Details

Time bar (total: 54.3s)

analyze9.4s (17.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
6.2%93.5%0.2%11
6.2%93.5%0.2%12
7.8%92%0.2%13
8.6%91.2%0.2%14
Compiler

Compiled 110 to 84 computations (23.6% saved)

sample1.2s (2.2%)

Algorithm
intervals
Results
264.0ms41×body4096valid
230.0ms61×body2048valid
215.0ms32×body4096invalid
173.0ms46×body2048invalid
81.0ms30×body1024valid
53.0ms111×body128valid
49.0ms21×body1024invalid
26.0msbody8192valid
16.0ms10×body512invalid
15.0ms36×body128invalid
11.0msbody512valid
3.0msbody256invalid
3.0msbody256valid
Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify116.0ms (0.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
05232172

prune15.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 42.0b

Counts
2 → 2
Compiler

Compiled 323 to 229 computations (29.1% saved)

localize46.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.8b
(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
26.8b
(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
26.8b
(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
29.3b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))

rewrite56.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
15×associate-*r/_binary64_20
frac-sub_binary64_87
associate-*l/_binary64_21
add-log-exp_binary64_117 frac-times_binary64_88
add-cbrt-cube_binary64_114 add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 add-exp-log_binary64_116 *-un-lft-identity_binary64_78 pow1_binary64_139
sub-div_binary64_85
flip3--_binary64_82 diff-log_binary64_170 flip--_binary64_53 cancel-sign-sub-inv_binary64_44 sub-neg_binary64_71
Counts
4 → 44
Calls

4 calls:

37.0ms
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))
2.0ms
(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms
(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

series1.6s (3%)

Counts
4 → 12
Calls

4 calls:

1.6s
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))
9.0ms
(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
9.0ms
(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
9.0ms
(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

simplify90.0ms (0.2%)

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
050655142

prune401.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New47956
Fresh101
Picked101
Done000
Total49958

Merged error: 32.1b

Counts
58 → 9
Compiler

Compiled 7566 to 5103 computations (32.6% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

5.2b
(*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale)))
9.4b
(*.f64 x-scale (*.f64 y-scale y-scale))
15.2b
(*.f64 (*.f64 b b) (*.f64 a a))
21.1b
(/.f64 (*.f64 (*.f64 b b) (*.f64 a a)) (*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale))))

rewrite54.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
132×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
79×cbrt-unprod_binary64_111 prod-exp_binary64_127
46×pow1_binary64_139
23×pow-prod-down_binary64_149
20×cbrt-undiv_binary64_112 div-exp_binary64_129
add-sqr-sqrt_binary64_100 associate-*l*_binary64_19
add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
add-log-exp_binary64_117 pow-prod-up_binary64_148 pow-plus_binary64_141
*-commutative_binary64_9 associate-*r*_binary64_18
pow2_binary64_159 pow-sqr_binary64_51 unswap-sqr_binary64_46
frac-2neg_binary64_89 times-frac_binary64_84 div-inv_binary64_75 associate-/l*_binary64_23 associate-/r*_binary64_22 clear-num_binary64_77
Counts
4 → 122
Calls

4 calls:

16.0ms
(/.f64 (*.f64 (*.f64 b b) (*.f64 a a)) (*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale))))
11.0ms
(*.f64 (*.f64 b b) (*.f64 a a))
7.0ms
(*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale)))
6.0ms
(*.f64 x-scale (*.f64 y-scale y-scale))

series163.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

82.0ms
(/.f64 (*.f64 (*.f64 b b) (*.f64 a a)) (*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale))))
29.0ms
(*.f64 x-scale (*.f64 y-scale y-scale))
26.0ms
(*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale)))
26.0ms
(*.f64 (*.f64 b b) (*.f64 a a))

simplify65.0ms (0.1%)

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049961898
149961898

prune157.0ms (0.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New12410134
Fresh538
Picked101
Done000
Total13013143

