 826× | distribute-rgt-in |
| 800× | associate-*r/ |
| 800× | +-commutative |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 204 | 5087 |
| 1 | 480 | 4479 |
| 2 | 1750 | 4313 |
| 3 | 7704 | 4313 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) 1) |
(*.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1) |
(*.f64 1 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) |
(*.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) |
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) |
(*.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (PI.f64))) (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 n)))) |
(*.f64 (pow.f64 1 (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2)))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2)))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2)))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2)))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(log.f64 (exp.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) |
(cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) |
(exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1)) |
(log1p.f64 (expm1.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) 1) |
(*.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (pow.f64 k -1/2)) |
(*.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) 1) |
(*.f64 1 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (*.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (pow.f64 k -1/2))) |
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) k))) |
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) k)) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (pow.f64 k -1/2))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) |
(*.f64 (neg.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (/.f64 1 (neg.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (pow.f64 k 1/4))) |
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) 1) (/.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) 1) (/.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (pow.f64 k 1/4))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) |
(pow.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) 1) |
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))) 2) |
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))) 3) |
(pow.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) 3) 1/3) |
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) -1) |
(neg.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (neg.f64 (sqrt.f64 k)))) |
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) k)) |
(log.f64 (exp.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))))) |
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) 3)) |
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 3) (pow.f64 k 3/2))) |
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) |
(exp.f64 (-.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (log.f64 (sqrt.f64 k)))) |
(exp.f64 (*.f64 (-.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (log.f64 (sqrt.f64 k))) 1)) |
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (sqrt.f64 2) -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) -1/2)) (fma.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k))) (sqrt.f64 2)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (sqrt.f64 (*.f64 n (PI.f64))))))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k)))) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (sqrt.f64 2))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (fma.f64 (*.f64 (sqrt.f64 2) -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/8 (*.f64 k (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/8 (*.f64 k (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (fma.f64 (*.f64 (sqrt.f64 2) -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 -1/2 k 1/2)) |
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) |
(pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 -1/2 k 1/2)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))) |
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (sqrt.f64 (/.f64 1 k))) |
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(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) 1) (/.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (/.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (pow.f64 k 1/4))) |
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (/.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 k))) |
(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (/.f64 (cbrt.f64 k) (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))))) |
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 k))) |
(pow.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) 1) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))) 2) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))) 3) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(pow.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) 3) 1/3) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) -1) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(neg.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)) |
(log.f64 (exp.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))))) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) 3)) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 3) (pow.f64 k 3/2))) |
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3) (pow.f64 k 3/2))) |
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) 3) (pow.f64 k 3/2))) |
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(exp.f64 (-.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (log.f64 (sqrt.f64 k)))) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(exp.f64 (*.f64 (-.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (log.f64 (sqrt.f64 k))) 1)) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)))) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
Compiled 25109 to 17338 computations (30.9% saved)
25 alts after pruning (19 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1048 | 14 | 1062 |
| Fresh | 5 | 5 | 10 |
| Picked | 0 | 1 | 1 |
| Done | 4 | 5 | 9 |
| Total | 1057 | 25 | 1082 |
| Status | Error | Program |
|---|---|---|
| 21.6b | (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 3) 1/3) | |
| ▶ | 22.1b | (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) |
| ✓ | 0.3b | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| ✓ | 3.9b | (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) |
| 0.3b | (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (+.f64 -1/2 (/.f64 k 2)))) | |
| 0.7b | (/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k 1/2))) | |
| 22.0b | (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (sqrt.f64 k)) | |
| 22.0b | (/.f64 (*.f64 (sqrt.f64 (*.f64 2 n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)) | |
| ▶ | 0.3b | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
| ✓ | 21.9b | (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| ✓ | 3.3b | (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) |
| 32.8b | (/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) | |
| 17.0b | (*.f64 (pow.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) 1/3) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) | |
| 0.3b | (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (/.f64 1 k))) | |
| 3.9b | (*.f64 (pow.f64 k -1/2) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) | |
| ▶ | 21.9b | (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
| ✓ | 0.8b | (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
| ▶ | 22.0b | (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
| ✓ | 3.9b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
| 22.0b | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 k -1/2))) | |
| 12.1b | (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) | |
| 14.5b | (sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) | |
| 33.8b | (sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) | |
| 33.8b | (sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) | |
| ▶ | 33.8b | (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
Compiled 665 to 545 computations (18% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.1b | (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) |
| ✓ | 0.1b | (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) |
| ✓ | 0.2b | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
| ✓ | 0.2b | (*.f64 (*.f64 n 2) (PI.f64)) |
Compiled 52 to 34 computations (34.6% saved)
21 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | k | @ | 0 | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
| 0.0ms | k | @ | 0 | (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) |
| 0.0ms | k | @ | -inf | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
| 0.0ms | k | @ | inf | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
| 0.0ms | k | @ | 0 | (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) |
| 1× | batch-egg-rewrite |
| 1530× | associate-/r* |
| 1406× | associate-*r/ |
| 1194× | associate-*l/ |
| 338× | add-sqr-sqrt |
| 328× | *-un-lft-identity |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 110 |
| 1 | 335 | 110 |
| 2 | 4281 | 110 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (*.f64 n 2) (PI.f64)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) |
(pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) |
| Outputs |
|---|
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3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (*.f64 n 2) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (*.f64 n 2) (PI.f64)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))))))) |
| 1× | egg-herbie |
| 1136× | associate-/r/ |
| 794× | associate-/l* |
| 736× | associate-*r* |
| 594× | associate-*l* |
| 504× | times-frac |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 440 | 10965 |
| 1 | 1118 | 9685 |
| 2 | 5498 | 9621 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1 (*.f64 (/.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 1/2 (*.f64 (/.f64 (*.f64 (pow.f64 k 2) (-.f64 (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))) (pow.f64 (*.f64 -1 (*.f64 (/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1 (*.f64 (/.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 1/2 (*.f64 (/.f64 (*.f64 (pow.f64 k 2) (-.f64 (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))) (pow.f64 (*.f64 -1 (*.f64 (/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1 (*.f64 (/.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/2 (*.f64 (/.f64 (*.f64 (pow.f64 k 3) (-.f64 (*.f64 -1/3 (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (PI.f64)))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))) (pow.f64 (*.f64 -1 (*.f64 (/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))) 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 (sqrt.f64 2) 2))))) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64))))))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) |
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) |
