Details

Time bar (total: 15.7s)

sample71.0ms

Algorithm
intervals
Results
21.0ms52×body10240exit
17.0ms351×body80nan
16.0ms255×body80valid
0.0ms1×body160valid

simplify4.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
1139
2229
3459
41109
52689
67489
726749
done50009

prune2.0ms

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))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
11×unpow-prod-up
9×prod-diff
6×pow1 unpow-prod-down sqrt-prod
5×pow-unpow
4×add-exp-log
3×expm1-log1p-u pow-pow add-cbrt-cube log1p-expm1-u add-log-exp
2×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 → 63
Calls
3 calls:
5.0ms
(pow (sqrt (atan2 b b)) (- b a))
6.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms
(sqrt (atan2 b b))

series92.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
64.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms
(sqrt (atan2 b b))

simplify3.0s

Counts
72 → 72
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
0117962
1256840
2554757
31304728
43979699
done5001699

prune139.0ms

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))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
15×sqrt-prod
11×unpow-prod-up
9×pow1 unpow-prod-down prod-diff
6×sqrt-pow1
5×add-exp-log pow-unpow pow-pow
4×expm1-log1p-u pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
2×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 → 83
Calls
4 calls:
6.0ms
(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))

series132.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
84.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
9.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify1.3s

Counts
95 → 95
Iterations

Useful iterations: 3 (441.0ms)

IterNodesCost
01411350
13111104
26871017
31790977
done5001977

prune251.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
12×unpow-prod-down sqrt-prod
11×unpow-prod-up
9×pow1 prod-diff
6×add-exp-log pow-unpow pow-pow
5×sqrt-pow1
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/2
2×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 → 85
Calls
4 calls:
6.0ms
(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))

series185.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
22.0ms
(pow (atan2 b b) (* (- b a) 1/4))
126.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* (- b a) 1/4))))
10.0ms
(sqrt (atan2 b b))

simplify1.5s

Counts
97 → 97
Iterations

Useful iterations: 3 (648.0ms)

IterNodesCost
01771562
13991405
29061284
324941210
done50011210

prune267.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
24×log-prod
17×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down sqrt-prod
11×unpow-prod-up
9×prod-diff
7×add-exp-log
6×pow1
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-log-exp
2×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 → 79
Calls
4 calls:
1.0ms
(pow (atan2 b b) (* (- b a) 1/4))
12.0ms
(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))
7.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (atan2 b b) (* (- b a) 1/4))
122.0ms
(sin (* (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))) (pow (atan2 b b) (* (- b a) 1/4))))
9.0ms
(sqrt (atan2 b b))
78.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify1.4s

Counts
91 → 91
Iterations

Useful iterations: 3 (544.0ms)

IterNodesCost
01941605
14271441
29201289
326301222
done50001222

prune277.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

regimes41.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01624
11824
done1824

end0.0ms

sample2.1s

Algorithm
intervals
Results
759.0ms1843×body10240exit
465.0ms7995×body80valid
456.0ms9963×body80nan
1.0ms1×body2560valid
1.0ms1×body1280valid
0.0ms1×body640valid
0.0ms1×body320valid
0.0ms1×body160valid