Details

Time bar (total: 14.9s)

sample425.0ms

Algorithm
intervals
Results
236.0ms94×body10240exit
128.0ms75×body1280valid
25.0ms38×body640valid
10.0ms31×body320valid
9.0ms94×body80valid
4.0ms18×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
087
187
done87

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b
(expm1 (sin (expm1 a)))
0.2b
(sin (expm1 a))
37.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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)

series69.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms
(expm1 (sin (expm1 a)))
62.0ms
(sin (expm1 a))
3.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify119.0ms

Counts
40 → 40
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
039248
144212
254212
368212
4114212
5228212
6919212
73184212
85001212
done5001212

prune156.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 31.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(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)
37.0b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite9.0ms

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))
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)

series99.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(sin (expm1 a))
2.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
36.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify126.0ms

Counts
70 → 70
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0112584
1390527
22787521
35001521
done5001521

prune218.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 31.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (expm1 a))
0.7b
(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
37.0b
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
21×unpow-prod-down cube-prod
15×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×cube-mult unpow3 add-log-exp sqr-pow
3×pow-unpow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cube-cbrt
Counts
4 → 78
Calls
4 calls:
2.0ms
(sin (expm1 a))
7.0ms
(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
3.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

series97.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(sin (expm1 a))
3.0ms
(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
35.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
4.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

simplify32.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0201976
1622871
25001855
done5001855

prune253.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 31.2b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
37.0b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
37.0b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
37.0b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite4.0ms

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)

series44.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
6.0ms
(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)

simplify123.0ms

Counts
56 → 56
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
088540
1337452
22685448
35002448
done5002448

prune212.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 31.0b

regimes294.0ms

Accuracy

0% (1.6b remaining)

Error of 33.7b against oracle of 32.1b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02032
12032
done2032

end0.0ms

sample12.6s

Algorithm
intervals
Results
6.7s2701×body10240exit
3.8s2323×body1280valid
1.1s1702×body640valid
264.0ms808×body320valid
263.0ms2761×body80valid
87.0ms403×body160valid
9.0ms2×body5120valid
2.0ms1×body2560valid