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(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) |
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(exp.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)))) |
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(*.f64 (pow.f64 (*.f64 n 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) |
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(*.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) |
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(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (-.f64 1/2 (/.f64 k 2)))) |
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(*.f64 (pow.f64 (pow.f64 (*.f64 n 2) (-.f64 1 k)) 1/2) (pow.f64 (pow.f64 (PI.f64) (-.f64 1 k)) 1/2)) |
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(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 1) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
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(pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1/2 (/.f64 k 2))) |
(pow.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) 1/2) |
(pow.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) 1) |
(pow.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) 1/4) 2) |
(pow.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) 3) |
(pow.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) 3/2) 1/3) |
(fabs.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) |
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) |
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) 3/2)) |
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) |
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (*.f64 n 2) (PI.f64)))) 1/2)) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) 1)) |
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) 1) |
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(/.f64 (*.f64 n 2) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (PI.f64))) |
(/.f64 (PI.f64) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (*.f64 n 2))) |
(/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) |
(/.f64 1 (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (*.f64 (*.f64 n 2) (PI.f64)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(/.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 2) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 n 2) (PI.f64))) (neg.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (*.f64 n 2)) (pow.f64 (*.f64 n 2) k)) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (PI.f64)) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (*.f64 n 2))) |
(/.f64 (*.f64 1 (neg.f64 (*.f64 (*.f64 n 2) (PI.f64)))) (neg.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (*.f64 2 (-.f64 1 k)))) (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64)))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (pow.f64 (*.f64 n 2) (-.f64 1 k)) (PI.f64)) (pow.f64 (PI.f64) k)) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) n) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (*.f64 2 (PI.f64)))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (*.f64 n 2)) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (PI.f64))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (*.f64 (*.f64 n 2) (PI.f64))) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (*.f64 (*.f64 n 2) (PI.f64)))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64)))) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 2)) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (neg.f64 (*.f64 (*.f64 n 2) (PI.f64)))) (neg.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 1) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(/.f64 (*.f64 (PI.f64) (pow.f64 (*.f64 n 2) (-.f64 1 k))) (pow.f64 (PI.f64) k)) |
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 2) 1) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(/.f64 (*.f64 (neg.f64 (*.f64 (*.f64 n 2) (PI.f64))) 1) (neg.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (*.f64 2 (-.f64 1 k))))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (*.f64 n 2) (pow.f64 (PI.f64) (-.f64 1 k))) (pow.f64 (*.f64 n 2) k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) 1) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (/.f64 k 2))) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (/.f64 k 2))) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (PI.f64) k)) (pow.f64 (*.f64 n 2) k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (*.f64 n 2) k)) (pow.f64 (PI.f64) k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 n k)) (pow.f64 (*.f64 2 (PI.f64)) k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 1 k)) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 2) k)) (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) k)) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (*.f64 2 (-.f64 1 k)))) |
(log.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) |
(exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (*.f64 n 2) (PI.f64)))) 1)) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) |
| Outputs |
|---|
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)) |
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) |
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1 (*.f64 (/.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 k (/.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (neg.f64 (*.f64 (/.f64 k (sqrt.f64 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 (sqrt.f64 2) (*.f64 (/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)) k))) |
(+.f64 (*.f64 1/2 (*.f64 (/.f64 (*.f64 (pow.f64 k 2) (-.f64 (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))) (pow.f64 (*.f64 -1 (*.f64 (/.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1 (*.f64 (/.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64))))))) |
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(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (neg.f64 (*.f64 (*.f64 n 2) (PI.f64))) (neg.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (*.f64 2 n) (neg.f64 (PI.f64))) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (PI.f64) (*.f64 n -2)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (*.f64 n 2)) (pow.f64 (*.f64 n 2) k)) |
(/.f64 (*.f64 n (*.f64 2 (pow.f64 (PI.f64) (-.f64 1 k)))) (pow.f64 (*.f64 2 n) k)) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (PI.f64)) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (*.f64 n 2))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 1 (neg.f64 (*.f64 (*.f64 n 2) (PI.f64)))) (neg.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (*.f64 2 n) (neg.f64 (PI.f64))) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (PI.f64) (*.f64 n -2)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (*.f64 2 (-.f64 1 k)))) (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64)))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1 k)))))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 n 2) (-.f64 1 k)) (PI.f64)) (pow.f64 (PI.f64) k)) |
(/.f64 (PI.f64) (/.f64 (pow.f64 (PI.f64) k) (pow.f64 (*.f64 2 n) (-.f64 1 k)))) |
(/.f64 (pow.f64 (*.f64 2 n) (-.f64 1 k)) (/.f64 (pow.f64 (PI.f64) k) (PI.f64))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) n) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (*.f64 2 (PI.f64)))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (*.f64 n 2)) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (PI.f64))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (*.f64 (*.f64 n 2) (PI.f64))) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (*.f64 (*.f64 n 2) (PI.f64)))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64)))) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 2)) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (pow.f64 1 (-.f64 1 k)) (neg.f64 (*.f64 (*.f64 n 2) (PI.f64)))) (neg.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (*.f64 2 n) (neg.f64 (PI.f64))) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (PI.f64) (*.f64 n -2)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 1) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (PI.f64) (pow.f64 (*.f64 n 2) (-.f64 1 k))) (pow.f64 (PI.f64) k)) |
(/.f64 (PI.f64) (/.f64 (pow.f64 (PI.f64) k) (pow.f64 (*.f64 2 n) (-.f64 1 k)))) |
(/.f64 (pow.f64 (*.f64 2 n) (-.f64 1 k)) (/.f64 (pow.f64 (PI.f64) k) (PI.f64))) |
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 2) 1) (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k) (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (neg.f64 (*.f64 (*.f64 n 2) (PI.f64))) 1) (neg.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (*.f64 (*.f64 2 n) (neg.f64 (PI.f64))) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (PI.f64) (*.f64 n -2)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (*.f64 2 (-.f64 1 k))))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1 k)))))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1 k))))) |
(/.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) (*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) (pow.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) 4)) |
(/.f64 (*.f64 (*.f64 n 2) (pow.f64 (PI.f64) (-.f64 1 k))) (pow.f64 (*.f64 n 2) k)) |
(/.f64 (*.f64 n (*.f64 2 (pow.f64 (PI.f64) (-.f64 1 k)))) (pow.f64 (*.f64 2 n) k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) 1) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (/.f64 k 2))) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (/.f64 k 2))) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (PI.f64) k)) (pow.f64 (*.f64 n 2) k)) |
(/.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (*.f64 2 n) k) (pow.f64 (PI.f64) k))) |
(/.f64 (/.f64 (PI.f64) (/.f64 (pow.f64 (PI.f64) k) (*.f64 2 n))) (pow.f64 (*.f64 2 n) k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (*.f64 n 2) k)) (pow.f64 (PI.f64) k)) |
(/.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (*.f64 2 n) k) (pow.f64 (PI.f64) k))) |
(/.f64 (/.f64 (PI.f64) (/.f64 (pow.f64 (PI.f64) k) (*.f64 2 n))) (pow.f64 (*.f64 2 n) k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 n k)) (pow.f64 (*.f64 2 (PI.f64)) k)) |
(/.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k))) |
(*.f64 (/.f64 2 (pow.f64 (*.f64 2 (PI.f64)) k)) (/.f64 (*.f64 n (PI.f64)) (pow.f64 n k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 1 k)) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k)) |
(*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) k)) |
(/.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) k) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) k))) |
(/.f64 (*.f64 2 (*.f64 n (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 2 k))) |
(*.f64 (/.f64 n (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 2 k))) (*.f64 2 (PI.f64))) |
(/.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) 2) k)) (pow.f64 (cbrt.f64 (*.f64 (*.f64 n 2) (PI.f64))) k)) |
(/.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) k) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) k))) |
(*.f64 (/.f64 2 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) k)) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) k))) |
(sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (*.f64 2 (-.f64 1 k)))) |
