Details

Time bar (total: 15.2s)

sample370.0ms

Algorithm
intervals
Results
201.0ms82×body10240exit
101.0ms63×body1280valid
29.0ms44×body640valid
14.0ms106×body80valid
10.0ms30×body320valid
3.0ms13×body160valid

simplify2.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
087

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (sin (expm1 a)))
0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.2b
(sin (expm1 a))
34.6b
(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:
0.0ms
(expm1 (sin (expm1 a)))
0.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms
(sin (expm1 a))
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series159.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(expm1 (sin (expm1 a)))
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
64.0ms
(sin (expm1 a))
3.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify121.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0108302
1242264
2720264
32933264
45001264

prune205.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
34.7b
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series348.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
118.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
113.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify91.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
042714
172632
2149626
3483611
42459611
55002611

prune264.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 28.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
34.7b
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
34.7b
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
34.7b
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod
1×pow1/3
Counts
4 → 40
Calls
4 calls:
1.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series124.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
3.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
4.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify96.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
042990
172848
2149846
3483801
42459801
55002801

prune325.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 28.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
34.7b
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
34.7b
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
34.7b
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod
1×pow1/3
Counts
4 → 40
Calls
4 calls:
1.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
0.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series128.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
3.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
4.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify52.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 4 (45.0ms)

IterNodesCost
0721023
1124881
2314879
31187834
45001833

prune278.0ms

Pruning

25 alts after pruning (23 fresh and 2 done)

Merged error: 28.7b

regimes336.0ms

Accuracy

0% (1.8b remaining)

Error of 33.3b against oracle of 31.5b and baseline of 33.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11222

end0.0ms

sample12.2s

Algorithm
intervals
Results
6.4s2582×body10240exit
3.8s2314×body1280valid
1.1s1673×body640valid
268.0ms2850×body80valid
240.0ms774×body320valid
77.0ms383×body160valid
14.0ms3×body5120valid
6.0ms3×body2560valid