Details

Time bar (total: 15.8s)

sample416.0ms

Algorithm
intervals
Results
220.0ms88×body10240exit
118.0ms73×body1280valid
42.0ms55×body640valid
9.0ms88×body80valid
8.0ms26×body320valid
8.0ms14×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
087

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

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)))
0.2b
(sin (expm1 a))
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

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)))
2.0ms
(sin (expm1 a))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series157.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
82.0ms
(expm1 (sin (expm1 a)))
64.0ms
(sin (expm1 a))
9.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify124.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0108302
1242264
2720264
32933264
45001264

prune210.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 32.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (expm1 a))
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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
1×sin-diff expm1-udef
Counts
4 → 37
Calls
4 calls:
1.0ms
(sin (expm1 a))
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series64.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(sin (expm1 a))
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify65.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
067360
1138315
2360315
31390315
45001315

prune277.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
38.8b
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×add-cube-cbrt *-un-lft-identity
11×pow1
6×add-exp-log pow1/3 swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 69
Calls
4 calls:
7.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series151.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify68.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0151788
1447697
21900571
35001561

prune510.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 32.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (cbrt (cbrt (sin (expm1 a)))) 4)
38.8b
(fmod (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod unpow-prod-down
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-unpow
2×pow-pow
1×pow-to-exp pow1/3 pow-exp sqr-pow
Counts
4 → 53
Calls
4 calls:
3.0ms
(pow (cbrt (cbrt (sin (expm1 a)))) 4)
0.0ms
(fmod (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series161.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(pow (cbrt (cbrt (sin (expm1 a)))) 4)
3.0ms
(fmod (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify69.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0180743
1492656
21705648
35001648

prune377.0ms

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 31.9b

regimes520.0ms

Accuracy

0% (1.8b remaining)

Error of 33.4b against oracle of 31.6b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03058
13058

end0.0ms

sample12.5s

Algorithm
intervals
Results
6.6s2609×body10240exit
3.8s2259×body1280valid
1.2s1730×body640valid
288.0ms2815×body80valid
261.0ms783×body320valid
87.0ms410×body160valid
9.0ms2×body5120valid
2.0ms1×body2560valid