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 2 (-.f64 1 k)))) |
(log.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) |
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))))) |
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) |
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) 3)) |
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) |
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) |
(exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (*.f64 n 2) (PI.f64))))) |
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) |
(exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (*.f64 n 2) (PI.f64)))) 1)) |
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)))) |
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) |
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.2b | (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) |
| ✓ | 0.4b | (*.f64 (PI.f64) (/.f64 2 k)) |
| ✓ | 11.4b | (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
Compiled 29 to 18 computations (37.9% saved)
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | k | @ | -inf | (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) |
| 1.0ms | k | @ | -inf | (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
| 0.0ms | n | @ | inf | (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) |
| 0.0ms | n | @ | 0 | (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) |
| 0.0ms | k | @ | inf | (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) |
| 1× | batch-egg-rewrite |
| 1214× | associate-*r/ |
| 954× | associate-*l/ |
| 928× | unswap-sqr |
| 780× | swap-sqr |
| 478× | associate-/r* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 12 | 61 |
| 1 | 246 | 61 |
| 2 | 2985 | 61 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(*.f64 (PI.f64) (/.f64 2 k)) |
(*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) |
| Outputs |
|---|
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k))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 (PI.f64) (/.f64 2 k)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 2 k)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))))))) |
| 1× | egg-herbie |
| 1006× | distribute-rgt-in |
| 994× | distribute-lft-in |
| 956× | times-frac |
| 858× | associate-/l/ |
| 722× | associate-*l* |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 562 | 7253 |
| 1 | 1343 | 7141 |
| 2 | 5579 | 7141 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) 1) |
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 1) |
(*.f64 1 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1/4) (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1/4)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k)))) |
(*.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 2 k))) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) |
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 1/2)) |
(*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/2) (sqrt.f64 (/.f64 2 k))) |
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k)))) (sqrt.f64 (sqrt.f64 n))) (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k)))) (sqrt.f64 (sqrt.f64 n)))) |
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))))) |
(*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1/4))) (*.f64 (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1/4)))) |
(*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) (*.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))))) |
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1/4)) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1/4)) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))))) |
(*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) (*.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))))) |
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1/4)) (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1/4)) (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))))) |
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) 2))) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1) (sqrt.f64 (*.f64 k 1/2))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 -2)) (sqrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/2) 1) (sqrt.f64 (*.f64 k 1/2))) |
(/.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/2) (sqrt.f64 2)) (sqrt.f64 k)) |
(/.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/2) (sqrt.f64 -2)) (sqrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 n)) (sqrt.f64 k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1/2) |
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 1) |
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1/4) 2) |
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) 3) |
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2) 1/3) |
(fabs.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) |
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))))) |
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2)) |
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) |
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 1/2)) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) 1)) |
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 2 k)))) 1) |
(/.f64 (PI.f64) (*.f64 k 1/2)) |
(/.f64 2 (/.f64 k (PI.f64))) |
(/.f64 (*.f64 (PI.f64) (/.f64 2 k)) 1) |
(/.f64 1 (/.f64 k (*.f64 (PI.f64) 2))) |
(/.f64 (sqrt.f64 (PI.f64)) (/.f64 (*.f64 k 1/2) (sqrt.f64 (PI.f64)))) |
(/.f64 (sqrt.f64 (PI.f64)) (/.f64 k (*.f64 (sqrt.f64 (PI.f64)) 2))) |
(/.f64 (cbrt.f64 (PI.f64)) (/.f64 (*.f64 k 1/2) (pow.f64 (cbrt.f64 (PI.f64)) 2))) |
(/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (/.f64 (*.f64 k 1/2) (cbrt.f64 (PI.f64)))) |
(/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (/.f64 k (*.f64 (cbrt.f64 (PI.f64)) 2))) |
(/.f64 (*.f64 (PI.f64) 2) k) |
(/.f64 -2 (/.f64 (neg.f64 k) (PI.f64))) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 k (sqrt.f64 (*.f64 (PI.f64) 2)))) |
(/.f64 (*.f64 (cbrt.f64 (*.f64 (PI.f64) 2)) (cbrt.f64 (*.f64 (PI.f64) 2))) (/.f64 k (cbrt.f64 (*.f64 (PI.f64) 2)))) |
(/.f64 (*.f64 (PI.f64) (sqrt.f64 (/.f64 2 k))) (sqrt.f64 (*.f64 k 1/2))) |
(/.f64 (/.f64 (PI.f64) k) 1/2) |
(/.f64 (/.f64 (PI.f64) 1/2) k) |
(/.f64 (/.f64 (PI.f64) (/.f64 (sqrt.f64 k) 2)) (sqrt.f64 k)) |
(/.f64 (/.f64 (*.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k)) |
(/.f64 (/.f64 (PI.f64) 1) (*.f64 k 1/2)) |
(/.f64 (*.f64 (PI.f64) -2) (neg.f64 k)) |
(/.f64 (*.f64 (*.f64 (PI.f64) 2) 1) k) |
(/.f64 (*.f64 (*.f64 (PI.f64) 2) 1) (/.f64 k 1)) |
(/.f64 (*.f64 (PI.f64) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) |
(/.f64 (*.f64 (PI.f64) (/.f64 2 (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(/.f64 (*.f64 (PI.f64) -1) (*.f64 k -1/2)) |
(/.f64 (*.f64 1 (/.f64 (PI.f64) 1/2)) k) |
(/.f64 (*.f64 1 (/.f64 (PI.f64) (/.f64 (sqrt.f64 k) 2))) (sqrt.f64 k)) |
(/.f64 (*.f64 1 (/.f64 (*.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) (sqrt.f64 (*.f64 (PI.f64) 2))) (sqrt.f64 k)) |
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) 2) (cbrt.f64 (*.f64 (PI.f64) 2))) (cbrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (PI.f64) 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (PI.f64) 2) (/.f64 1 (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (PI.f64) 2) -1) (neg.f64 k)) |
(/.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 (/.f64 2 k))) 1) (sqrt.f64 (*.f64 k 1/2))) |
(/.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 (/.f64 2 k))) (sqrt.f64 2)) (sqrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 (/.f64 2 k))) (sqrt.f64 -2)) (sqrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 2 k)) 2)) 1) (cbrt.f64 (*.f64 k 1/2))) |
(/.f64 (*.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 2 k)) 2)) (cbrt.f64 2)) (cbrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 2 k)) 2)) (cbrt.f64 -2)) (cbrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 (/.f64 (PI.f64) 1) 2) k) |
(/.f64 (*.f64 (/.f64 (PI.f64) 1) 1) (*.f64 k 1/2)) |
(/.f64 (*.f64 (/.f64 (PI.f64) 1) -2) (neg.f64 k)) |
(/.f64 (*.f64 (/.f64 (PI.f64) 1) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) |
(/.f64 (*.f64 (/.f64 (PI.f64) 1) (/.f64 2 (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(/.f64 (*.f64 (/.f64 (PI.f64) 1) -1) (*.f64 k -1/2)) |
(/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) 2) (sqrt.f64 k)) |
(/.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 (cbrt.f64 k) 2)) 2) (cbrt.f64 k)) |
(/.f64 (*.f64 -1 (PI.f64)) (*.f64 k -1/2)) |
(/.f64 (*.f64 (/.f64 2 (sqrt.f64 k)) (PI.f64)) (sqrt.f64 k)) |
(/.f64 (*.f64 (/.f64 2 (pow.f64 (cbrt.f64 k) 2)) (PI.f64)) (cbrt.f64 k)) |
(/.f64 (*.f64 (/.f64 (PI.f64) 1/2) 1) k) |
(/.f64 (*.f64 (/.f64 (PI.f64) (/.f64 (sqrt.f64 k) 2)) 1) (sqrt.f64 k)) |
(/.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 k) 2)) 1) (cbrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (PI.f64) -2) 1) (neg.f64 k)) |
(/.f64 (*.f64 1 (*.f64 (PI.f64) (sqrt.f64 (/.f64 2 k)))) (sqrt.f64 (*.f64 k 1/2))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (PI.f64) (sqrt.f64 (/.f64 2 k)))) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 -2) (*.f64 (PI.f64) (sqrt.f64 (/.f64 2 k)))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k)))) (sqrt.f64 k)) |
(/.f64 (*.f64 (cbrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) 2)) (cbrt.f64 k)) |
(/.f64 (*.f64 (PI.f64) (/.f64 2 (cbrt.f64 k))) (pow.f64 (cbrt.f64 k) 2)) |
(/.f64 (/.f64 (*.f64 (PI.f64) 2) (cbrt.f64 k)) (pow.f64 (cbrt.f64 k) 2)) |
(/.f64 (/.f64 (PI.f64) (*.f64 (cbrt.f64 (*.f64 k 1/2)) (cbrt.f64 (*.f64 k 1/2)))) (cbrt.f64 (*.f64 k 1/2))) |
(/.f64 (/.f64 (/.f64 (PI.f64) 1/2) 1) k) |
(/.f64 (/.f64 (/.f64 (PI.f64) 1/2) (cbrt.f64 k)) (pow.f64 (cbrt.f64 k) 2)) |
(/.f64 (/.f64 (/.f64 (PI.f64) (/.f64 (sqrt.f64 k) 2)) 1) (sqrt.f64 k)) |
(/.f64 (/.f64 (/.f64 (PI.f64) (/.f64 (sqrt.f64 k) 2)) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (/.f64 (PI.f64) (/.f64 (sqrt.f64 k) 2)) (sqrt.f64 (pow.f64 (cbrt.f64 k) 2))) (sqrt.f64 (cbrt.f64 k))) |
(/.f64 (/.f64 (/.f64 (PI.f64) (/.f64 (sqrt.f64 k) 2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (/.f64 (*.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 k) 2)) 1) (cbrt.f64 k)) |
(/.f64 (/.f64 (/.f64 (*.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 k) 2)) (sqrt.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 k))) |
(/.f64 (/.f64 (/.f64 (*.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 (cbrt.f64 k))) |
(/.f64 (/.f64 (/.f64 (*.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (/.f64 (*.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 k) 2)) (*.f64 (cbrt.f64 (cbrt.f64 k)) (cbrt.f64 (cbrt.f64 k)))) (cbrt.f64 (cbrt.f64 k))) |
(/.f64 (/.f64 (*.f64 (PI.f64) -2) 1) (neg.f64 k)) |
(/.f64 (/.f64 (*.f64 (PI.f64) -2) (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (*.f64 (PI.f64) -2) (pow.f64 (cbrt.f64 k) 2)) (neg.f64 (cbrt.f64 k))) |
(/.f64 (/.f64 (*.f64 (PI.f64) -2) (sqrt.f64 (neg.f64 k))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (/.f64 (*.f64 (PI.f64) -2) (*.f64 (cbrt.f64 (neg.f64 k)) (cbrt.f64 (neg.f64 k)))) (cbrt.f64 (neg.f64 k))) |
