Details

Time bar (total: 12.7s)

sample67.0ms

Algorithm
intervals
Results
20.0ms52×body10240exit
16.0ms351×body80nan
14.0ms255×body80valid
0.0ms1×body160valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
1139
2229
3459
41109
52489
67249
726129
done50009

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.1b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity
7×add-cube-cbrt
6×pow1 unpow-prod-down sqrt-prod
5×pow-unpow
4×add-exp-log
3×pow-pow add-cbrt-cube add-log-exp
2×unpow-prod-up sqrt-pow1 pow1/2
1×pow-to-exp sub-neg rem-sqrt-square pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
3 → 48
Calls
3 calls:
4.0ms
(pow (sqrt (atan2 b b)) (- b a))
4.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms
(sqrt (atan2 b b))

series91.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
61.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms
(sqrt (atan2 b b))

simplify1.8s

Counts
57 → 57
Iterations

Useful iterations: 3 (154.0ms)

IterNodesCost
075614
1148571
2343536
3801527
42344527
done5000527

prune138.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
15×sqrt-prod
14×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt
9×pow1 unpow-prod-down
6×sqrt-pow1
5×add-exp-log pow-unpow pow-pow
4×pow1/2 add-cbrt-cube add-log-exp
2×unpow-prod-up rem-sqrt-square
1×pow-to-exp sub-neg pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
4 → 66
Calls
4 calls:
7.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
9.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series136.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
88.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify2.4s

Counts
78 → 78
Iterations

Useful iterations: 3 (226.0ms)

IterNodesCost
099950
1203794
2466756
31213735
43839735
done5000735

prune235.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.0b
(pow (atan2 b b) (* (- b a) 1/4))
0.1b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* (- b a) 1/4))))
1.0b
(sqrt (atan2 b b))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×unpow-prod-down *-un-lft-identity sqrt-prod
10×add-cube-cbrt
9×pow1
6×add-exp-log pow-unpow pow-pow
5×sqrt-pow1
4×add-cbrt-cube add-log-exp
3×pow1/2
2×unpow-prod-up pow-to-exp pow-exp sqr-pow
1×sub-neg rem-sqrt-square sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares
Counts
4 → 68
Calls
4 calls:
5.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms
(pow (atan2 b b) (* (- b a) 1/4))
9.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* (- b a) 1/4))))
1.0ms
(sqrt (atan2 b b))

series191.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
20.0ms
(pow (atan2 b b) (* (- b a) 1/4))
132.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* (- b a) 1/4))))
10.0ms
(sqrt (atan2 b b))

simplify1.0s

Counts
80 → 80
Iterations

Useful iterations: 3 (368.0ms)

IterNodesCost
01331152
12861070
26591000
31854942
done5000942

prune262.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (atan2 b b) (* (- b a) 1/4))
0.1b
(sin (* (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))) (pow (atan2 b b) (* (- b a) 1/4))))
1.0b
(sqrt (atan2 b b))
4.5b
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
15×log-prod
12×unpow-prod-down sqrt-prod
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
7×add-exp-log
6×pow1
4×add-cbrt-cube add-log-exp
3×rem-log-exp
2×unpow-prod-up pow-to-exp pow-exp sqr-pow
1×sub-neg rem-sqrt-square log-div pow-unpow pow-pow sqrt-pow1 pow1/2 log-pow pow-sub
Counts
4 → 62
Calls
4 calls:
1.0ms
(pow (atan2 b b) (* (- b a) 1/4))
13.0ms
(sin (* (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))) (pow (atan2 b b) (* (- b a) 1/4))))
1.0ms
(sqrt (atan2 b b))
4.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (atan2 b b) (* (- b a) 1/4))
128.0ms
(sin (* (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))) (pow (atan2 b b) (* (- b a) 1/4))))
10.0ms
(sqrt (atan2 b b))
99.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify980.0ms

Counts
74 → 74
Iterations

Useful iterations: 3 (343.0ms)

IterNodesCost
01361171
12881085
2634982
31958933
done5000933

prune295.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes45.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01422
11622
done1622

end0.0ms

sample2.1s

Algorithm
intervals
Results
767.0ms1843×body10240exit
469.0ms9963×body80nan
442.0ms7995×body80valid
1.0ms1×body2560valid
1.0ms1×body320valid
1.0ms1×body1280valid
0.0ms1×body640valid
0.0ms1×body160valid