Details

Time bar (total: 15.8s)

sample496.0ms

Algorithm
intervals
Results
290.0ms104×body5120exit
132.0ms80×body1280valid
40.0ms54×body640valid
10.0ms88×body80valid
9.0ms23×body320valid
3.0ms11×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
087

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.1b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b
(sin (expm1 a))
0.0b
(expm1 (sin (expm1 a)))
39.1b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×log1p-expm1-u
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
2×expm1-udef
1×expm1-log1p sin-diff
Counts
4 → 39
Calls
4 calls:
1.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms
(sin (expm1 a))
1.0ms
(expm1 (sin (expm1 a)))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series156.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
62.0ms
(sin (expm1 a))
89.0ms
(expm1 (sin (expm1 a)))
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify123.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0108302
1242264
2720264
32934264
45001264

prune195.0ms

Filtered
51 candidates to 39 candidates (76.5%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New381351
Fresh000
Picked011
Done000
Total381452

Merged error: 32.9b

Counts
52 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (sin (expm1 a)))
0.7b
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.1b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
5×pow1 add-exp-log add-cbrt-cube log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp expm1-log1p pow-pow pow1/3 pow-exp rem-cbrt-cube expm1-udef rem-cube-cbrt
Counts
4 → 68
Calls
4 calls:
1.0ms
(expm1 (sin (expm1 a)))
2.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
2.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series129.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(expm1 (sin (expm1 a)))
2.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
33.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify138.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0150655
1516595
23329589
35001589

prune254.0ms

Filtered
80 candidates to 43 candidates (53.8%)
Pruning

20 alts after pruning (18 fresh and 2 done)

PrunedKeptTotal
New73780
Fresh11112
Picked011
Done011
Total742094

Merged error: 32.5b

Counts
94 → 20

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))
0.7b
(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.1b
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
93×cbrt-prod
39×unpow-prod-down cube-prod
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×cube-mult unpow3 sqr-pow
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×pow1/3
1×pow-to-exp pow-pow pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 118
Calls
4 calls:
5.0ms
(cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))
6.0ms
(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
3.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

series76.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))
2.0ms
(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
34.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

simplify41.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02051471
16251301
250021277

prune291.0ms

Filtered
130 candidates to 48 candidates (36.9%)
Pruning

22 alts after pruning (19 fresh and 3 done)

PrunedKeptTotal
New1282130
Fresh01717
Picked011
Done022
Total12822150

Merged error: 32.4b

Counts
150 → 22

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.1b
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
39.1b
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
39.1b
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow cube-prod
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 52
Calls
4 calls:
2.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
1.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
1.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

series44.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
2.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)
3.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

simplify132.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
097674
1356574
22852570
35002570

prune284.0ms

Filtered
64 candidates to 44 candidates (68.8%)
Pruning

26 alts after pruning (24 fresh and 2 done)

PrunedKeptTotal
New58664
Fresh01818
Picked101
Done123
Total602686

Merged error: 32.3b

Counts
86 → 26

regimes332.0ms

Accuracy

0% (1.7b remaining)

Error of 33.4b against oracle of 31.7b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02238
12238

end0.0ms

sample13.0s

Algorithm
intervals
Results
7.1s2559×body5120exit
3.8s2228×body1280valid
1.2s1682×body640valid
318.0ms2812×body80valid
301.0ms837×body320valid
100.0ms431×body160valid
28.0ms6×body5120valid
8.0ms4×body2560valid