Details

Time bar (total: 10.0m)

sample269.0ms

Algorithm
intervals
Results
91.0ms256×body80valid
59.0ms58×body10240exit
35.0ms327×body80nan

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
1139
2229
3459
41159
52689
68349
731979
done50019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite22.0ms

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 add-log-exp
2×unpow-prod-up 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 → 48
Calls
3 calls:
9.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
7.0ms
(pow (sqrt (atan2 b b)) (- b a))
3.0ms
(sqrt (atan2 b b))

series163.0ms

Counts
3 → 9
Calls
3 calls:
107.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
35.0ms
(pow (sqrt (atan2 b b)) (- b a))
20.0ms
(sqrt (atan2 b b))

simplify2.7s

Counts
57 → 57
Iterations

Useful iterations: 3 (334.0ms)

IterNodesCost
075614
1147571
2337536
3836527
42732527
done5001527

prune215.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
93×sqrt-prod
87×unpow-prod-down
82×add-sqr-sqrt
28×*-un-lft-identity
26×add-cube-cbrt
25×unswap-sqr
23×swap-sqr
17×add-exp-log
15×associate-*r* associate-*l* sqr-pow
14×unpow-prod-up
9×pow1 prod-exp
7×pow-to-exp sub-neg pow-exp
6×sqrt-pow1 add-cbrt-cube
5×pow-unpow pow-pow pow-sub
4×pow1/2 add-log-exp
2×rem-sqrt-square
1×pow2 frac-times associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up sqrt-pow2 cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
4 → 162
Calls
4 calls:
8.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
85.0ms
(* (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))

series154.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
80.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
20.0ms
(sqrt (atan2 b b))
15.0ms
(sqrt (atan2 b b))

simplify3.5s

Counts
174 → 174
Iterations

Useful iterations: done (3.5s)

IterNodesCost
01443870
12922885
29962741
337132692
done50012683

prune495.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(sin (* (pow 1 (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
0.0b
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-prod
9×unpow-prod-down
8×add-sqr-sqrt
7×pow1 add-cube-cbrt *-un-lft-identity
5×pow-pow sqrt-pow1
4×unpow-prod-up add-exp-log
3×pow1/2 add-cbrt-cube add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in
1×pow-to-exp rem-sqrt-square pow-unpow pow-exp sqrt-pow2 sqr-pow
Counts
3 → 50
Calls
3 calls:
40.0ms
(sin (* (pow 1 (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
7.0ms
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0ms
(sqrt (atan2 b b))

series8.7m

Counts
3 → 9
Calls
3 calls:
8.7m
(sin (* (pow 1 (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
41.0ms
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
18.0ms
(sqrt (atan2 b b))

simplify1.2s

Counts
59 → 59
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0101915
1223795
2499700
31579668
done5000610

prune145.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (log (sin (pow (sqrt (atan2 b b)) (- b a)))))
0.0b
(pow (sqrt (atan2 b b)) (- b a))
0.5b
(log (sin (pow (sqrt (atan2 b b)) (- b a))))
1.0b
(sqrt (atan2 b b))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×*-un-lft-identity
11×add-cube-cbrt
9×pow1
6×add-exp-log unpow-prod-down log-prod sqrt-prod
5×pow-unpow
4×exp-prod add-cbrt-cube add-log-exp
3×pow-pow exp-sum
2×unpow-prod-up sqrt-pow1 pow1/2 log-pow
1×pow-to-exp sub-neg rem-sqrt-square rem-log-exp pow-exp sqrt-pow2 rem-exp-log distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
4 → 68
Calls
4 calls:
9.0ms
(exp (log (sin (pow (sqrt (atan2 b b)) (- b a)))))
7.0ms
(pow (sqrt (atan2 b b)) (- b a))
7.0ms
(log (sin (pow (sqrt (atan2 b b)) (- b a))))
1.0ms
(sqrt (atan2 b b))

series191.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(exp (log (sin (pow (sqrt (atan2 b b)) (- b a)))))
22.0ms
(pow (sqrt (atan2 b b)) (- b a))
93.0ms
(log (sin (pow (sqrt (atan2 b b)) (- b a))))
11.0ms
(sqrt (atan2 b b))

simplify1.9s

Counts
80 → 80
Iterations

Useful iterations: 4 (944.0ms)

IterNodesCost
0102985
1190905
2417827
31017818
43191808
done5000808

prune185.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes92.0ms

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
01318
11718
done1718

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.0s1777×body10240exit
850.0ms9788×body80nan
641.0ms7988×body80valid
12.0ms4×body5120valid
1.0ms1×body2560valid
1.0ms5×body160valid
0.0ms1×body640valid
0.0ms1×body320valid

end59.2s