(/.f64 (/.f64 (*.f64 (PI.f64) -2) -1) k) |
(/.f64 (/.f64 (*.f64 (PI.f64) -2) (neg.f64 (sqrt.f64 k))) (sqrt.f64 k)) |
(/.f64 (/.f64 (*.f64 (PI.f64) -2) (neg.f64 (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(pow.f64 (*.f64 (PI.f64) (/.f64 2 k)) 1) |
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) 2) |
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) 3) |
(pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 2 k)) 3) 1/3) |
(neg.f64 (/.f64 (*.f64 (PI.f64) 2) (neg.f64 k))) |
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 2 k)) 2)) |
(log.f64 (pow.f64 (exp.f64 (/.f64 2 k)) (PI.f64))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 2 k))))) |
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 2 k)) 3)) |
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 2 k) 3))) |
(cbrt.f64 (*.f64 (pow.f64 (/.f64 2 k) 3) (pow.f64 (PI.f64) 3))) |
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 2 k)))) |
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 2 k)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (/.f64 2 k))) 1)) |
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 2 k)))) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) 1) |
(/.f64 n (/.f64 k (*.f64 (PI.f64) 2))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(/.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1) |
(/.f64 1 (/.f64 (*.f64 k 1/2) (*.f64 n (PI.f64)))) |
(/.f64 (sqrt.f64 n) (/.f64 (*.f64 k 1/2) (*.f64 (sqrt.f64 n) (PI.f64)))) |
(/.f64 (pow.f64 (cbrt.f64 n) 2) (/.f64 (*.f64 k 1/2) (*.f64 (cbrt.f64 n) (PI.f64)))) |
(/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)) |
(/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) |
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 k 1/2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 k 1/2) (cbrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 n (sqrt.f64 (PI.f64))) (/.f64 (*.f64 k 1/2) (sqrt.f64 (PI.f64)))) |
(/.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) 2)) (/.f64 (*.f64 k 1/2) (cbrt.f64 (PI.f64)))) |
(/.f64 (*.f64 (*.f64 n (PI.f64)) 2) k) |
(/.f64 (*.f64 (*.f64 n (PI.f64)) 1) (*.f64 k 1/2)) |
(/.f64 (*.f64 (*.f64 n (PI.f64)) (sqrt.f64 (/.f64 2 k))) (sqrt.f64 (*.f64 k 1/2))) |
(/.f64 (*.f64 n (*.f64 (PI.f64) 2)) k) |
(/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (neg.f64 k)) |
(/.f64 (*.f64 (*.f64 (PI.f64) 2) n) k) |
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (/.f64 (*.f64 k 1/2) (*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))))) |
(/.f64 (*.f64 n (/.f64 (PI.f64) 1/2)) k) |
(/.f64 (*.f64 n (/.f64 (PI.f64) (/.f64 (sqrt.f64 k) 2))) (sqrt.f64 k)) |
(/.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(/.f64 (*.f64 n (*.f64 (PI.f64) -2)) (neg.f64 k)) |
(/.f64 (*.f64 1 (*.f64 (*.f64 n (PI.f64)) 2)) k) |
(/.f64 (*.f64 1 (*.f64 (*.f64 n (PI.f64)) 1)) (*.f64 k 1/2)) |
(/.f64 (*.f64 1 (*.f64 n (*.f64 (PI.f64) 2))) k) |
(/.f64 (*.f64 1 (*.f64 (*.f64 n (PI.f64)) -2)) (neg.f64 k)) |
(/.f64 (*.f64 1 (*.f64 (*.f64 (PI.f64) 2) n)) k) |
(/.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) |
(/.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 2 (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(/.f64 (*.f64 (*.f64 n (PI.f64)) -1) (*.f64 k -1/2)) |
(/.f64 (*.f64 (*.f64 n (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k)))) (sqrt.f64 (*.f64 (PI.f64) 2))) (sqrt.f64 k)) |
(/.f64 (*.f64 (*.f64 n (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) 2)) (cbrt.f64 (*.f64 (PI.f64) 2))) (cbrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) (sqrt.f64 n)) (sqrt.f64 (*.f64 (PI.f64) 2))) (sqrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 2) 1) k) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 2) 1) (/.f64 k 1)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 2) (/.f64 1 (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 2) -1) (neg.f64 k)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 1) 2) k) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 1) 1) (*.f64 k 1/2)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 1) -2) (neg.f64 k)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 1) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 1) (/.f64 2 (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) 1) -1) (*.f64 k -1/2)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) (sqrt.f64 (/.f64 2 k))) 1) (sqrt.f64 (*.f64 k 1/2))) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) (sqrt.f64 (/.f64 2 k))) (sqrt.f64 2)) (sqrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) (sqrt.f64 (/.f64 2 k))) (sqrt.f64 -2)) (sqrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (cbrt.f64 (/.f64 2 k)) 2)) 1) (cbrt.f64 (*.f64 k 1/2))) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (cbrt.f64 (/.f64 2 k)) 2)) (cbrt.f64 2)) (cbrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (cbrt.f64 (/.f64 2 k)) 2)) (cbrt.f64 -2)) (cbrt.f64 (neg.f64 k))) |
(/.f64 (*.f64 2 (*.f64 n (PI.f64))) k) |
(/.f64 (*.f64 -2 (*.f64 n (PI.f64))) (neg.f64 k)) |
(/.f64 (*.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 n (PI.f64))) (sqrt.f64 k)) |
(/.f64 (*.f64 (/.f64 2 (pow.f64 (cbrt.f64 k) 2)) (*.f64 n (PI.f64))) (cbrt.f64 k)) |
(/.f64 (*.f64 -1 (*.f64 n (PI.f64))) (*.f64 k -1/2)) |
(/.f64 (*.f64 (/.f64 (PI.f64) 1/2) n) k) |
(/.f64 (*.f64 (/.f64 (PI.f64) (/.f64 (sqrt.f64 k) 2)) n) (sqrt.f64 k)) |
(/.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 k) 2)) n) (cbrt.f64 k)) |
(/.f64 (*.f64 (*.f64 (PI.f64) -2) n) (neg.f64 k)) |
(/.f64 (*.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1) k) |
(/.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) -2) 1) (neg.f64 k)) |
(/.f64 (*.f64 (*.f64 (*.f64 (PI.f64) 2) n) 1) k) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) n)) (sqrt.f64 k)) |
(/.f64 (/.f64 (*.f64 n (PI.f64)) k) 1/2) |
(/.f64 (/.f64 (*.f64 n (PI.f64)) 1) (*.f64 k 1/2)) |
(/.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 (*.f64 k 1/2))) (sqrt.f64 (*.f64 k 1/2))) |
(/.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 (cbrt.f64 (*.f64 k 1/2)) (cbrt.f64 (*.f64 k 1/2)))) (cbrt.f64 (*.f64 k 1/2))) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) 2) 1) k) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) 2) (sqrt.f64 k)) (sqrt.f64 k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) 2) (cbrt.f64 k)) (pow.f64 (cbrt.f64 k) 2)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) 2) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) 1) k) 1/2) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) 1) 1) (*.f64 k 1/2)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) 1) (*.f64 (cbrt.f64 (*.f64 k 1/2)) (cbrt.f64 (*.f64 k 1/2)))) (cbrt.f64 (*.f64 k 1/2))) |
(/.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1) k) |
(/.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) 2)) (sqrt.f64 k)) (sqrt.f64 k)) |
(/.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) 2)) (cbrt.f64 k)) (pow.f64 (cbrt.f64 k) 2)) |
(/.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) 2)) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) 1) (neg.f64 k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (sqrt.f64 k)) (neg.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (pow.f64 (cbrt.f64 k) 2)) (neg.f64 (cbrt.f64 k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (sqrt.f64 (neg.f64 k))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (*.f64 (cbrt.f64 (neg.f64 k)) (cbrt.f64 (neg.f64 k)))) (cbrt.f64 (neg.f64 k))) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) -1) k) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (neg.f64 (sqrt.f64 k))) (sqrt.f64 k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (neg.f64 (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(/.f64 (/.f64 (*.f64 (*.f64 (PI.f64) 2) n) 1) k) |
(/.f64 (/.f64 (*.f64 (*.f64 (PI.f64) 2) n) (sqrt.f64 k)) (sqrt.f64 k)) |
(/.f64 (/.f64 (*.f64 (*.f64 (PI.f64) 2) n) (cbrt.f64 k)) (pow.f64 (cbrt.f64 k) 2)) |
(/.f64 (/.f64 (*.f64 (*.f64 (PI.f64) 2) n) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1) |
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 2) |
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 3) |
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 2) 1/2) |
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3) 1/3) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 2)) |
(log.f64 (exp.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) |
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3)) |
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 (PI.f64) (/.f64 2 k)) 3))) |
(cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 2 k)) 3) (pow.f64 n 3))) |
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(exp.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
| Outputs |
|---|
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (PI.f64) k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
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(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (pow.f64 (cbrt.f64 k) 2)) (neg.f64 (cbrt.f64 k))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (sqrt.f64 (neg.f64 k))) (sqrt.f64 (neg.f64 k))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (*.f64 (cbrt.f64 (neg.f64 k)) (cbrt.f64 (neg.f64 k)))) (cbrt.f64 (neg.f64 k))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) -1) k) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (neg.f64 (sqrt.f64 k))) (sqrt.f64 k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(/.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) -2) (neg.f64 (pow.f64 (cbrt.f64 k) 2))) (cbrt.f64 k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(/.f64 (/.f64 (*.f64 (*.f64 (PI.f64) 2) n) 1) k) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(/.f64 (/.f64 (*.f64 (*.f64 (PI.f64) 2) n) (sqrt.f64 k)) (sqrt.f64 k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(/.f64 (/.f64 (*.f64 (*.f64 (PI.f64) 2) n) (cbrt.f64 k)) (pow.f64 (cbrt.f64 k) 2)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(/.f64 (/.f64 (*.f64 (*.f64 (PI.f64) 2) n) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 1) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 2) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 3) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 2) 1/2) |
(sqrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) 2)) |
(fabs.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3) 1/3) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 2)) |
(sqrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) 2)) |
(fabs.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
(log.f64 (exp.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3)) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 (PI.f64) (/.f64 2 k)) 3))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 2 k)) 3) (pow.f64 n 3))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(exp.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))))) |
(/.f64 (PI.f64) (/.f64 (*.f64 k 1/2) n)) |
(*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (pow.f64 k -1/2) | |
| 0.2b | (*.f64 n (PI.f64)) | |