Merged error: 18.4b

Counts
143 → 13
Compiler

Compiled 3014 to 1368 computations (54.6% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (*.f64 b a) 2)
5.2b
(*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale)))
9.4b
(*.f64 x-scale (*.f64 y-scale y-scale))
21.1b
(/.f64 (pow.f64 (*.f64 b a) 2) (*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale))))

rewrite35.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
77×add-exp-log_binary64_116
38×prod-exp_binary64_127
32×add-cbrt-cube_binary64_114
21×pow1_binary64_139
16×div-exp_binary64_129
15×cbrt-unprod_binary64_111
10×add-sqr-sqrt_binary64_100 pow-exp_binary64_146 pow-prod-down_binary64_149
add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
associate-*l*_binary64_19 times-frac_binary64_84 associate-/l*_binary64_23
pow-to-exp_binary64_147
add-log-exp_binary64_117 cbrt-undiv_binary64_112
unpow-prod-down_binary64_157 unpow2_binary64_143 sqr-pow_binary64_50 pow-unpow_binary64_155
*-commutative_binary64_9 associate-*r*_binary64_18 pow-pow_binary64_150
frac-2neg_binary64_89 div-inv_binary64_75 associate-/r*_binary64_22 unswap-sqr_binary64_46 clear-num_binary64_77
Counts
4 → 101
Calls

4 calls:

10.0ms
(/.f64 (pow.f64 (*.f64 b a) 2) (*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale))))
7.0ms
(*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale)))
6.0ms
(*.f64 x-scale (*.f64 y-scale y-scale))
4.0ms
(pow.f64 (*.f64 b a) 2)

series151.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

73.0ms
(/.f64 (pow.f64 (*.f64 b a) 2) (*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale))))
28.0ms
(*.f64 x-scale (*.f64 x-scale (*.f64 y-scale y-scale)))
26.0ms
(*.f64 x-scale (*.f64 y-scale y-scale))
23.0ms
(pow.f64 (*.f64 b a) 2)

simplify66.0ms (0.1%)

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049981469
149981469

prune133.0ms (0.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New10112113
Fresh8412
Picked101
Done000
Total11016126

Merged error: 1.2b

Counts
126 → 16
Compiler

Compiled 2455 to 1205 computations (50.9% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 -4 (*.f64 (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale)))))
0.3b
(*.f64 (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))))
8.6b
(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
8.6b
(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))

rewrite46.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt_binary64_100
44×times-frac_binary64_84
37×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
35×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
32×associate-*l*_binary64_19
30×associate-*r*_binary64_18
20×pow1_binary64_139
12×cbrt-unprod_binary64_111 prod-exp_binary64_127
10×unswap-sqr_binary64_46
cbrt-undiv_binary64_112 div-exp_binary64_129
pow-prod-down_binary64_149
*-commutative_binary64_9 add-log-exp_binary64_117 div-inv_binary64_75
swap-sqr_binary64_45
frac-times_binary64_88 associate-*l/_binary64_21 associate-*r/_binary64_20
pow2_binary64_159 sqr-abs_binary64_93 pow-sqr_binary64_51 pow-prod-up_binary64_148 pow-plus_binary64_141
Counts
4 → 145
Calls

4 calls:

13.0ms
(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
11.0ms
(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
5.0ms
(*.f64 -4 (*.f64 (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale)))))
4.0ms
(*.f64 (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))))

series156.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

56.0ms
(*.f64 -4 (*.f64 (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale)))))
36.0ms
(*.f64 (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))))
34.0ms
(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
30.0ms
(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))

simplify76.0ms (0.1%)

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
050702268

prune159.0ms (0.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New14710157
Fresh31215
Picked101
Done000
Total15122173

Merged error: 1.0b

Counts
173 → 22
Compiler

Compiled 3504 to 826 computations (76.4% saved)

regimes2.5s (4.5%)

Compiler

Compiled 38364 to 27320 computations (28.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01834
11834

end0.0ms (0%)

sample37.7s (69.3%)

Algorithm
intervals
Results
9.2s1423×body4096valid
6.2s1658×body2048valid
5.7s844×body4096invalid
4.3s1139×body2048invalid
2.1s847×body1024valid
1.8s3503×body128valid
1.5s619×body1024invalid
847.0ms60×body8192valid
610.0ms377×body512valid
504.0ms35×body8192invalid
443.0ms1001×body128invalid
396.0ms254×body512invalid
130.0ms132×body256valid
100.0ms107×body256invalid
Compiler

Compiled 4897 to 3488 computations (28.8% saved)

Profiling

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