Details

analyze19.7s (17%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5141	1925
0	5	5
1	5	5

Search

True	Other	False	Iter
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)

sample2.5s (2.1%)

Algorithm

1×

intervals

Results

824.0ms	40×	body	2048	invalid
516.0ms	41×	body	4096	valid
403.0ms	52×	body	2048	valid
221.0ms	18×	body	4096	invalid
157.0ms	26×	body	1024	valid
128.0ms	117×	body	128	valid
48.0ms	10×	body	1024	invalid
41.0ms	13×	body	512	valid
29.0ms	31×	body	128	invalid
25.0ms	8×	body	512	invalid
14.0ms	7×	body	256	valid
10.0ms	5×	body	256	invalid

Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5232	172

prune28.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

39.1b

Counts

2 → 2

Compiler

Compiled 323 to 229 computations (29.1% saved)

localize95.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.6b	(-.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)))

rewrite114.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`associate-*r/_binary64_20`
9×	`frac-sub_binary64_87`
7×	`associate-*l/_binary64_21`
6×	`add-log-exp_binary64_117` `frac-times_binary64_88`
4×	`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`
2×	`sub-div_binary64_85`
1×	`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:

76.0ms	(-.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)))
4.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
4.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
4.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

series8.7s (7.5%)

Counts

4 → 24

Calls

4 calls:

8.5s	(-.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)))
60.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
59.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
58.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4404 to 3505 computations (20.4% saved)

simplify191.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	5067	6456

prune744.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Error

27.7b

Counts

70 → 7

Compiler

Compiled 8161 to 5291 computations (35.2% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

3.7b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
7.1b	(.f64 x-scale (.f64 y-scale y-scale))
14.8b	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
15.9b	(.f64 (.f64 b b) (*.f64 a a))

rewrite96.0ms (0.1%)

Algorithm

1×	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`
7×	`add-sqr-sqrt_binary64_100` `associate-l_binary64_19`
6×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`add-log-exp_binary64_117` `pow-prod-up_binary64_148` `pow-plus_binary64_141`
3×	`-commutative_binary64_9` `associate-r*_binary64_18`
2×	`pow2_binary64_159` `pow-sqr_binary64_51` `unswap-sqr_binary64_46`
1×	`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:

31.0ms	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
16.0ms	(.f64 (.f64 b b) (*.f64 a a))
14.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
11.0ms	(.f64 x-scale (.f64 y-scale y-scale))

series991.0ms (0.9%)

Counts

4 → 30

Calls

4 calls:

621.0ms	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
133.0ms	(.f64 (.f64 b b) (*.f64 a a))
128.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
107.0ms	(.f64 x-scale (.f64 y-scale y-scale))

Compiler

Compiled 1020 to 996 computations (2.4% saved)

simplify135.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4996	2177
1	4996	2177

prune305.0ms (0.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	144	8	152
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	147	12	159

Error

12.0b

Counts

159 → 12

Compiler

Compiled 3379 to 1416 computations (58.1% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (/.f64 (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))) (.f64 (.f64 b a) (.f64 b a))))
3.7b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
7.1b	(.f64 x-scale (.f64 y-scale y-scale))
14.5b	(/.f64 (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))) (.f64 (.f64 b a) (.f64 b a)))

rewrite145.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

450×	`add-exp-log_binary64_116`
257×	`prod-exp_binary64_127`
244×	`add-cbrt-cube_binary64_114`
133×	`cbrt-unprod_binary64_111`
122×	`div-exp_binary64_129`
61×	`cbrt-undiv_binary64_112`
21×	`1-exp_binary64_122` `rec-exp_binary64_128`
20×	`times-frac_binary64_84`
19×	`pow1_binary64_139`
17×	`add-sqr-sqrt_binary64_100`
16×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`pow-prod-down_binary64_149`
6×	`associate-l_binary64_19` `div-inv_binary64_75` `associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117` `associate-/l*_binary64_23`
2×	`-commutative_binary64_9` `frac-2neg_binary64_89` `associate-r*_binary64_18` `clear-num_binary64_77`
1×	`inv-pow_binary64_163` `pow-flip_binary64_152` `unswap-sqr_binary64_46` `associate-/r/_binary64_24`

Counts

4 → 213

Calls

4 calls:

33.0ms	(/.f64 1 (/.f64 (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))) (.f64 (.f64 b a) (.f64 b a))))
32.0ms	(/.f64 (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))) (.f64 (.f64 b a) (.f64 b a)))
14.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
10.0ms	(.f64 x-scale (.f64 y-scale y-scale))

series1.5s (1.3%)

Counts

4 → 36

Calls

4 calls:

643.0ms	(/.f64 (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))) (.f64 (.f64 b a) (.f64 b a)))
626.0ms	(/.f64 1 (/.f64 (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))) (.f64 (.f64 b a) (.f64 b a))))
132.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
101.0ms	(.f64 x-scale (.f64 y-scale y-scale))

Compiler

Compiled 1320 to 1308 computations (0.9% saved)

simplify232.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	4984	4839
1	4984	4839

prune448.0ms (0.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	240	9	249
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	245	16	261

