Details

Time bar (total: 35.0s)

sample755.0ms

Algorithm
intervals
Results
409.0ms97×body10240exit
189.0ms78×body1280valid
44.0ms37×body640valid
17.0ms99×body80valid
13.0ms29×body320valid
5.0ms13×body160valid

simplify24.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize21.0ms

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))
36.4b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite6.0ms

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)))
3.0ms
(sin (expm1 a))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series126.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms
(expm1 (sin (expm1 a)))
76.0ms
(sin (expm1 a))
42.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.2s

Counts
40 → 40

prune269.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 30.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(sin (expm1 a))
0.7b
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
36.4b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
5×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 58
Calls
4 calls:
2.0ms
(sin (expm1 a))
2.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
4.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series127.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(sin (expm1 a))
3.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
37.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify2.5s

Counts
70 → 70

prune457.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 30.3b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
36.4b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
36.4b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
36.4b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
3×unpow-prod-down pow-unpow cube-prod
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 44
Calls
4 calls:
3.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series86.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
5.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
4.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify2.5s

Counts
56 → 56

prune470.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 30.1b

localize68.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
36.4b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
36.4b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
36.4b
(fmod (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 2))) a)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
3×unpow-prod-down pow-unpow cube-prod
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 44
Calls
4 calls:
3.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 2))) a)

series69.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
6.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
4.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
4.0ms
(fmod (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 2))) a)

simplify2.5s

Counts
56 → 56

prune399.0ms

Pruning

24 alts after pruning (22 fresh and 2 done)

Merged error: 30.1b

regimes532.0ms

Accuracy

0% (1.7b remaining)

Error of 33.7b against oracle of 32.0b and baseline of 33.7b

bsearch0.0ms

simplify724.0ms

end0.0ms

sample22.0s

Algorithm
intervals
Results
11.6s2702×body10240exit
6.6s2309×body1280valid
1.9s1646×body640valid
627.0ms2773×body80valid
598.0ms826×body320valid
186.0ms439×body160valid
19.0ms4×body5120valid
10.0ms3×body2560valid