| ✓ | 0.3b | (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
| 0.4b | (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
Compiled 34 to 19 computations (44.1% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | k | @ | -inf | (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
| 0.0ms | n | @ | 0 | (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
| 0.0ms | k | @ | 0 | (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
| 0.0ms | n | @ | inf | (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
| 0.0ms | k | @ | inf | (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
| 1× | batch-egg-rewrite |
| 1162× | sqrt-prod |
| 1054× | unswap-sqr |
| 842× | swap-sqr |
| 510× | sqr-pow |
| 476× | pow-sqr |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 14 | 31 |
| 1 | 283 | 31 |
| 2 | 3267 | 31 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) 1) (+.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) 1) (+.f64 (*.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 1 (*.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 2 (*.f64 n (PI.f64))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) |
| 1× | egg-herbie |
| 1372× | associate-*r* |
| 1240× | associate-/l* |
| 1216× | associate-*l* |
| 762× | associate-/r* |
| 632× | associate-+r+ |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 65 | 744 |
| 1 | 166 | 710 |
| 2 | 559 | 692 |
| 3 | 4301 | 692 |
| 1× | node limit |
| Inputs |
|---|
(+.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) -1) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1) |
(/.f64 (-.f64 (*.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) 1) (+.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1)) |
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) 1) (+.f64 (*.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 1 (*.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1)))) |
(pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1) |
(pow.f64 (*.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) 2) |
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 3) |
(pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3) 1/3) |
(sqrt.f64 (*.f64 (*.f64 2 (*.f64 n (PI.f64))) (pow.f64 k -1))) |
(fabs.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3)) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))) |
(cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 k -1/2) 3))) |
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
| Outputs |
|---|
(+.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) -1) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(/.f64 (-.f64 (*.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) 1) (+.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1)) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) 1) (+.f64 (*.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 1 (*.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1)))) |
(/.f64 (+.f64 (pow.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) -1) (fma.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (+.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1))) |
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)) (+.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (+.f64 1 (exp.f64 (*.f64 2 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) |
(/.f64 (expm1.f64 (*.f64 3 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (+.f64 1 (pow.f64 (exp.f64 2) (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) |
(pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(pow.f64 (*.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) 2) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/2)) |
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 3) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3) 1/3) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(sqrt.f64 (*.f64 (*.f64 2 (*.f64 n (PI.f64))) (pow.f64 k -1))) |
(sqrt.f64 (*.f64 2 (*.f64 (*.f64 n (PI.f64)) (/.f64 1 k)))) |
(sqrt.f64 (*.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 1 k))) |
(sqrt.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))) |
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64))))) |
(fabs.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3)) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))) |
(cbrt.f64 (*.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))) |
(cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 k -1/2) 3))) |
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))) |
(cbrt.f64 (*.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))) |
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(exp.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.1b | (sqrt.f64 (*.f64 n (PI.f64))) |
| 0.2b | (*.f64 n (PI.f64)) | |
| ✓ | 0.3b | (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
| ✓ | 0.5b | (/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
Compiled 32 to 16 computations (50% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | k | @ | -inf | (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
| 1.0ms | n | @ | -inf | (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
| 0.0ms | k | @ | -inf | (/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
| 0.0ms | n | @ | -inf | (sqrt.f64 (*.f64 n (PI.f64))) |
| 0.0ms | k | @ | 0 | (/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
| 1× | batch-egg-rewrite |
| 1046× | associate-*r/ |
| 984× | associate-/r* |
| 858× | swap-sqr |
| 842× | associate-*l/ |
| 718× | associate-/l* |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 14 | 53 |
| 1 | 281 | 49 |
| 2 | 3400 | 49 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) (cbrt.f64 (/.f64 2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 k)) (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 2)) (/.f64 -1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 2) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 2) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (sqrt.f64 k)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (sqrt.f64 k) (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (sqrt.f64 2) (/.f64 -1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 1 (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 2 k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 2 1/4) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 2 1/4) (/.f64 (sqrt.f64 k) (*.f64 (pow.f64 2 1/4) (sqrt.f64 (*.f64 n (PI.f64))))))))) 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(2) ((x /.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4)) (/.f64 (sqrt.f64 k) (*.f64 (pow.f64 2 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k 1/4)) (/.f64 (pow.f64 k 1/4) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 1 1/2) (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2) 1/2) (/.f64 (sqrt.f64 (/.f64 k 2)) (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 2 1/4)) (/.f64 (sqrt.f64 k) (pow.f64 2 1/4)))))) 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (cbrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (PI.f64)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64))))))))) |
| 1× | egg-herbie |
| 1252× | associate-/l* |
| 1156× | distribute-rgt-in |
| 1154× | distribute-lft-in |
| 558× | times-frac |
| 496× | associate-*l* |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 451 | 6768 |
| 1 | 1021 | 6428 |
| 2 | 5465 | 6428 |
| 1× | node limit |
| Inputs |
|---|
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) 1) |
(*.f64 (sqrt.f64 2) (pow.f64 k -1/2)) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 1) |
(*.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) (pow.f64 k -1/2))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) (cbrt.f64 (/.f64 2 k))) |
(*.f64 (cbrt.f64 (/.f64 2 k)) (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 k -1/2))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 2)) |
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 -1 (sqrt.f64 k))) |
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 2) (pow.f64 k 1/4))) |
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 2) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))) |
(*.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 2 1/4) (sqrt.f64 k)) (pow.f64 2 1/4)) |
(*.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 k 1/4))) |
(*.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
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(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 2) |
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 3) |
(pow.f64 (pow.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 3) 1/3) |
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(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 k))))) |
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(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 2 k))) |
(log.f64 (exp.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 3)) |
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 3) (pow.f64 (*.f64 n (PI.f64)) 3/2))) |
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) (pow.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 3))) |
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(exp.f64 (log.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 1)) |
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64))))) 1) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1) |
(*.f64 1 (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) |
(*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4)) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (cbrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 1/2)) |
(pow.f64 (*.f64 n (PI.f64)) 1/2) |
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1) |
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 2) |
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 3) |
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) 1/3) |
(fabs.f64 (sqrt.f64 (*.f64 n (PI.f64)))) |
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2)) |
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1/2)) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 1)) |
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
| Outputs |
|---|
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) 1) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 2) (pow.f64 k -1/2)) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 1) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(*.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) (pow.f64 k -1/2))) |
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 k -1/2) (pow.f64 2 1/4))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 2 1/2)) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) (cbrt.f64 (/.f64 2 k))) |
(*.f64 (cbrt.f64 (/.f64 2 k)) (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) (cbrt.f64 (/.f64 2 k))) |
(*.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 k -1/2))) |
(*.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))) (pow.f64 k -1/2)) |
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 k -1/2) (cbrt.f64 2))) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 k -1/2)) |
