Details

Time bar (total: 23.7s)

sample178.0ms

Algorithm
intervals
Results
60.0ms54×body10240exit
47.0ms294×body80nan
32.0ms255×body80valid
1.0ms1×body320valid

simplify9.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1139
2229
3459
41179
54449
645969
done50019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.2b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite30.0ms

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:
9.0ms
(pow (sqrt (atan2 b b)) (- b a))
17.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms
(sqrt (atan2 b b))

series106.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(pow (sqrt (atan2 b b)) (- b a))
71.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
12.0ms
(sqrt (atan2 b b))

simplify685.0ms

Counts
72 → 72
Iterations

Useful iterations: done (683.0ms)

IterNodesCost
0117962
1315839
21100762
done5000737

prune246.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.3b
(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))

rewrite129.0ms

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:
87.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
30.0ms
(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))

series273.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
149.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
26.0ms
(sqrt (atan2 b b))
21.0ms
(sqrt (atan2 b b))

simplify2.9s

Counts
183 → 183
Iterations

Useful iterations: done (2.9s)

IterNodesCost
02094894
15003395
225993082
done50003036

prune689.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt (sqrt (sqrt (atan2 b b)))) (cbrt (sqrt (sqrt (atan2 b b)))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
81×sqrt-prod
72×cbrt-prod
70×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
18×swap-sqr
16×unswap-sqr
14×pow1
12×associate-*r* associate-*l*
6×add-exp-log pow1/3
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 123
Calls
4 calls:
46.0ms
(* (cbrt (sqrt (sqrt (atan2 b b)))) (cbrt (sqrt (sqrt (atan2 b b)))))
3.0ms
(sqrt (atan2 b b))
3.0ms
(sqrt (atan2 b b))
3.0ms
(sqrt (atan2 b b))

series194.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (cbrt (sqrt (sqrt (atan2 b b)))) (cbrt (sqrt (sqrt (atan2 b b)))))
14.0ms
(sqrt (atan2 b b))
19.0ms
(sqrt (atan2 b b))
20.0ms
(sqrt (atan2 b b))

simplify865.0ms

Counts
135 → 135
Iterations

Useful iterations: done (858.0ms)

IterNodesCost
0861934
11451740
26731684
done50001622

prune782.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (* (* (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))) (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
94.0ms
(sin (* (* (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))) (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a))))
2.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series309.0ms

Counts
4 → 12
Calls
4 calls:
257.0ms
(sin (* (* (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))) (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a))))
19.0ms
(sqrt (atan2 b b))
19.0ms
(sqrt (atan2 b b))
12.0ms
(sqrt (atan2 b b))

simplify1.0s

Counts
66 → 66
Iterations

Useful iterations: done (1.0s)

IterNodesCost
064812
1135767
2381697
31629595
done5000593

prune362.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes67.0ms

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
0920
done920

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.7s10000×body80nan
1.6s1832×body10240exit
1.4s7992×body80valid
2.0ms1×body2560valid
1.0ms3×body320valid
1.0ms3×body160valid
1.0ms1×body1280valid