Details

Time bar (total: 19.9s)

sample119.0ms

Algorithm
intervals
Results
44.0ms59×body10240exit
28.0ms327×body80nan
25.0ms255×body80valid
0.0ms1×body160valid

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done5019
61161
5250
4110
345
222
113
07

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity
7×add-cube-cbrt
6×pow1 unpow-prod-down sqrt-prod
5×pow-unpow
4×add-exp-log
3×pow-pow add-cbrt-cube insert-posit16 add-log-exp
2×unpow-prod-up 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 → 51
Calls
3 calls:
13.0ms
(pow (sqrt (atan2 b b)) (- b a))
19.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms
(sqrt (atan2 b b))

series141.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(pow (sqrt (atan2 b b)) (- b a))
78.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
25.0ms
(sqrt (atan2 b b))

simplify2.6s

Counts
60 → 60
Iterations
IterNodes
done5007
43718
31092
2392
1184
078

prune243.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

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))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
84×sqrt-prod
78×unpow-prod-down
76×add-sqr-sqrt
25×unswap-sqr
23×swap-sqr
22×*-un-lft-identity add-cube-cbrt
16×add-exp-log
15×associate-*r* associate-*l*
14×sqr-pow
12×unpow-prod-up
9×prod-exp
6×pow-to-exp pow1 sub-neg add-cbrt-cube pow-exp
4×insert-posit16 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 → 140
Calls
4 calls:
83.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
60.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
2.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series206.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
100.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
18.0ms
(sqrt (atan2 b b))
19.0ms
(sqrt (atan2 b b))

simplify3.0s

Counts
152 → 152
Iterations
IterNodes
done5001
33171
2930
1318
0149

prune635.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize36.0ms

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))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×cbrt-prod unpow-prod-down
6×pow1 sqrt-prod
5×pow-unpow add-exp-log
4×pow-pow add-cbrt-cube insert-posit16 add-log-exp
3×pow1/3
2×unpow-prod-up 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 → 65
Calls
4 calls:
15.0ms
(pow (sqrt (cbrt (atan2 b b))) (- b a))
31.0ms
(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (sqrt (cbrt (atan2 b b))) (- b a))))
1.0ms
(cbrt (atan2 b b))
1.0ms
(cbrt (atan2 b b))

series508.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(pow (sqrt (cbrt (atan2 b b))) (- b a))
182.0ms
(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (sqrt (cbrt (atan2 b b))) (- b a))))
146.0ms
(cbrt (atan2 b b))
138.0ms
(cbrt (atan2 b b))

simplify1.8s

Counts
77 → 77
Iterations
IterNodes
done5003
31671
2653
1274
0112

prune557.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize53.0ms

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))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
6×cbrt-prod
5×pow1 pow-unpow add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
3×unpow-prod-down
2×unpow-prod-up pow1/3
1×pow-to-exp sub-neg pow-pow pow-exp distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
4 → 55
Calls
4 calls:
14.0ms
(pow (fabs (cbrt (atan2 b b))) (- b a))
53.0ms
(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (cbrt (atan2 b b)) (/ (- b a) 2))))
1.0ms
(cbrt (atan2 b b))
2.0ms
(cbrt (atan2 b b))

series568.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(pow (fabs (cbrt (atan2 b b))) (- b a))
220.0ms
(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (cbrt (atan2 b b)) (/ (- b a) 2))))
198.0ms
(cbrt (atan2 b b))
126.0ms
(cbrt (atan2 b b))

simplify1.8s

Counts
67 → 67
Iterations
IterNodes
done5002
31859
2578
1227
098

prune366.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes74.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done13
113
012

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.0s9799×body80nan
1.8s1797×body10240exit
1.0s7991×body80valid
7.0ms4×body2560valid
3.0ms1×body5120valid
1.0ms3×body160valid
1.0ms1×body640valid