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 -1 (sqrt.f64 k))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 2) (pow.f64 k 1/4))) |
(/.f64 1 (/.f64 (pow.f64 k 1/2) (sqrt.f64 2))) |
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 2) (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (*.f64 (/.f64 1 (cbrt.f64 k)) (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k)) |
(*.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(*.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (sqrt.f64 k))) |
(*.f64 (pow.f64 2 1/4) (/.f64 (pow.f64 2 1/4) (sqrt.f64 k))) |
(/.f64 (pow.f64 2 1/2) (sqrt.f64 k)) |
(*.f64 (/.f64 (pow.f64 2 1/4) (sqrt.f64 k)) (pow.f64 2 1/4)) |
(*.f64 (pow.f64 2 1/4) (/.f64 (pow.f64 2 1/4) (sqrt.f64 k))) |
(/.f64 (pow.f64 2 1/2) (sqrt.f64 k)) |
(*.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (sqrt.f64 k)))) |
(/.f64 (*.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 k)) (pow.f64 2 1/4)) (cbrt.f64 (sqrt.f64 k))) |
(/.f64 (/.f64 (pow.f64 2 1/2) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 k 1/4))) |
(/.f64 (*.f64 (/.f64 (cbrt.f64 2) (pow.f64 k 1/4)) (cbrt.f64 (sqrt.f64 2))) (pow.f64 k 1/4)) |
(*.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) (/.f64 (cbrt.f64 2) (cbrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 2) (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 2))) |
(*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 k))) |
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 k) (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2))) |
(*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (sqrt.f64 k))) |
(*.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 k))) |
(pow.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 1) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) 2) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) 3) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(pow.f64 (/.f64 2 k) 1/2) |
(sqrt.f64 (/.f64 2 k)) |
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 3) 1/3) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(pow.f64 (sqrt.f64 (/.f64 k 2)) -1) |
(/.f64 1 (sqrt.f64 (/.f64 k 2))) |
(neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(neg.f64 (*.f64 (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 k))) 1)) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(neg.f64 (*.f64 (sqrt.f64 2) (/.f64 -1 (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(neg.f64 (*.f64 1 (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 k))))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 2 k)) |
(log.f64 (exp.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 3)) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(exp.f64 (log.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))) 1)) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
(/.f64 (sqrt.f64 2) (sqrt.f64 k)) |
(-.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) 1) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2))) |
(/.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 1) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2))) |
(/.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 n))) |
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k 2))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k 2)))) |
(/.f64 (pow.f64 2 1/4) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 2 1/4))) |
(*.f64 (/.f64 (pow.f64 2 1/4) (sqrt.f64 k)) (*.f64 (pow.f64 2 1/4) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 (pow.f64 2 1/2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(/.f64 (pow.f64 2 1/4) (/.f64 (sqrt.f64 k) (*.f64 (pow.f64 2 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 (pow.f64 2 1/4) (sqrt.f64 k)) (*.f64 (pow.f64 2 1/4) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 (pow.f64 2 1/2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 (PI.f64)))) |
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k 2))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k 2)))) |
(/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (/.f64 (sqrt.f64 (/.f64 k 2)) (pow.f64 (*.f64 n (PI.f64)) 1/4))) |
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2))) |
(/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))) (cbrt.f64 2))) |
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64))))) (cbrt.f64 2)) |
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 k)) (*.f64 (cbrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (cbrt.f64 2) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 2)))) |
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64))))) (cbrt.f64 2)) |
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 k)) (*.f64 (cbrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (cbrt.f64 2) (/.f64 (sqrt.f64 k) (*.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64))))) (cbrt.f64 2)) |
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 k)) (*.f64 (cbrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (/.f64 k 2)) (cbrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 k 2))) (cbrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 k 2)))) |
(/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 (/.f64 k 2)) (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 k 2))) (cbrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 k 2)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (sqrt.f64 k)) |
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(/.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2)) (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 (cbrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (/.f64 k 2))) (sqrt.f64 (cbrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 n (PI.f64)))) (/.f64 (fabs.f64 (cbrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 k 2)))) |
(/.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 k))) |
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(/.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 n)) (/.f64 (sqrt.f64 k) (sqrt.f64 (PI.f64)))) |
(/.f64 (sqrt.f64 2) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (PI.f64))) (sqrt.f64 n))) |
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 n (PI.f64)) 1/4)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (PI.f64)) 1/4))) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 2) (cbrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 (*.f64 (sqrt.f64 2) (cbrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 (/.f64 k 2)))) |
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 (sqrt.f64 (/.f64 k 2))) (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k))))) |
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 (/.f64 k 2)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)))) |
(/.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 k) (pow.f64 2 1/4))) |
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(cbrt.f64 (*.f64 (pow.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) 3) (pow.f64 (*.f64 n (PI.f64)) 3/2))) |
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(exp.f64 (log.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 1)) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))) |
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64))))) 1) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(*.f64 1 (sqrt.f64 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) |
(*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4)) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (cbrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (cbrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (fabs.f64 (cbrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 1/2)) |
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (fabs.f64 (cbrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 (*.f64 n (PI.f64))))) |
(pow.f64 (*.f64 n (PI.f64)) 1/2) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 2) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 3) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) 1/3) |
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2)) |
(fabs.f64 (sqrt.f64 (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2)) |
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1/2)) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 1)) |
(sqrt.f64 (*.f64 n (PI.f64))) |
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64))))) |
(sqrt.f64 (*.f64 n (PI.f64))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.2b | (*.f64 n (PI.f64)) | |
| ✓ | 0.3b | (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) |
| ✓ | 0.3b | (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) |
| ✓ | 0.5b | (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) |
Compiled 45 to 26 computations (42.2% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | k | @ | -inf | (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) |
| 1.0ms | n | @ | 0 | (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) |
| 1.0ms | n | @ | inf | (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) |
| 1.0ms | n | @ | -inf | (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) |
| 0.0ms | n | @ | 0 | (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) |
| 1× | batch-egg-rewrite |
| 936× | associate-/r* |
| 922× | swap-sqr |
| 878× | associate-/l* |
| 540× | associate-*r/ |
| 426× | associate-*l/ |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 15 | 73 |
| 1 | 316 | 65 |
| 2 | 3819 | 65 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) |
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) |
(/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (neg.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8) (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (neg.f64 (neg.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 n)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 2))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) (neg.f64 (sqrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))) (neg.f64 (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4)) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 2 1/4)) (pow.f64 (*.f64 n (PI.f64)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 2)) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 n) 1/2) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 2 1/4) 2) (pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))) (sqrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (*.f64 (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))))) (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n 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| 1× | egg-herbie |
| 1774× | unswap-sqr |
| 1356× | associate-/r* |
| 628× | distribute-lft-neg-out |
| 546× | distribute-rgt-neg-out |
| 514× | associate-/l/ |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 284 | 5265 |
| 1 | 639 | 4203 |
| 2 | 2703 | 4179 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2) |
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) |
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) 1) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (neg.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) 1) |
