Details

analyze17.5s (15.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5001	3121
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
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 184 to 125 computations (32.1% saved)

sample2.6s (2.3%)

Algorithm

1×

intervals

Results

1.3s	127×	body	4096	valid
859.0ms	48×	body	8192	valid
315.0ms	57×	body	2048	valid
51.0ms	15×	body	1024	valid
17.0ms	3×	body	2048	invalid
10.0ms	7×	body	256	valid
2.0ms	1×	body	512	valid
2.0ms	1×	body	512	invalid
1.0ms	1×	body	128	valid
1.0ms	1×	body	128	invalid

Compiler

Compiled 367 to 254 computations (30.8% saved)

simplify25.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5065	287

prune25.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

64.0b

Counts

2 → 1

Compiler

Compiled 360 to 236 computations (34.4% saved)

localize74.0ms (0.1%)

Local error

Found 4 expressions with local error:

29.9b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
29.9b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
29.9b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
37.5b	(-.f64 (+.f64 (/.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)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.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) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))

rewrite321.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-log-exp_binary64` `cancel-sign-sub-inv_binary64`
7×	`sqrt-prod_binary64`
6×	`add-cube-cbrt_binary64` `frac-sub_binary64` `sqrt-div_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`pow1_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
3×	`distribute-lft-out--_binary64`
2×	`diff-log_binary64` `frac-add_binary64` `difference-of-squares_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 53

Calls

4 calls:

283.0ms	(-.f64 (+.f64 (/.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)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.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) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))
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))

series11.7s (10.5%)

Counts

4 → 12

Calls

4 calls:

11.6s	(-.f64 (+.f64 (/.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)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.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) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))
13.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
9.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
8.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

simplify120.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5084	11841

prune825.0ms (0.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	2	66

Error

60.1b

Counts

66 → 2

Compiler

Compiled 15104 to 9051 computations (40.1% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

15.0b	(.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
16.3b	(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
17.8b	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0)
20.3b	(.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))

rewrite206.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

1310×	`add-exp-log_binary64`
1005×	`prod-exp_binary64`
542×	`add-cbrt-cube_binary64`
412×	`cbrt-unprod_binary64`
268×	`pow1_binary64`
218×	`pow-prod-down_binary64`
145×	`div-exp_binary64`
70×	`pow-exp_binary64`
40×	`cbrt-undiv_binary64`
35×	`pow-to-exp_binary64`
24×	`associate-l_binary64`
22×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
11×	`distribute-rgt-neg-out_binary64`
5×	`associate-r_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`unpow2_binary64` `distribute-lft-neg-out_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `*-commutative_binary64`
2×	`div-inv_binary64` `sqrt-prod_binary64`
1×	`associate-/l/_binary64` `associate-/r*_binary64` `mul0-rgt_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`

Counts

4 → 403

Calls

4 calls:

38.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
33.0ms	(.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))
16.0ms	(.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
11.0ms	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0)

series136.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
9.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
7.0ms	(.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))
3.0ms	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0)

simplify139.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

415 → 415

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5023	3009

prune555.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	414	1	415
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	415	2	417

Error

42.4b

Counts

417 → 2

Compiler

Compiled 11691 to 5074 computations (56.6% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.3b	(pow.f64 (*.f64 x-scale y-scale) 2)
14.3b	(.f64 0 (pow.f64 (.f64 x-scale y-scale) 2))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64` `prod-exp_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64`
2×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-pow_binary64` `unpow-prod-down_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `mul0-lft_binary64` `*-commutative_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms	(.f64 0 (pow.f64 (.f64 x-scale y-scale) 2))
4.0ms	(pow.f64 (*.f64 x-scale y-scale) 2)

series28.0ms (0%)

Counts

2 → 6

Calls

2 calls:

26.0ms	(pow.f64 (*.f64 x-scale y-scale) 2)
2.0ms	(.f64 0 (pow.f64 (.f64 x-scale y-scale) 2))

simplify65.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4835	286
1	4835	286

prune41.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	50	2	52

Error

41.4b

Counts

52 → 2

Compiler

Compiled 528 to 380 computations (28% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

41.4b

Counts

2 → 2

Compiler

Compiled 0 to 0 computations (0% saved)

regimes328.0ms (0.3%)

Accuracy

Total 0.2b remaining (0.5%)

Threshold costs 0.2b (0.5%)

Compiler

Compiled 4656 to 3426 computations (26.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	8
1	7	8

end0.0ms (0%)

sample1.3min (68.6%)

Algorithm

1×

intervals

Results

33.5s	3707×	body	4096	valid
28.4s	1523×	body	8192	valid
9.8s	1818×	body	2048	valid
2.1s	611×	body	1024	valid
445.0ms	207×	body	512	valid
186.0ms	30×	body	2048	invalid
129.0ms	90×	body	256	valid
93.0ms	9×	body	4096	invalid
71.0ms	21×	body	1024	invalid
34.0ms	17×	body	512	invalid
29.0ms	44×	body	128	valid
9.0ms	6×	body	256	invalid
6.0ms	9×	body	128	invalid

Compiler

Compiled 722 to 527 computations (27% saved)

Details

analyze17.5s (15.8%)

sample2.6s (2.3%)

simplify25.0ms (0%)

prune25.0ms (0%)

localize74.0ms (0.1%)

rewrite321.0ms (0.3%)

series11.7s (10.5%)

simplify120.0ms (0.1%)

prune825.0ms (0.7%)

localize18.0ms (0%)

rewrite206.0ms (0.2%)

series136.0ms (0.1%)

simplify139.0ms (0.1%)

prune555.0ms (0.5%)

localize6.0ms (0%)

rewrite11.0ms (0%)

series28.0ms (0%)

simplify65.0ms (0.1%)

prune41.0ms (0%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0%)

prune1.0ms (0%)

regimes328.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3min (68.6%)

Profiling