Details

Time bar (total: 16.7s)

sample448.0ms

Algorithm
intervals
Results
255.0ms91×body5120exit
124.0ms70×body1280valid
34.0ms48×body640valid
12.0ms102×body80valid
9.0ms24×body320valid
3.0ms12×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: 31.2b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b
(expm1 (sin (expm1 a)))
0.1b
(sin (expm1 a))
35.7b
(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))
1.0ms
(expm1 (sin (expm1 a)))
2.0ms
(sin (expm1 a))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series152.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
85.0ms
(expm1 (sin (expm1 a)))
62.0ms
(sin (expm1 a))
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify122.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0108302
1242264
2720264
32933264
45001264

prune202.0ms

Filtered
51 candidates to 39 candidates (76.5%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New391251
Fresh000
Picked011
Done000
Total391352

Merged error: 30.0b

Counts
52 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (expm1 (sin (expm1 a))))
0.4b
(cbrt (expm1 (sin (expm1 a))))
0.4b
(cbrt (expm1 (sin (expm1 a))))
35.7b
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite5.0ms

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 (expm1 (sin (expm1 a))))
1.0ms
(cbrt (expm1 (sin (expm1 a))))
1.0ms
(cbrt (expm1 (sin (expm1 a))))
1.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series510.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(cbrt (expm1 (sin (expm1 a))))
169.0ms
(cbrt (expm1 (sin (expm1 a))))
168.0ms
(cbrt (expm1 (sin (expm1 a))))
3.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify72.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 4 (67.0ms)

IterNodesCost
088549
1181487
2472481
31562470
45001467

prune290.0ms

Filtered
60 candidates to 45 candidates (75.0%)
Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New481260
Fresh11011
Picked101
Done011
Total502373

Merged error: 29.7b

Counts
73 → 23

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (expm1 (sin (expm1 a))))
35.7b
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
35.7b
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
35.7b
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite4.0ms

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 (expm1 (sin (expm1 a))))
1.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
1.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
1.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series183.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(cbrt (expm1 (sin (expm1 a))))
3.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
3.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
3.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify77.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 4 (66.0ms)

IterNodesCost
088807
1181693
2472691
31562658
45001657

prune378.0ms

Filtered
52 candidates to 42 candidates (80.8%)
Pruning

32 alts after pruning (31 fresh and 1 done)

PrunedKeptTotal
New421052
Fresh02121
Picked101
Done011
Total433275

Merged error: 29.6b

Counts
75 → 32

localize31.0ms

Local error

Found 4 expressions with local error:

35.7b
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
35.7b
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
35.7b
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
35.7b
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 36
Calls
4 calls:
1.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
1.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
1.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)
1.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series11.0ms

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

simplify105.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 3 (6.0ms)

IterNodesCost
023936
126796
232796
348752
476752
5150752
6651752
72191752
85001752

prune236.0ms

Filtered
48 candidates to 40 candidates (83.3%)
Pruning

34 alts after pruning (33 fresh and 1 done)

PrunedKeptTotal
New44448
Fresh12930
Picked101
Done011
Total463480

Merged error: 29.5b

Counts
80 → 34

regimes651.0ms

Accuracy

0% (1.8b remaining)

Error of 33.2b against oracle of 31.4b and baseline of 33.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02485
12485

end0.0ms

sample13.1s

Algorithm
intervals
Results
7.1s2570×body5120exit
3.9s2281×body1280valid
1.2s1587×body640valid
328.0ms2839×body80valid
299.0ms846×body320valid
104.0ms442×body160valid
25.0ms5×body5120valid