Details

Time bar (total: 18.6s)

sample549.0ms

Algorithm
intervals
Results
314.0ms105×body10240exit
166.0ms92×body1280valid
33.0ms45×body640valid
11.0ms85×body80valid
9.0ms23×body320valid
3.0ms11×body160valid

simplify2.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize16.0ms

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))
39.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

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)))
2.0ms
(sin (expm1 a))
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series355.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms
(expm1 (sin (expm1 a)))
348.0ms
(sin (expm1 a))
3.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify109.0ms

Counts
40 → 40

prune170.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 33.2b

localize19.0ms

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))))
39.8b
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite12.0ms

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:
2.0ms
(sin (expm1 a))
2.0ms
(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms
(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.0ms
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series102.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(sin (expm1 a))
33.0ms
(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms
(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify89.0ms

Counts
52 → 52

prune247.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 33.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(log (cbrt (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3)))
0.4b
(cbrt (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3))
1.0b
(pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3)
39.8b
(fmod (log (cbrt (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3))) a)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
15×add-sqr-sqrt add-cube-cbrt log-prod *-un-lft-identity
9×unpow-prod-down cube-prod
6×pow1
5×add-exp-log add-cbrt-cube
4×pow-pow add-log-exp
3×cube-mult pow-unpow exp-prod unpow3 sqr-pow
2×pow1/3 log-pow
1×pow-to-exp rem-log-exp pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 79
Calls
4 calls:
5.0ms
(log (cbrt (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3)))
3.0ms
(cbrt (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3))
5.0ms
(pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3)
0.0ms
(fmod (log (cbrt (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3))) a)

series131.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(log (cbrt (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3)))
37.0ms
(cbrt (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3))
87.0ms
(pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3)
3.0ms
(fmod (log (cbrt (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3))) a)

simplify137.0ms

Counts
91 → 91

prune312.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 33.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b
(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
39.8b
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.8b
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.8b
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log log-pow add-cbrt-cube add-log-exp
3×log-prod exp-prod
1×rem-log-exp
Counts
4 → 36
Calls
4 calls:
3.0ms
(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.0ms
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms
(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series12.0ms

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

simplify77.0ms

Counts
48 → 48

prune218.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 32.8b

regimes362.0ms

Accuracy

0% (1.8b remaining)

Error of 33.7b against oracle of 31.9b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample15.6s

Algorithm
intervals
Results
7.9s2694×body10240exit
4.7s2303×body1280valid
1.4s1627×body640valid
783.0ms2777×body80valid
464.0ms844×body320valid
110.0ms440×body160valid
32.0ms7×body5120valid
4.0ms2×body2560valid