Details

Time bar (total: 16.7s)

sample470.0ms

Algorithm
intervals
Results
223.0ms80×body10240exit
168.0ms86×body1280valid
43.0ms52×body640valid
13.0ms88×body80valid
9.0ms21×body320valid
3.0ms9×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: 33.6b

localize12.0ms

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))
38.9b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms
(expm1 (sin (expm1 a)))
1.0ms
(sin (expm1 a))
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series154.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
87.0ms
(expm1 (sin (expm1 a)))
63.0ms
(sin (expm1 a))
2.0ms
(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

prune197.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 32.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(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)
38.9b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite5.0ms

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
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp sin-diff rem-cbrt-cube expm1-udef rem-cube-cbrt
Counts
4 → 67
Calls
4 calls:
1.0ms
(sin (expm1 a))
1.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series97.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sin (expm1 a))
2.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
35.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify143.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0156650
1538592
23301586
35002586

prune272.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 32.1b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
38.9b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
38.9b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
38.9b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite3.0ms

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:
1.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series40.0ms

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

simplify125.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
092608
1341520
22697516
35002516

prune337.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 32.0b

localize28.0ms

Local error

Found 4 expressions with local error:

38.9b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
38.9b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
38.9b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
38.9b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite1.0ms

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:
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series9.0ms

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

simplify91.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
028504
147428
269428
3127428
4543428
51738428
65001428

prune245.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 32.0b

regimes324.0ms

Accuracy

0% (1.8b remaining)

Error of 33.6b against oracle of 31.9b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0119

end0.0ms

sample14.0s

Algorithm
intervals
Results
7.3s2664×body10240exit
4.3s2305×body1280valid
1.3s1641×body640valid
375.0ms2784×body80valid
365.0ms854×body320valid
117.0ms411×body160valid
8.0ms4×body2560valid
5.0ms1×body5120valid