Details

Time bar (total: 39.1s)

sample1.1s

Algorithm
intervals
Results
519.0ms84×body10240exit
278.0ms76×body1280valid
149.0ms60×body640valid
36.0ms28×body320valid
26.0ms81×body80valid
7.0ms11×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done8
08

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b
(sin (expm1 a))
0.0b
(expm1 (sin (expm1 a)))
40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×log1p-expm1-u
3×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
2×expm1-udef
1×expm1-log1p sin-diff
Counts
3 → 33
Calls
3 calls:
5.0ms
(sin (expm1 a))
2.0ms
(expm1 (sin (expm1 a)))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series265.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(sin (expm1 a))
170.0ms
(expm1 (sin (expm1 a)))
11.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.2s

Counts
42 → 42
Iterations
IterNodes
done2003
52003
4994
3405
2193
1108
064

prune378.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 34.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×*-un-lft-identity add-cube-cbrt
11×pow1
6×pow1/3 swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 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 → 73
Calls
4 calls:
17.0ms
(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (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)
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series237.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
11.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.8s

Counts
85 → 85
Iterations
IterNodes
done2002
52002
41345
3489
2229
1109
059

prune552.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 34.1b

localize73.0ms

Local error

Found 4 expressions with local error:

40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 40
Calls
4 calls:
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)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series14.0ms

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

simplify2.3s

Counts
52 → 52
Iterations
IterNodes
done2052
102052
91166
8374
7173
6102
545
433
325
220
118
017

prune534.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 34.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b
(exp (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))))
40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 exp-prod
9×log-pow
6×pow1/3
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 log-prod pow-plus exp-sum rem-exp-log
Counts
4 → 54
Calls
4 calls:
19.0ms
(exp (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (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)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series247.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(exp (log (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))))
4.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.4s

Counts
66 → 66
Iterations
IterNodes
done2024
62024
51331
4528
3249
2138
179
052

prune449.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 34.1b

regimes480.0ms

Accuracy

0% (1.1b remaining)

Error of 33.3b against oracle of 32.2b and baseline of 33.3b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done19
219
117
014

end0.0ms

sample27.8s

Algorithm
intervals
Results
14.2s2572×body10240exit
8.1s2298×body1280valid
2.6s1566×body640valid
971.0ms2837×body80valid
844.0ms851×body320valid
659.0ms440×body160valid
67.0ms7×body5120valid
4.0ms1×body2560valid