Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2
Time bar (total: 2.4s)
| 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% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 3 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 4 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 5 |
| 66.7% | 49.9% | 25% | 0.1% | 0% | 25% | 0% | 6 |
| 66.7% | 49.9% | 25% | 0.1% | 0% | 25% | 0% | 7 |
| 66.7% | 49.9% | 25% | 0.1% | 0% | 25% | 0% | 8 |
| 80% | 49.9% | 12.5% | 0.1% | 0% | 37.4% | 0% | 9 |
| 80% | 49.9% | 12.5% | 0.1% | 0% | 37.4% | 0% | 10 |
| 80% | 49.9% | 12.5% | 0.1% | 0% | 37.4% | 0% | 11 |
| 88.9% | 49.9% | 6.2% | 0.1% | 0% | 43.7% | 0% | 12 |
Compiled 13 to 9 computations (30.8% saved)
| 762.0ms | 4827× | body | 256 | infinite |
| 514.0ms | 3429× | body | 256 | valid |
| 87.0ms | 1049× | body | 256 | invalid |
| 2× | egg-herbie |
| 1636× | unswap-sqr |
| 1152× | times-frac |
| 1026× | fma-def |
| 896× | associate-*r* |
| 706× | associate-/r/ |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 108 |
| 1 | 57 | 92 |
| 2 | 136 | 92 |
| 3 | 302 | 92 |
| 4 | 543 | 92 |
| 5 | 1235 | 92 |
| 6 | 5025 | 92 |
| 0 | 3 | 3 |
| 1× | saturated |
| 1× | node limit |
| Inputs |
|---|
0 |
1 |
2 |
| Outputs |
|---|
0 |
1 |
2 |
| Inputs |
|---|
(exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
(exp.f64 (-.f64 (+.f64 y (*.f64 x (log.f64 x))) z)) |
(exp.f64 (-.f64 (+.f64 z (*.f64 y (log.f64 y))) x)) |
(exp.f64 (-.f64 (+.f64 x (*.f64 z (log.f64 z))) y)) |
| Outputs |
|---|
(exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
(exp.f64 (+.f64 x (-.f64 (*.f64 y (log.f64 y)) z))) |
(exp.f64 (-.f64 (fma.f64 y (log.f64 y) x) z)) |
(*.f64 (pow.f64 y y) (exp.f64 (-.f64 x z))) |
(exp.f64 (-.f64 (+.f64 y (*.f64 x (log.f64 x))) z)) |
(exp.f64 (+.f64 y (-.f64 (*.f64 x (log.f64 x)) z))) |
(exp.f64 (-.f64 (fma.f64 x (log.f64 x) y) z)) |
(*.f64 (pow.f64 x x) (exp.f64 (-.f64 y z))) |
(exp.f64 (-.f64 (+.f64 z (*.f64 y (log.f64 y))) x)) |
(exp.f64 (+.f64 z (-.f64 (*.f64 y (log.f64 y)) x))) |
(exp.f64 (-.f64 (fma.f64 y (log.f64 y) z) x)) |
(*.f64 (pow.f64 y y) (exp.f64 (-.f64 z x))) |
(exp.f64 (-.f64 (+.f64 x (*.f64 z (log.f64 z))) y)) |
(exp.f64 (+.f64 x (-.f64 (*.f64 z (log.f64 z)) y))) |
(exp.f64 (-.f64 (fma.f64 z (log.f64 z) x) y)) |
(*.f64 (pow.f64 z z) (exp.f64 (-.f64 x y))) |
Compiled 15 to 11 computations (26.7% saved)
| 1× | egg-herbie |
| 1234× | fma-def |
| 1016× | unswap-sqr |
| 784× | associate-*r/ |
| 778× | associate-/l/ |
| 654× | associate-/r/ |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 27 |
| 1 | 20 | 23 |
| 2 | 44 | 23 |
| 3 | 92 | 23 |
| 4 | 160 | 23 |
| 5 | 315 | 23 |
| 6 | 973 | 23 |
| 7 | 2567 | 23 |
| 8 | 5244 | 23 |
| 9 | 5941 | 23 |
| 10 | 7376 | 23 |
| 1× | node limit |
| Inputs |
|---|
(exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
| Outputs |
|---|
(exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
(exp.f64 (+.f64 x (-.f64 (*.f64 y (log.f64 y)) z))) |
(exp.f64 (-.f64 (fma.f64 y (log.f64 y) x) z)) |
(*.f64 (pow.f64 y y) (exp.f64 (-.f64 x z))) |
Compiled 37 to 18 computations (51.4% saved)
3 alts after pruning (3 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2 | 2 | 4 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 0 | 0 |
| Total | 2 | 3 | 5 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 78.1% | (*.f64 (pow.f64 y y) (exp.f64 (-.f64 x z))) |
| ▶ | 100.0% | (exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
