Details

Time bar (total: 36.2s)

sample780.0ms

Algorithm
intervals
Results
349.0ms96×body10240exit
260.0ms84×body1280valid
51.0ms47×body640valid
17.0ms32×body320valid
13.0ms83×body80valid
3.0ms10×body160valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0810
done810

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize62.0ms

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))
40.2b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
Counts
4 → 28
Calls
4 calls:
0.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms
(expm1 (sin (expm1 a)))
5.0ms
(sin (expm1 a))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series87.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms
(expm1 (sin (expm1 a)))
72.0ms
(sin (expm1 a))
10.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.1s

Counts
40 → 40
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
035339
139339
244293
355293
484293
5217293
6519293
71209293
84017293
done5001293

prune257.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(sin (expm1 a))
0.3b
(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b
(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
40.2b
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×exp-prod
5×pow1 add-log-exp
4×add-exp-log log-pow add-cbrt-cube
3×log-prod
1×rem-log-exp rem-exp-log
Counts
4 → 40
Calls
4 calls:
14.0ms
(sin (expm1 a))
4.0ms
(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms
(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
1.0ms
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series114.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sin (expm1 a))
33.0ms
(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
5.0ms
(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
6.0ms
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.1s

Counts
52 → 52
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
051562
167507
299446
3149446
4255446
5534446
61471446
done5001446

prune285.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 33.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (sin (expm1 a)))
0.4b
(cbrt (sin (expm1 a)))
0.6b
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
40.2b
(fmod (log (exp (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)))) a)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×pow1
8×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube 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:
3.0ms
(cbrt (sin (expm1 a)))
4.0ms
(cbrt (sin (expm1 a)))
41.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms
(fmod (log (exp (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)))) a)

series771.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(cbrt (sin (expm1 a)))
255.0ms
(cbrt (sin (expm1 a)))
249.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
7.0ms
(fmod (log (exp (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)))) a)

simplify1.8s

Counts
81 → 81
Iterations

Useful iterations: done (1.8s)

IterNodesCost
065965
1122864
2569648
done5000609

prune547.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 32.9b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a)))))
0.6b
(* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1)))
0.6b
(pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))
40.1b
(fmod (log (exp (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)))) a)

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-prod
45×add-sqr-sqrt
27×unpow-prod-down
23×associate-*r*
20×add-exp-log *-un-lft-identity
18×add-cube-cbrt
15×unswap-sqr
11×pow1
10×associate-*l* prod-exp
7×add-cbrt-cube
5×sqr-pow
4×pow-unpow pow-prod-up cbrt-unprod add-log-exp
3×pow-to-exp pow-exp
2×unpow-prod-up pow-pow *-commutative
1×pow-plus pow1/3 pow-prod-down distribute-lft-out
Counts
4 → 111
Calls
4 calls:
70.0ms
(* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a)))))
44.0ms
(* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1)))
15.0ms
(pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))
1.0ms
(fmod (log (exp (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)))) a)

series896.0ms

Counts
4 → 12
Calls
4 calls:
312.0ms
(* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a)))))
306.0ms
(* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1)))
273.0ms
(pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))
6.0ms
(fmod (log (exp (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (pow (cbrt (cbrt (sin (expm1 a)))) (+ 3 1))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)))) a)

simplify2.3s

Counts
123 → 123
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01512625
14042174
220971505
done50001431

prune733.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 32.6b

regimes786.0ms

Accuracy

0% (2.2b remaining)

Error of 33.5b against oracle of 31.4b and baseline of 33.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01723
11823
done1823

end0.0ms

sample23.2s

Algorithm
intervals
Results
11.5s2718×body10240exit
7.2s2262×body1280valid
2.0s1656×body640valid
1.2s2809×body80valid
620.0ms862×body320valid
200.0ms410×body160valid
9.0ms1×body5120valid