Details

Time bar (total: 33.2s)

sample698.0ms

Algorithm
intervals
Results
251.0ms70×body10240exit
187.0ms70×body1280valid
130.0ms59×body640valid
16.0ms90×body80valid
10.0ms20×body320valid
5.0ms16×body160valid
5.0ms1×body5120valid

simplify12.0ms

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: 33.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (sin (expm1 a)))
0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.2b
(sin (expm1 a))
38.1b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite44.0ms

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
(expm1 (sin (expm1 a)))
0.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms
(sin (expm1 a))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series101.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(expm1 (sin (expm1 a)))
3.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
83.0ms
(sin (expm1 a))
12.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.6s

Counts
40 → 40
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
035339
139339
244293
355293
470293
5101293
6176293
7436293
81564293
done5001293

prune263.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 32.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (expm1 (sin (expm1 a))))
0.4b
(cbrt (expm1 (sin (expm1 a))))
0.4b
(cbrt (expm1 (sin (expm1 a))))
38.1b
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
Counts
4 → 40
Calls
4 calls:
1.0ms
(cbrt (expm1 (sin (expm1 a))))
1.0ms
(cbrt (expm1 (sin (expm1 a))))
3.0ms
(cbrt (expm1 (sin (expm1 a))))
0.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series521.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(cbrt (expm1 (sin (expm1 a))))
171.0ms
(cbrt (expm1 (sin (expm1 a))))
150.0ms
(cbrt (expm1 (sin (expm1 a))))
4.0ms
(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify1.3s

Counts
52 → 52
Iterations

Useful iterations: 3 (37.0ms)

IterNodesCost
031602
140590
269421
3130388
4345388
51411388
done5000388

prune346.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 32.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
38.1b
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
Counts
4 → 40
Calls
4 calls:
2.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series565.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
195.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
175.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.3s

Counts
52 → 52
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
030833
139821
268565
3129532
4343532
51385532
done5000532

prune287.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 31.9b

localize22.0ms

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)
38.1b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite13.0ms

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:
3.0ms
(sin (expm1 a))
3.0ms
(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)

series144.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sin (expm1 a))
5.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
52.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
7.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify2.4s

Counts
70 → 70
Iterations

Useful iterations: 3 (553.0ms)

IterNodesCost
067966
1114791
2286693
31997685
done5001685

prune251.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 31.7b

regimes469.0ms

Accuracy

0% (1.8b remaining)

Error of 33.5b against oracle of 31.7b and baseline of 33.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01424
11524
done1524

end0.0ms

sample22.7s

Algorithm
intervals
Results
11.2s2583×body10240exit
7.2s2312×body1280valid
2.4s1622×body640valid
580.0ms2810×body80valid
579.0ms802×body320valid
160.0ms446×body160valid
33.0ms5×body5120valid
8.0ms3×body2560valid