(*.f64 1 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8) (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) |
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (neg.f64 (neg.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))))) |
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(*.f64 (sqrt.f64 (*.f64 2 n)) (sqrt.f64 (PI.f64))) |
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 2))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) (neg.f64 (sqrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))))) |
(*.f64 (*.f64 (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))) (neg.f64 (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))))) |
(*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4)) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4))) |
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8)) |
(*.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4))) |
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 2 1/4)) (pow.f64 (*.f64 n (PI.f64)) 1/4)) |
(*.f64 -1 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(*.f64 (neg.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))) |
(*.f64 (pow.f64 1 1/2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 2)) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/2)) |
(*.f64 (pow.f64 (*.f64 2 n) 1/2) (sqrt.f64 (PI.f64))) |
(*.f64 (pow.f64 (pow.f64 2 1/4) 2) (pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 2)) |
(*.f64 (neg.f64 (sqrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))) (sqrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))) |
(*.f64 (neg.f64 (*.f64 (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))))) (cbrt.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))) |
(*.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(*.f64 (neg.f64 (neg.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(*.f64 (*.f64 (pow.f64 1 1/4) (pow.f64 1 1/4)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) |
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 2)) 1/4) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 2)) 1/4)) (*.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/4) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/4))) |
(*.f64 (*.f64 (pow.f64 (*.f64 2 n) 1/4) (pow.f64 (*.f64 2 n) 1/4)) (*.f64 (pow.f64 (PI.f64) 1/4) (pow.f64 (PI.f64) 1/4))) |
(neg.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) |
(fabs.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) |
(log.f64 (exp.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))) |
(cbrt.f64 (pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) 3)) |
(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(exp.f64 (log.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) 1)) |
(log1p.f64 (expm1.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) 1) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 1) |
(*.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8)) |
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(*.f64 (pow.f64 2 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4)) |
(*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 2 1/4)) |
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (pow.f64 1 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/4) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/4)) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 2)) 1/4) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/4)) |
(*.f64 (pow.f64 (*.f64 2 n) 1/4) (pow.f64 (PI.f64) 1/4)) |
(*.f64 (*.f64 (pow.f64 1 1/8) (pow.f64 1 1/8)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 2)) 1/8) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 2)) 1/8)) (*.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/8) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/8))) |
(*.f64 (*.f64 (pow.f64 (*.f64 2 n) 1/8) (pow.f64 (*.f64 2 n) 1/8)) (*.f64 (pow.f64 (PI.f64) 1/8) (pow.f64 (PI.f64) 1/8))) |
(sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(fabs.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(log.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)))) |
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/4)) |
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(exp.f64 (*.f64 1/4 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) |
(exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)) |
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) 1) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (sqrt.f64 k))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (pow.f64 k -1/2)) |
(*.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) 1) |
(*.f64 1 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k))) (cbrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) |
(*.f64 (cbrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) (pow.f64 k -1/2))) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) |
(*.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) (/.f64 -1 (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) |
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (pow.f64 k 1/4))) |
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 -1 (sqrt.f64 k)) (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 1) (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (sqrt.f64 k))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 (sqrt.f64 k)))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) (sqrt.f64 k))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) (pow.f64 k 1/4))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 k) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) 1) |
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k))) 2) |
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k))) 3) |
(pow.f64 (pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) 3) 1/3) |
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) -1) |
(neg.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (neg.f64 (sqrt.f64 k)))) |
(neg.f64 (/.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) (sqrt.f64 k))) |
(neg.f64 (*.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (neg.f64 (sqrt.f64 k))) 1)) |
(neg.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (/.f64 -1 (sqrt.f64 k)))) |
(neg.f64 (*.f64 1 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (neg.f64 (sqrt.f64 k))))) |
(sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) |
(log.f64 (exp.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k))))) |
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) 3)) |
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
(exp.f64 (log.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k))) 1)) |
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
| Outputs |
|---|
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) 2) |
(exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) 1/2)) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) 2) |
(exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) 1/2)) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) 2) |
(exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) 1/2)) |
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 2) |
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) 2) |
(exp.f64 (*.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))) 1/2)) |
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) |
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) |
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(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
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(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 2)) |
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(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
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(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 2)) |
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2)) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4)))) |
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4)))) |
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 2 1/4)) (pow.f64 (*.f64 n (PI.f64)) 1/4)) |
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(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (*.f64 (pow.f64 2 1/4) (pow.f64 (*.f64 (PI.f64) n) 1/4))) |
(*.f64 -1 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2))) |
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
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(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 2) |
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(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k))) 3) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(pow.f64 (pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) 3) 1/3) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) -1) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(neg.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (neg.f64 (sqrt.f64 k)))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(neg.f64 (/.f64 (neg.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)) (sqrt.f64 k))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(neg.f64 (*.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (neg.f64 (sqrt.f64 k))) 1)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(neg.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (/.f64 -1 (sqrt.f64 k)))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(neg.f64 (*.f64 1 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (neg.f64 (sqrt.f64 k))))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) |
(sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) |
(log.f64 (exp.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k))))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) 3)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(exp.f64 (log.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k))) 1)) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)))) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
Compiled 20559 to 12573 computations (38.8% saved)
30 alts after pruning (22 fresh and 8 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1175 | 19 | 1194 |
| Fresh | 11 | 3 | 14 |
| Picked | 1 | 0 | 1 |
| Done | 2 | 8 | 10 |
| Total | 1189 | 30 | 1219 |
| Status | Error | Program |
|---|---|---|
| 41.5b | (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2) 1/3) | |
| ✓ | 0.3b | (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
| ✓ | 3.9b | (/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) |
| ✓ | 0.3b | (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
| 0.4b | (/.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) (sqrt.f64 k)) | |
| 0.4b | (/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (neg.f64 k)))) (sqrt.f64 k)) | |
| 22.0b | (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k 1/2))) | |
| ✓ | 21.9b | (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
| ✓ | 3.3b | (/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) |
| 22.0b | (/.f64 1 (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64))))) | |
