Details

Time bar (total: 21.3s)

sample306.0ms

Algorithm
intervals
Results
134.0ms42×body10240exit
32.0ms318×body80nan
28.0ms253×body80valid
1.0ms1×body640valid
0.0ms1×body320valid
0.0ms1×body160valid

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
079
1139
2229
3459
41159
52749
68379
732179
done50019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.5b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite33.0ms

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:
10.0ms
(pow (sqrt (atan2 b b)) (- b a))
13.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms
(sqrt (atan2 b b))

series193.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(pow (sqrt (atan2 b b)) (- b a))
129.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
32.0ms
(sqrt (atan2 b b))

simplify4.7s

Counts
72 → 72
Iterations

Useful iterations: 4 (3.0s)

IterNodesCost
0117962
1246836
2485757
31274728
44144699
done5000699

prune248.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.6b
(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))

rewrite49.0ms

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:
10.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
33.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series227.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
157.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
19.0ms
(sqrt (atan2 b b))
15.0ms
(sqrt (atan2 b b))

simplify1.9s

Counts
95 → 95
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01411350
13011095
26111012
31815972
done5001943

prune438.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (fabs (cbrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (cbrt (atan2 b b)))) (- b a)))))
1.0b
(cbrt (atan2 b b))
1.0b
(cbrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 50
Calls
4 calls:
160.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (fabs (cbrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (cbrt (atan2 b b)))) (- b a)))))
1.0ms
(cbrt (atan2 b b))
1.0ms
(cbrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series741.0ms

Counts
4 → 12
Calls
4 calls:
335.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (fabs (cbrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (cbrt (atan2 b b)))) (- b a)))))
194.0ms
(cbrt (atan2 b b))
191.0ms
(cbrt (atan2 b b))
20.0ms
(sqrt (atan2 b b))

simplify1.5s

Counts
62 → 62
Iterations

Useful iterations: done (1.5s)

IterNodesCost
090858
1177825
2471728
31884708
done5000705

prune461.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (fabs (cbrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (cbrt (atan2 b b)))) (- b a)))))
1.0b
(cbrt (atan2 b b))
1.0b
(cbrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 50
Calls
4 calls:
142.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (fabs (cbrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (cbrt (atan2 b b)))) (- b a)))))
2.0ms
(cbrt (atan2 b b))
2.0ms
(cbrt (atan2 b b))
3.0ms
(sqrt (atan2 b b))

series759.0ms

Counts
4 → 12
Calls
4 calls:
407.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (fabs (cbrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (cbrt (atan2 b b)))) (- b a)))))
154.0ms
(cbrt (atan2 b b))
177.0ms
(cbrt (atan2 b b))
21.0ms
(sqrt (atan2 b b))

simplify1.3s

Counts
62 → 62
Iterations

Useful iterations: done (1.3s)

IterNodesCost
090858
1177825
2471728
31884708
done5000705

prune486.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

regimes98.0ms

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
01222
11422
done1422

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s1736×body10240exit
704.0ms9724×body80nan
685.0ms7993×body80valid
1.0ms2×body640valid
1.0ms2×body320valid
1.0ms3×body160valid