Error

6.2b

Counts

261 → 16

Compiler

Compiled 5564 to 2445 computations (56.1% saved)

localize27.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 (.f64 x-scale y-scale)) (fabs.f64 (*.f64 x-scale y-scale)))
0.2b	(.f64 (.f64 b a) (*.f64 b a))
0.3b	(/.f64 1 (/.f64 (.f64 (fabs.f64 (.f64 x-scale y-scale)) (fabs.f64 (.f64 x-scale y-scale))) (.f64 (.f64 b a) (.f64 b a))))
14.5b	(/.f64 (.f64 (fabs.f64 (.f64 x-scale y-scale)) (fabs.f64 (.f64 x-scale y-scale))) (.f64 (.f64 b a) (.f64 b a)))

rewrite102.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

196×	`add-exp-log_binary64_116`
112×	`add-cbrt-cube_binary64_114`
93×	`prod-exp_binary64_127`
62×	`div-exp_binary64_129`
51×	`cbrt-unprod_binary64_111` `pow1_binary64_139`
31×	`cbrt-undiv_binary64_112`
20×	`add-sqr-sqrt_binary64_100` `times-frac_binary64_84`
18×	`add-cube-cbrt_binary64_113` `pow-prod-down_binary64_149` `*-un-lft-identity_binary64_78`
11×	`1-exp_binary64_122` `rec-exp_binary64_128`
6×	`div-inv_binary64_75` `associate-/r*_binary64_22`
5×	`pow-sqr_binary64_51` `pow-prod-up_binary64_148`
4×	`associate-l_binary64_19` `add-log-exp_binary64_117` `swap-sqr_binary64_45` `associate-r_binary64_18` `associate-/l*_binary64_23`
3×	`pow-plus_binary64_141`
2×	`pow2_binary64_159` `*-commutative_binary64_9` `frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`sqr-abs_binary64_93` `inv-pow_binary64_163` `pow-flip_binary64_152` `unswap-sqr_binary64_46` `associate-/r/_binary64_24`

Counts

4 → 173

Calls

4 calls:

25.0ms	(/.f64 1 (/.f64 (.f64 (fabs.f64 (.f64 x-scale y-scale)) (fabs.f64 (.f64 x-scale y-scale))) (.f64 (.f64 b a) (.f64 b a))))
21.0ms	(/.f64 (.f64 (fabs.f64 (.f64 x-scale y-scale)) (fabs.f64 (.f64 x-scale y-scale))) (.f64 (.f64 b a) (.f64 b a)))
12.0ms	(.f64 (.f64 b a) (*.f64 b a))
7.0ms	(.f64 (fabs.f64 (.f64 x-scale y-scale)) (fabs.f64 (*.f64 x-scale y-scale)))

series1.6s (1.4%)

Counts

4 → 36

Calls

4 calls:

716.0ms	(/.f64 1 (/.f64 (.f64 (fabs.f64 (.f64 x-scale y-scale)) (fabs.f64 (.f64 x-scale y-scale))) (.f64 (.f64 b a) (.f64 b a))))
702.0ms	(/.f64 (.f64 (fabs.f64 (.f64 x-scale y-scale)) (fabs.f64 (.f64 x-scale y-scale))) (.f64 (.f64 b a) (.f64 b a)))
132.0ms	(.f64 (.f64 b a) (*.f64 b a))
91.0ms	(.f64 (fabs.f64 (.f64 x-scale y-scale)) (fabs.f64 (*.f64 x-scale y-scale)))

Compiler

Compiled 1284 to 1272 computations (0.9% saved)

simplify193.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4988	3405
1	4988	3405

prune362.0ms (0.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	202	7	209
Fresh	7	8	15
Picked	1	0	1
Done	0	0	0
Total	210	15	225

Error

4.6b

Counts

225 → 15

Compiler

Compiled 4092 to 1519 computations (62.9% saved)

regimes3.7s (3.2%)

Accuracy

Total 0.9b remaining (16.6%)

Threshold costs 0.9b (16.6%)

Compiler

Compiled 35084 to 25120 computations (28.4% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	29
1	16	29

end0.0ms (0%)

sample1.2min (63.8%)

Algorithm

1×

intervals

Results

17.4s	1420×	body	4096	valid
12.1s	1662×	body	2048	valid
10.4s	810×	body	4096	invalid
8.5s	1151×	body	2048	invalid
4.4s	909×	body	1024	valid
3.6s	3429×	body	128	valid
3.4s	697×	body	1024	invalid
1.6s	59×	body	8192	valid
1.1s	367×	body	512	valid
1.1s	42×	body	8192	invalid
919.0ms	1027×	body	128	invalid
863.0ms	280×	body	512	invalid
284.0ms	154×	body	256	valid
207.0ms	110×	body	256	invalid

Compiler

Compiled 4484 to 3211 computations (28.4% saved)

Details

analyze19.7s (17%)

sample2.5s (2.1%)

simplify62.0ms (0.1%)

prune28.0ms (0%)

localize95.0ms (0.1%)

rewrite114.0ms (0.1%)

series8.7s (7.5%)

simplify191.0ms (0.2%)

prune744.0ms (0.6%)

localize23.0ms (0%)

rewrite96.0ms (0.1%)

series991.0ms (0.9%)

simplify135.0ms (0.1%)

prune305.0ms (0.3%)

localize22.0ms (0%)

rewrite145.0ms (0.1%)

series1.5s (1.3%)

simplify232.0ms (0.2%)

prune448.0ms (0.4%)

localize27.0ms (0%)

rewrite102.0ms (0.1%)

series1.6s (1.4%)

simplify193.0ms (0.2%)

prune362.0ms (0.3%)

regimes3.7s (3.2%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample1.2min (63.8%)

Profiling