| 32.8b | (/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) | |
| 11.2b | (/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) | |
| 17.0b | (*.f64 (pow.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) 1/3) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) | |
| ✓ | 21.9b | (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
| ✓ | 0.8b | (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
| 21.9b | (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) | |
| 22.0b | (*.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64)))) | |
| 22.0b | (*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 n (PI.f64)))) | |
| 22.0b | (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) (sqrt.f64 n)) | |
| 22.0b | (*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) | |
| 12.1b | (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) k)) | |
| 33.8b | (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) | |
| 14.5b | (sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) | |
| 33.8b | (sqrt.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) | |
| 33.8b | (sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) | |
| 33.8b | (sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) | |
| ✓ | 33.8b | (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
| 33.8b | (sqrt.f64 (fabs.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)))) | |
| 35.7b | (exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 1/2)) | |
| 40.1b | (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2)) |
Compiled 414 to 337 computations (18.6% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)))) |
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k 1/2))) |
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2)) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 1/2)) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2) 1/3) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) k)) |
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k -1/2)) |
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (+.f64 -1/2 (/.f64 k 2)))) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (/.f64 (-.f64 1 k) 2))) k)) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (/.f64 1 k))) |
(/.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))) |
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 n)) (sqrt.f64 (PI.f64))) (sqrt.f64 k)) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 k -1/2))) |
(*.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k)) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (sqrt.f64 n)) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 k)) |
(*.f64 (pow.f64 (pow.f64 k 1/4) -2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 2 (-.f64 1/2 (/.f64 k 2))))) (sqrt.f64 k)) |
(pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 -1 k) -4)) (pow.f64 k 1/4)) 2) |
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (*.f64 (pow.f64 k 1/4) (pow.f64 k 1/4))) |
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))) |
(*.f64 (pow.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) k) 1/3) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k)) |
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) |
(/.f64 (pow.f64 (exp.f64 (-.f64 1/2 (/.f64 k 2))) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k)) |
(*.f64 (pow.f64 k -1/2) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k)) |
(/.f64 (exp.f64 (*.f64 (-.f64 1/2 (/.f64 k 2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) k))) (sqrt.f64 k)) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 n 2) (PI.f64)) (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (neg.f64 k)))) (sqrt.f64 k)) |
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 3) 1/3) |
(/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k 1/2))) |
| Outputs |
|---|
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
4 calls:
| 27.0ms | (*.f64 (*.f64 2 (PI.f64)) n) |
| 26.0ms | k |
| 25.0ms | n |
| 14.0ms | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| Error | Segments | Branch |
|---|---|---|
| 0.3b | 1 | k |
| 0.3b | 1 | n |
| 0.3b | 1 | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 0.3b | 1 | (*.f64 (*.f64 2 (PI.f64)) n) |
Compiled 811 to 533 computations (34.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)))) |
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k 1/2))) |
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2)) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 1/2)) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2) 1/3) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 n 2) (PI.f64)) (-.f64 1 k)) k)) |
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))) |
| Outputs |
|---|
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k)) |
2 calls:
| 40.0ms | n |
| 22.0ms | k |
| Error | Segments | Branch |
|---|---|---|
| 0.2b | 2 | k |
| 8.8b | 4 | n |
Compiled 230 to 145 computations (37% saved)
| 1× | binary-search |
| Time | Left | Right |
|---|---|---|
| 16.0ms | 6.699067909767029e-57 | 6.369330002346791e-56 |
| 14.0ms | 96× | body | 256 | valid |
| 0.0ms | 1× | body | 256 | invalid |
Compiled 185 to 151 computations (18.4% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)))) |
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k 1/2))) |
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2)) |
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) 1/2)) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) |
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2) 1/3) |
| Outputs |
|---|
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2)) |
2 calls:
| 19.0ms | k |
| 10.0ms | n |
| Error | Segments | Branch |
|---|---|---|
| 20.5b | 2 | k |
| 21.9b | 1 | n |
Compiled 192 to 120 computations (37.5% saved)
| 1× | binary-search |
| Time | Left | Right |
|---|---|---|
| 16.0ms | 5.4363859740399647e+39 | 8.57814609164564e+39 |
| 10.0ms | 64× | body | 256 | valid |
| 5.0ms | 32× | body | 256 | infinite |
| 0.0ms | 2× | body | 256 | invalid |
Compiled 123 to 103 computations (16.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)))) |
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k 1/2))) |
| Outputs |
|---|
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
2 calls:
| 9.0ms | k |
| 8.0ms | n |
| Error | Segments | Branch |
|---|---|---|
| 21.9b | 1 | k |
| 21.9b | 1 | n |
Compiled 128 to 79 computations (38.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)))) |
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
2 calls:
| 9.0ms | k |
| 7.0ms | n |
| Error | Segments | Branch |
|---|---|---|
| 22.0b | 1 | k |
| 22.0b | 1 | n |
Compiled 110 to 69 computations (37.3% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)))) |
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))) (sqrt.f64 n)) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) |
2 calls:
| 7.0ms | n |
| 6.0ms | k |
| Error | Segments | Branch |
|---|---|---|
| 22.0b | 1 | k |
| 22.0b | 1 | n |
Compiled 101 to 64 computations (36.6% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k)))) |
| Outputs |
|---|
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
2 calls:
| 6.0ms | n |
| 5.0ms | k |
| Error | Segments | Branch |
|---|---|---|
| 32.8b | 1 | k |
| 32.8b | 1 | n |
Compiled 83 to 53 computations (36.1% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
| Outputs |
|---|
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
2 calls:
| 5.0ms | n |
| 5.0ms | k |
| Error | Segments | Branch |
|---|---|---|
| 33.8b | 1 | k |
| 33.8b | 1 | n |
Compiled 64 to 42 computations (34.4% saved)
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 n (PI.f64)))) |
(sqrt.f64 (*.f64 (/.f64 2 k) (*.f64 (PI.f64) n))) |
(sqrt.f64 (*.f64 (/.f64 (PI.f64) 1/2) (/.f64 n k))) |
| Outputs |
|---|
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
2 calls:
| 5.0ms | n |
| 4.0ms | k |
| Error | Segments | Branch |
|---|---|---|
| 33.8b | 1 | k |
| 33.8b | 1 | n |
Compiled 56 to 37 computations (33.9% saved)
Total -0.0b remaining (-0.1%)
Threshold costs -0.0b (-0.1%)
| Inputs |
|---|
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
| Outputs |
|---|
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
2 calls:
| 4.0ms | n |
| 3.0ms | k |
| Error | Segments | Branch |
|---|---|---|
| 33.8b | 1 | k |
| 33.8b | 1 | n |
Compiled 24 to 17 computations (29.2% saved)
| 1× | egg-herbie |
| 28× | *-commutative |
| 8× | sub-neg |
| 8× | +-commutative |
| 4× | neg-mul-1 |
| 4× | neg-sub0 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 63 | 405 |
| 1 | 81 | 405 |
| 2 | 89 | 405 |
| 3 | 93 | 405 |
| 4 | 95 | 405 |
| 1× | fuel |
| 1× | saturated |
| Inputs |
|---|
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(if (<=.f64 k 6625676492918941/110427941548649020598956093796432407239217743554726184882600387580788736) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k))) |
(if (<=.f64 k 8499999999999999714201505336369988239360) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
| Outputs |
|---|
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) |
(if (<=.f64 k 6625676492918941/110427941548649020598956093796432407239217743554726184882600387580788736) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k))) |
(if (<=.f64 k 6625676492918941/110427941548649020598956093796432407239217743554726184882600387580788736) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k))) |
(if (<=.f64 k 8499999999999999714201505336369988239360) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2))) |
(if (<=.f64 k 8499999999999999714201505336369988239360) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k))) 3/2))) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) |
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) |
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 (PI.f64) n))) |
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 n (PI.f64))))) |
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k 2) (*.f64 (PI.f64) n)))) |
(sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) |
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))) |
(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64))))) |
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 2 k)))) |
Compiled 153 to 121 computations (20.9% saved)
| 4× | egg-herbie |
| 1792× | distribute-lft-in |
| 1364× | associate-*r/ |
| 1078× | associate-*l/ |
| 1058× | associate-*r/ |
| 1052× | associate-/r* |
Useful iterations: 5 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 49 |
| 1 | 35 | 43 |
| 2 | 69 | 43 |
| 3 | 151 | 43 |
| 4 | 399 | 43 |
| 5 | 948 | 39 |
| 6 | 1876 | 39 |
| 7 | 4291 | 39 |
| 8 | 7087 | 39 |
| 0 | 302 | 6630 |
| 1 | 714 | 6086 |
| 2 | 2860 | 6080 |
| 0 | 540 | 12603 |
| 1 | 1301 | 12271 |
| 2 | 5889 | 12217 |
| 0 | 172 | 2417 |
| 1 | 403 | 2409 |
| 2 | 1424 | 2197 |
| 3 | 5505 | 1951 |
| 1× | node limit |
| 1× | node limit |
| 1× | node limit |
| 1× | node limit |
Compiled 658 to 507 computations (22.9% saved)
Compiled 133 to 84 computations (36.8% saved)
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