Details

Time bar (total: 3.2s)

sample18.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0209
1409
2789
31349
42009
52339
62399
72399

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize8.0ms

Local error

Found 2 expressions with local error:

4.5b
(- (* x x) (* (* y 4.0) y))
34.2b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff clear-num flip-+ div-inv
Counts
2 → 50
Calls
2 calls:
3.0ms
(- (* x x) (* (* y 4.0) y))
12.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series104.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(- (* x x) (* (* y 4.0) y))
63.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify39.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0237617
11114565
25002555

prune138.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune6.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 4 expressions with local error:

2.3b
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
2.8b
(/ x (/ (fma x x (* (* y 4.0) y)) x))
18.0b
(/ (fma x x (* (* y 4.0) y)) y)
21.5b
(/ (fma x x (* (* y 4.0) y)) x)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
124×times-frac
76×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×associate-/r*
25×add-exp-log add-cbrt-cube
11×cbrt-undiv div-exp
10×div-inv associate-/l*
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×prod-exp associate-/r/ cbrt-unprod
Counts
4 → 178
Calls
4 calls:
6.0ms
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
5.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
2.0ms
(/ (fma x x (* (* y 4.0) y)) y)
2.0ms
(/ (fma x x (* (* y 4.0) y)) x)

series242.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
53.0ms
(/ x (/ (fma x x (* (* y 4.0) y)) x))
63.0ms
(/ (fma x x (* (* y 4.0) y)) y)
69.0ms
(/ (fma x x (* (* y 4.0) y)) x)

simplify91.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06131740
132201580
250011575

prune441.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

18.7b
(cbrt (/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y)))
18.7b
(cbrt (/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y)))
18.7b
(cbrt (/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y)))
21.5b
(/ (fma x x (* (* y 4.0) y)) x)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
54×cbrt-prod
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×div-inv
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 associate-/r* associate-/r/ associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num
Counts
4 → 116
Calls
4 calls:
4.0ms
(cbrt (/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y)))
4.0ms
(cbrt (/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y)))
4.0ms
(cbrt (/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y)))
2.0ms
(/ (fma x x (* (* y 4.0) y)) x)

series692.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(cbrt (/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y)))
209.0ms
(cbrt (/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y)))
203.0ms
(cbrt (/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y)))
73.0ms
(/ (fma x x (* (* y 4.0) y)) x)

simplify145.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 3 (131.0ms)

IterNodesCost
02691348
17681279
243681273
350011270

prune453.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.7b

regimes225.0ms

Accuracy

55.1% (14.4b remaining)

Error of 14.8b against oracle of 0.4b and baseline of 32.4b

bsearch125.0ms

Steps
ItersRangePoint
8
3.3248230496188427e+259
1.4319432875630967e+262
9.401781485752867e+260
7
1.8173292678763835e+227
5.8320208877262626e+228
2.369436021557519e+227
8
2.542928968208428e+183
1.6225623410013362e+188
1.7671028773181022e+187
7
7.077277380847662e+31
3.0375193260880744e+33
7.163245107763861e+31
11
5.484209576279347e-94
4.482275143764029e-70
6.5123029565822326e-77
5
3.113930443487508e-214
1.0257908551054914e-213
6.568174626165863e-214

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03439
13439

end0.0ms

sample374.0ms

Algorithm
intervals
Results
247.0ms8000×body80valid