| ▶ | 78.1% | (*.f64 (pow.f64 y y) (exp.f64 (-.f64 x z))) |
| ▶ | 100.0% | (exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
Compiled 46 to 30 computations (34.8% saved)
Found 1 expressions with local accuracy:
| New | Accuracy | Program |
|---|---|---|
| ✓ | 99.7% | (*.f64 y (log.f64 y)) |
Compiled 57 to 13 computations (77.2% saved)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 57.0ms | y | @ | inf | (*.f64 y (log.f64 y)) |
| 32.0ms | y | @ | 0 | (*.f64 y (log.f64 y)) |
| 17.0ms | y | @ | -inf | (*.f64 y (log.f64 y)) |
| 1× | batch-egg-rewrite |
| 1044× | pow1 |
| 992× | add-sqr-sqrt |
| 950× | add-exp-log |
| 950× | log1p-expm1-u |
| 950× | expm1-log1p-u |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 11 |
| 1 | 113 | 11 |
| 2 | 1320 | 11 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 y (log.f64 y)) |
| Outputs |
|---|
(-.f64 (+.f64 1 (*.f64 y (log.f64 y))) 1) |
(pow.f64 (*.f64 y (log.f64 y)) 1) |
(pow.f64 (cbrt.f64 (*.f64 y (log.f64 y))) 3) |
(pow.f64 (pow.f64 (*.f64 y (log.f64 y)) 3) 1/3) |
(pow.f64 (sqrt.f64 (*.f64 y (log.f64 y))) 2) |
(sqrt.f64 (pow.f64 (*.f64 y (log.f64 y)) 2)) |
(log.f64 (pow.f64 y y)) |
(cbrt.f64 (pow.f64 (*.f64 y (log.f64 y)) 3)) |
(expm1.f64 (log1p.f64 (*.f64 y (log.f64 y)))) |
(exp.f64 (log.f64 (*.f64 y (log.f64 y)))) |
(log1p.f64 (-.f64 (pow.f64 y y) 1)) |
| 1× | egg-herbie |
| 1472× | distribute-lft-neg-out |
| 1214× | log-prod |
| 726× | distribute-rgt-in |
| 716× | distribute-lft-in |
| 678× | unsub-neg |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 359 |
| 1 | 97 | 359 |
| 2 | 321 | 215 |
| 3 | 1678 | 215 |
| 4 | 5396 | 215 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 -1 (*.f64 y (log.f64 (/.f64 1 y)))) |
(*.f64 -1 (*.f64 y (log.f64 (/.f64 1 y)))) |
(*.f64 -1 (*.f64 y (log.f64 (/.f64 1 y)))) |
(*.f64 -1 (*.f64 y (log.f64 (/.f64 1 y)))) |
(*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)) y) |
(*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)) y) |
(*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)) y) |
(*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)) y) |
(-.f64 (+.f64 1 (*.f64 y (log.f64 y))) 1) |
(pow.f64 (*.f64 y (log.f64 y)) 1) |
(pow.f64 (cbrt.f64 (*.f64 y (log.f64 y))) 3) |
(pow.f64 (pow.f64 (*.f64 y (log.f64 y)) 3) 1/3) |
(pow.f64 (sqrt.f64 (*.f64 y (log.f64 y))) 2) |
(sqrt.f64 (pow.f64 (*.f64 y (log.f64 y)) 2)) |
(log.f64 (pow.f64 y y)) |
(cbrt.f64 (pow.f64 (*.f64 y (log.f64 y)) 3)) |
(expm1.f64 (log1p.f64 (*.f64 y (log.f64 y)))) |
(exp.f64 (log.f64 (*.f64 y (log.f64 y)))) |
(log1p.f64 (-.f64 (pow.f64 y y) 1)) |
| Outputs |
|---|
(*.f64 -1 (*.f64 y (log.f64 (/.f64 1 y)))) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(*.f64 -1 (*.f64 y (log.f64 (/.f64 1 y)))) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(*.f64 -1 (*.f64 y (log.f64 (/.f64 1 y)))) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(*.f64 -1 (*.f64 y (log.f64 (/.f64 1 y)))) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)) y) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)) y) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)) y) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)) y) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(-.f64 (+.f64 1 (*.f64 y (log.f64 y))) 1) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(pow.f64 (*.f64 y (log.f64 y)) 1) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(pow.f64 (cbrt.f64 (*.f64 y (log.f64 y))) 3) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(pow.f64 (pow.f64 (*.f64 y (log.f64 y)) 3) 1/3) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(pow.f64 (sqrt.f64 (*.f64 y (log.f64 y))) 2) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(sqrt.f64 (pow.f64 (*.f64 y (log.f64 y)) 2)) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(log.f64 (pow.f64 y y)) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(cbrt.f64 (pow.f64 (*.f64 y (log.f64 y)) 3)) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(expm1.f64 (log1p.f64 (*.f64 y (log.f64 y)))) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(exp.f64 (log.f64 (*.f64 y (log.f64 y)))) |
(neg.f64 (*.f64 y (neg.f64 (log.f64 y)))) |
(*.f64 y (neg.f64 (neg.f64 (log.f64 y)))) |
(*.f64 y (log.f64 y)) |
(log.f64 (pow.f64 y y)) |
(log1p.f64 (-.f64 (pow.f64 y y) 1)) |
(log1p.f64 (+.f64 (pow.f64 y y) -1)) |
(log1p.f64 (+.f64 -1 (pow.f64 y y))) |
Compiled 212 to 116 computations (45.3% saved)
2 alts after pruning (0 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 18 | 0 | 18 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 2 | 2 |
| Done | 0 | 0 | 0 |
| Total | 18 | 2 | 20 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 78.1% | (*.f64 (pow.f64 y y) (exp.f64 (-.f64 x z))) |
| ✓ | 100.0% | (exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
Compiled 43 to 27 computations (37.2% saved)
| Inputs |
|---|
(*.f64 (pow.f64 y y) (exp.f64 (-.f64 x z))) |
(exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
| Outputs |
|---|
(exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
7 calls:
| 20.0ms | (*.f64 y (log.f64 y)) |
| 3.0ms | (+.f64 x (*.f64 y (log.f64 y))) |
| 3.0ms | (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z) |
| 3.0ms | z |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | y |
| 100.0% | 1 | z |
| 100.0% | 1 | (exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
| 100.0% | 1 | (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z) |
| 100.0% | 1 | (+.f64 x (*.f64 y (log.f64 y))) |
| 100.0% | 1 | (*.f64 y (log.f64 y)) |
Compiled 71 to 47 computations (33.8% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
(*.f64 (pow.f64 y y) (exp.f64 (-.f64 x z))) |
| Outputs |
|---|
(*.f64 (pow.f64 y y) (exp.f64 (-.f64 x z))) |
3 calls:
| 3.0ms | z |
| 3.0ms | x |
| 2.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 78.1% | 1 | x |
| 78.1% | 1 | y |
| 78.1% | 1 | z |
Compiled 23 to 16 computations (30.4% saved)
| 1× | egg-herbie |
| 8× | +-commutative |
| 6× | sub-neg |
| 6× | *-commutative |
| 2× | neg-mul-1 |
| 2× | neg-sub0 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 15 | 50 |
| 1 | 21 | 50 |
| 2 | 27 | 50 |
| 3 | 29 | 50 |
| 4 | 30 | 50 |
| 1× | done |
| 1× | saturated |
| Inputs |
|---|
(exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
(*.f64 (pow.f64 y y) (exp.f64 (-.f64 x z))) |
| Outputs |
|---|
(exp.f64 (-.f64 (+.f64 x (*.f64 y (log.f64 y))) z)) |
(*.f64 (pow.f64 y y) (exp.f64 (-.f64 x z))) |
Compiled 23 to 15 computations (34.8% saved)
| 1234× | fma-def |
| 1016× | unswap-sqr |
| 784× | associate-*r/ |
| 778× | associate-/l/ |
| 654× | associate-/r/ |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 27 |
| 1 | 20 | 23 |
| 2 | 44 | 23 |
| 3 | 92 | 23 |
| 4 | 160 | 23 |
| 5 | 315 | 23 |
| 6 | 973 | 23 |
| 7 | 2567 | 23 |
| 8 | 5244 | 23 |
| 9 | 5941 | 23 |
| 10 | 7376 | 23 |
| 1× | node limit |
Compiled 58 to 22 computations (62.1% saved)
Compiled 88 to 56 computations (36.4% saved)
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