Details

Time bar (total: 20.5s)

sample371.0ms

Algorithm
intervals
Results
176.0ms70×body10240exit
129.0ms79×body1280valid
36.0ms57×body640valid
9.0ms87×body80valid
8.0ms25×body320valid
2.0ms8×body160valid

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0810
done810

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (sin (expm1 a)))
0.0b
(sin (expm1 a))
0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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

series149.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(expm1 (sin (expm1 a)))
59.0ms
(sin (expm1 a))
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.9s

Counts
51 → 51
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
070438
1110422
2224375
3637374
42883374
done5001374

prune205.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b
(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:
6.0ms
(* (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)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series147.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (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)
3.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.1s

Counts
81 → 81
Iterations

Useful iterations: 3 (169.0ms)

IterNodesCost
0571571
1931414
22461302
39791115
done50011115

prune321.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 33.2b

localize21.0ms

Local error

Found 4 expressions with local error:

40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) 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 (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)

series9.0ms

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

simplify1.7s

Counts
48 → 48
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
016588
117588
219516
324516
430516
550516
6107516
7334516
81169516
done5001516

prune282.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 33.2b

localize27.0ms

Local error

Found 4 expressions with local error:

40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) 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 (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)

series9.0ms

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

simplify1.5s

Counts
48 → 48
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
016588
117588
219516
324516
430516
550516
6107516
7334516
81169516
done5001516

prune223.0ms

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 33.2b

regimes239.0ms

Accuracy

0% (1.3b remaining)

Error of 33.7b against oracle of 32.4b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01133
11233
done1233

end0.0ms

sample12.3s

Algorithm
intervals
Results
6.5s2596×body10240exit
3.9s2359×body1280valid
1.1s1645×body640valid
271.0ms2776×body80valid
263.0ms814×body320valid
82.0ms402×body160valid
9.0ms2×body5120valid
4.0ms2×body2560valid