Details

Time bar (total: 21.7s)

sample198.0ms

Algorithm
intervals
Results
44.0ms59×body10240exit
25.0ms327×body80nan
24.0ms255×body80valid
0.0ms1×body160valid

simplify1.9s

Counts
1 → 1
Iterations
IterNodes
done5001
61114
5256
4110
345
222
113
07

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

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))

rewrite57.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
2×sqrt-pow1 pow1/2
1×pow-to-exp rem-sqrt-square sub-neg pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
3 → 66
Calls
3 calls:
15.0ms
(pow (sqrt (atan2 b b)) (- b a))
22.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms
(sqrt (atan2 b b))

series155.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(pow (sqrt (atan2 b b)) (- b a))
98.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
23.0ms
(sqrt (atan2 b b))

simplify1.9s

Counts
75 → 75
Iterations
IterNodes
done5005
31669
2674
1311
0120

prune333.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

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)))
0.2b
(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))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
100×add-sqr-sqrt
84×sqrt-prod
78×unpow-prod-down
48×unpow-prod-up
46×*-un-lft-identity add-cube-cbrt
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×pow-to-exp pow1 sub-neg add-cbrt-cube pow-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u pow-sub add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow2 frac-times pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod
Counts
4 → 175
Calls
4 calls:
115.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
67.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
3.0ms
(sqrt (atan2 b b))
3.0ms
(sqrt (atan2 b b))

series246.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
144.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
20.0ms
(sqrt (atan2 b b))
22.0ms
(sqrt (atan2 b b))

simplify3.0s

Counts
187 → 187
Iterations
IterNodes
done5008
34083
21305
1501
0217

prune813.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity
16×add-cube-cbrt
11×unpow-prod-up
9×cbrt-prod unpow-prod-down prod-diff
6×pow1 sqrt-prod
5×pow-unpow add-exp-log
4×expm1-log1p-u pow-pow add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×sqrt-pow1
1×pow-to-exp sub-neg pow1/2 pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
4 → 82
Calls
4 calls:
9.0ms
(pow (sqrt (cbrt (atan2 b b))) (- b a))
48.0ms
(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (sqrt (cbrt (atan2 b b))) (- b a))))
1.0ms
(cbrt (atan2 b b))
2.0ms
(cbrt (atan2 b b))

series500.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(pow (sqrt (cbrt (atan2 b b))) (- b a))
172.0ms
(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (sqrt (cbrt (atan2 b b))) (- b a))))
165.0ms
(cbrt (atan2 b b))
129.0ms
(cbrt (atan2 b b))

simplify2.6s

Counts
94 → 94
Iterations
IterNodes
done5002
32810
2970
1404
0154

prune994.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (fabs (cbrt (atan2 b b))) (- b a))
0.2b
(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (cbrt (atan2 b b)) (/ (- b a) 2))))
1.0b
(cbrt (atan2 b b))
1.0b
(cbrt (atan2 b b))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity
14×add-cube-cbrt
11×unpow-prod-up
9×prod-diff
6×cbrt-prod
5×pow1 pow-unpow add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×unpow-prod-down
2×pow1/3
1×pow-to-exp sub-neg pow-pow pow-exp distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
4 → 72
Calls
4 calls:
7.0ms
(pow (fabs (cbrt (atan2 b b))) (- b a))
51.0ms
(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (cbrt (atan2 b b)) (/ (- b a) 2))))
1.0ms
(cbrt (atan2 b b))
1.0ms
(cbrt (atan2 b b))

series545.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (fabs (cbrt (atan2 b b))) (- b a))
194.0ms
(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (cbrt (atan2 b b)) (/ (- b a) 2))))
144.0ms
(cbrt (atan2 b b))
179.0ms
(cbrt (atan2 b b))

simplify2.1s

Counts
84 → 84
Iterations
IterNodes
done5022
32993
2873
1356
0140

prune438.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes110.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done13
113
012

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.2s1797×body10240exit
1.5s9799×body80nan
1.1s7991×body80valid
6.0ms4×body2560valid
3.0ms1×body5120valid
1.0ms3×body160valid
0.0ms1×body640valid