Details

Time bar (total: 14.2s)

sample317.0ms

Algorithm
intervals
Results
23.0ms52×body10240exit
17.0ms351×body80nan
16.0ms255×body80valid
0.0ms1×body160valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
079
1139
2229
3459
41109
52549
67349
726429
done50009

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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))

rewrite17.0ms

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:
4.0ms
(pow (sqrt (atan2 b b)) (- b a))
6.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms
(sqrt (atan2 b b))

series103.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
66.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
17.0ms
(sqrt (atan2 b b))

simplify2.6s

Counts
72 → 72
Iterations

Useful iterations: 4 (1.6s)

IterNodesCost
0117962
1252836
2532757
31274728
43925699
done5000699

prune153.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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
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:
5.0ms
(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))
87.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms
(sqrt (atan2 b b))
13.0ms
(sqrt (atan2 b b))

simplify1.2s

Counts
95 → 95
Iterations

Useful iterations: 3 (416.0ms)

IterNodesCost
01411350
13071095
26541012
31739972
done5001972

prune259.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
33×*-un-lft-identity
25×add-cube-cbrt
24×pow-unpow
15×times-frac
12×unpow-prod-down sqrt-prod
11×unpow-prod-up
9×pow1 prod-diff
6×add-exp-log pow-pow
5×sqrt-pow1
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×pow1/2
2×pow-to-exp pow-exp pow-sub sqr-pow
1×sub-neg rem-sqrt-square div-sub sqrt-pow2 div-inv
Counts
4 → 104
Calls
4 calls:
6.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
4.0ms
(pow (atan2 b b) (/ (- b a) 4))
10.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (/ (- b a) 4))))
1.0ms
(sqrt (atan2 b b))

series193.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
22.0ms
(pow (atan2 b b) (/ (- b a) 4))
133.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (/ (- b a) 4))))
10.0ms
(sqrt (atan2 b b))

simplify1.5s

Counts
116 → 116
Iterations

Useful iterations: 3 (788.0ms)

IterNodesCost
02151783
15011590
211071481
330341396
done50001396

prune343.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
31×*-un-lft-identity
25×add-cube-cbrt
24×log-prod
19×pow-unpow
15×times-frac
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 distribute-lft-out-- difference-of-squares
2×pow-to-exp pow-exp pow-sub sqr-pow
1×sub-neg rem-sqrt-square log-div pow-pow sqrt-pow1 pow1/2 div-sub log-pow div-inv
Counts
4 → 98
Calls
4 calls:
4.0ms
(pow (atan2 b b) (/ (- b a) 4))
14.0ms
(sin (* (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))) (pow (atan2 b b) (/ (- b a) 4))))
1.0ms
(sqrt (atan2 b b))
5.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(pow (atan2 b b) (/ (- b a) 4))
129.0ms
(sin (* (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))) (pow (atan2 b b) (/ (- b a) 4))))
9.0ms
(sqrt (atan2 b b))
81.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify1.5s

Counts
110 → 110
Iterations

Useful iterations: 3 (810.0ms)

IterNodesCost
02361826
15321626
211441485
331841407
done50001407

prune360.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

regimes48.0ms

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
11924
done1924

end0.0ms

sample2.3s

Algorithm
intervals
Results
794.0ms1843×body10240exit
617.0ms9963×body80nan
467.0ms7995×body80valid
1.0ms1×body2560valid
1.0ms1×body1280valid
0.0ms1×body640valid
0.0ms1×body320valid
0.0ms1×body160valid