Details

Time bar (total: 15.4s)

sample415.0ms

Algorithm
intervals
Results
39.0ms305×body80nan
25.0ms57×body10240exit
14.0ms256×body80valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
079
1139
2229
3459
41159
52749
68379
732179
done50019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

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:
12.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
15.0ms
(pow (sqrt (atan2 b b)) (- b a))
4.0ms
(sqrt (atan2 b b))

series117.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
26.0ms
(pow (sqrt (atan2 b b)) (- b a))
20.0ms
(sqrt (atan2 b b))

simplify2.7s

Counts
72 → 72
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
0117962
1246836
2485757
31266728
44144699
done5000699

prune159.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
100×add-sqr-sqrt
84×sqrt-prod
78×unpow-prod-down
48×unpow-prod-up
46×add-cube-cbrt *-un-lft-identity
36×prod-diff
32×swap-sqr
25×unswap-sqr
24×associate-*r* associate-*l*
16×add-exp-log
14×sqr-pow
9×prod-exp
6×pow1 pow-to-exp sub-neg pow-exp add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u pow-sub add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow2 frac-times associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up cbrt-unprod
Counts
4 → 171
Calls
4 calls:
27.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
59.0ms
(* (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))

series166.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
43.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
15.0ms
(sqrt (atan2 b b))
12.0ms
(sqrt (atan2 b b))

simplify2.5s

Counts
183 → 183
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02094894
14343381
212473082
347012989
done50002988

prune425.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
0.0b
(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
0.8b
(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0b
(sqrt (atan2 b b))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
22×unpow-prod-up add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×prod-diff
12×sqrt-prod
11×distribute-rgt-in distribute-lft-in
9×pow1 unpow-prod-down
6×add-exp-log
5×pow-pow sqrt-pow1
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×log-prod pow1/2
2×sub-neg
1×pow-to-exp rem-sqrt-square pow-unpow rem-log-exp pow-exp log-pow sqrt-pow2 sqr-pow
Counts
4 → 88
Calls
4 calls:
10.0ms
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
24.0ms
(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
15.0ms
(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
2.0ms
(sqrt (atan2 b b))

series249.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
85.0ms
(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
118.0ms
(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
11.0ms
(sqrt (atan2 b b))

simplify1.9s

Counts
100 → 100
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02001956
14181708
28021499
324501388
done50001153

prune241.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
0.0b
(log1p (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
0.0b
(expm1 (log1p (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
1.0b
(sqrt (atan2 b b))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 expm1-log1p-u add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube log1p-expm1-u add-log-exp
3×sqrt-prod
1×rem-sqrt-square log1p-udef expm1-log1p sqrt-pow1 pow1/2 log1p-expm1 expm1-udef
Counts
4 → 46
Calls
4 calls:
22.0ms
(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
0.0ms
(log1p (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
0.0ms
(expm1 (log1p (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
2.0ms
(sqrt (atan2 b b))

series346.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
125.0ms
(log1p (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
125.0ms
(expm1 (log1p (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
12.0ms
(sqrt (atan2 b b))

simplify1.0s

Counts
58 → 58
Iterations

Useful iterations: done (1.0s)

IterNodesCost
080831
1139789
2316705
31081665
done5000637

prune188.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes36.0ms

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
01214
11314
done1314

end0.0ms

sample2.3s

Algorithm
intervals
Results
905.0ms1805×body10240exit
451.0ms9659×body80nan
433.0ms7991×body80valid
3.0ms1×body5120valid
2.0ms3×body1280valid
1.0ms1×body2560valid
0.0ms3×body160valid
0.0ms1×body640valid