Details

Time bar (total: 13.2s)

sample68.0ms

Algorithm
intervals
Results
21.0ms56×body10240exit
17.0ms256×body80valid
14.0ms325×body80nan

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
1139
2229
3459
41109
52559
69209
737079
done50009

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

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))

rewrite13.0ms

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:
6.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms
(pow (sqrt (atan2 b b)) (- b a))
1.0ms
(sqrt (atan2 b b))

series91.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
16.0ms
(sqrt (atan2 b b))

simplify1.1s

Counts
72 → 72
Iterations

Useful iterations: 3 (366.0ms)

IterNodesCost
0117962
1252836
2599748
31979710
done5001710

prune152.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
93×sqrt-prod
87×unpow-prod-down
59×unpow-prod-up
58×*-un-lft-identity
56×add-cube-cbrt
45×prod-diff
32×swap-sqr
25×unswap-sqr
24×associate-*r* associate-*l*
17×add-exp-log
15×sqr-pow
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×expm1-log1p-u pow1/2 log1p-expm1-u 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 → 206
Calls
4 calls:
6.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
42.0ms
(* (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))

series88.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
41.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify984.0ms

Counts
218 → 218
Iterations

Useful iterations: 2 (252.0ms)

IterNodesCost
02105420
14583874
216313520
done50003520

prune470.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize14.0ms

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)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
29×*-un-lft-identity
27×add-cube-cbrt sqrt-prod
24×associate-*l*
22×unpow-prod-up
21×unpow-prod-down
18×prod-diff
10×add-exp-log
9×pow1
6×sqrt-pow1 add-cbrt-cube
5×pow-unpow pow-pow unswap-sqr
4×expm1-log1p-u pow1/2 log1p-expm1-u add-log-exp
3×associate-*r* prod-exp sqr-pow
2×pow-to-exp sub-neg rem-sqrt-square pow-exp pow-sub
1×associate-*l/ *-commutative sqrt-pow2 cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
4 → 121
Calls
4 calls:
5.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
21.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series130.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
82.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify2.9s

Counts
133 → 133
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01632396
13611893
210091714
349281634
done50001634

prune421.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (sqrt (cbrt (atan2 b b)))) (* 2 (- b a)))
0.0b
(pow (sqrt (fabs (cbrt (atan2 b b)))) (* 2 (- b a)))
1.0b
(cbrt (atan2 b b))
1.0b
(cbrt (atan2 b b))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
44×unpow-prod-up
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity prod-diff
22×distribute-rgt-in distribute-lft-in
18×unpow-prod-down sqrt-prod
9×pow1 cbrt-prod pow-pow
7×sqrt-pow1
6×add-exp-log
4×expm1-log1p-u sub-neg add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/2 pow1/3
2×pow-to-exp pow-unpow pow-exp sqrt-pow2 sqr-pow
Counts
4 → 125
Calls
4 calls:
10.0ms
(pow (sqrt (sqrt (cbrt (atan2 b b)))) (* 2 (- b a)))
5.0ms
(pow (sqrt (fabs (cbrt (atan2 b b)))) (* 2 (- b a)))
0.0ms
(cbrt (atan2 b b))
1.0ms
(cbrt (atan2 b b))

series271.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(pow (sqrt (sqrt (cbrt (atan2 b b)))) (* 2 (- b a)))
28.0ms
(pow (sqrt (fabs (cbrt (atan2 b b)))) (* 2 (- b a)))
103.0ms
(cbrt (atan2 b b))
108.0ms
(cbrt (atan2 b b))

simplify954.0ms

Counts
137 → 137
Iterations

Useful iterations: done (949.0ms)

IterNodesCost
02462975
14862508
212212183
done50012101

prune356.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes110.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
11222
done1222

end0.0ms

sample2.0s

Algorithm
intervals
Results
724.0ms1753×body10240exit
463.0ms9664×body80nan
443.0ms7986×body80valid
6.0ms2×body5120valid
1.0ms3×body640valid
1.0ms6×body160valid
1.0ms1×body1280valid
0.0ms2×body320valid