Details

Time bar (total: 5.1s)

sample314.0ms

Algorithm
intervals
Results
17.0ms47×body10240exit
15.0ms295×body80nan
14.0ms256×body80valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1225
2445
31145
43155
516095
650015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(pow (sqrt (atan2 b b)) (- b a))
1.0b
(sqrt (atan2 b b))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity
6×add-cube-cbrt unpow-prod-down sqrt-prod
5×pow1 pow-unpow
3×add-exp-log pow-pow
2×unpow-prod-up sqrt-pow1 pow1/2 add-cbrt-cube add-log-exp
1×pow-to-exp sub-neg rem-sqrt-square pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
2 → 41
Calls
2 calls:
5.0ms
(pow (sqrt (atan2 b b)) (- b a))
4.0ms
(sqrt (atan2 b b))

series49.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(pow (sqrt (atan2 b b)) (- b a))
16.0ms
(sqrt (atan2 b b))

simplify41.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (36.0ms)

IterNodesCost
0120239
1357224
21225224
35001222

prune99.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite30.0ms

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:
6.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
14.0ms
(* (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))

series88.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
38.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
13.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify51.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
02921754
113191646
250021602

prune339.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- b a))
0.6b
(cbrt (- b a))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity
10×cbrt-prod
8×add-cube-cbrt
6×pow1 sqrt-prod
4×add-exp-log cbrt-div add-cbrt-cube add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 pow1/3 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 56
Calls
4 calls:
3.0ms
(cbrt (- b a))
3.0ms
(cbrt (- b a))
1.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series315.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(cbrt (- b a))
150.0ms
(cbrt (- b a))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify114.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 4 (110.0ms)

IterNodesCost
0161308
1327296
2871290
32911276
45001272

prune260.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- b a))
0.7b
(pow (pow (sqrt (sqrt (atan2 b b))) (* (cbrt (- b a)) (cbrt (- b a)))) (* (cbrt (sqrt (- b a))) (cbrt (sqrt (- b a)))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
22×unpow-prod-down
15×add-sqr-sqrt sqrt-prod
13×*-un-lft-identity
11×add-cube-cbrt
6×pow1 add-exp-log
5×cbrt-prod
4×pow-exp add-cbrt-cube add-log-exp
2×pow-to-exp rem-sqrt-square cbrt-div sqrt-pow1 pow1/2 sqr-pow
1×pow-unpow flip3-- pow-pow pow1/3 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 68
Calls
4 calls:
3.0ms
(cbrt (- b a))
8.0ms
(pow (pow (sqrt (sqrt (atan2 b b))) (* (cbrt (- b a)) (cbrt (- b a)))) (* (cbrt (sqrt (- b a))) (cbrt (sqrt (- b a)))))
1.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series802.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(cbrt (- b a))
638.0ms
(pow (pow (sqrt (sqrt (atan2 b b))) (* (cbrt (- b a)) (cbrt (- b a)))) (* (cbrt (sqrt (- b a))) (cbrt (sqrt (- b a)))))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify54.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04811128
116191068
250011040

prune331.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01419
11419

end0.0ms

sample2.1s

Algorithm
intervals
Results
751.0ms1767×body10240exit
480.0ms9759×body80nan
443.0ms7992×body80valid
4.0ms3×body2560valid
3.0ms1×body5120valid
1.0ms2×body1280valid
1.0ms2×body320valid