Details

analyze18.0s (15.6%)

Algorithm

1×

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)

sample2.7s (2.4%)

Algorithm

1×

intervals

Results

1.2s	111×	body	4096	valid
1.1s	60×	body	8192	valid
324.0ms	60×	body	2048	valid
43.0ms	13×	body	1024	valid
15.0ms	7×	body	512	valid
11.0ms	2×	body	2048	invalid
10.0ms	1×	body	4096	invalid
6.0ms	4×	body	256	valid
3.0ms	1×	body	1024	invalid
3.0ms	2×	body	256	invalid
2.0ms	1×	body	512	invalid
1.0ms	1×	body	128	valid

Compiler

Compiled 367 to 254 computations (30.8% saved)

simplify132.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5065	287

prune25.0ms (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

63.9b

Counts

2 → 2

Compiler

Compiled 543 to 360 computations (33.7% saved)

localize73.0ms (0.1%)

Local error

Found 4 expressions with local error:

30.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
39.0b	(-.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))))

rewrite323.0ms (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:

286.0ms	(-.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))))
3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

series11.9s (10.3%)

Counts

4 → 12

Calls

4 calls:

11.8s	(-.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))))
14.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
12.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
12.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

simplify136.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4971	11862
1	4971	11862

prune820.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	4	67

Error

60.2b

Counts

67 → 4

Compiler

Compiled 15479 to 9301 computations (39.9% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

16.1b	(.f64 (/.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)))) (pow.f64 (*.f64 x-scale y-scale) 2))
17.8b	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0)
18.0b	(/.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))))
23.0b	(.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))

rewrite219.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

1300×	`add-exp-log_binary64`
997×	`prod-exp_binary64`
526×	`add-cbrt-cube_binary64`
400×	`cbrt-unprod_binary64`
250×	`pow1_binary64`
205×	`pow-prod-down_binary64`
145×	`div-exp_binary64`
72×	`pow-exp_binary64`
40×	`cbrt-undiv_binary64`
36×	`pow-to-exp_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
8×	`distribute-rgt-neg-out_binary64` `times-frac_binary64`
5×	`associate-*l/_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`distribute-lft-neg-out_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
2×	`unpow2_binary64` `sqr-pow_binary64` `div-inv_binary64`
1×	`associate-/l/_binary64` `associate-/r*_binary64` `mul0-rgt_binary64` `clear-num_binary64` `unpow-prod-down_binary64` `frac-2neg_binary64` `sqrt-div_binary64`

Counts

4 → 386

Calls

4 calls:

41.0ms	(.f64 (/.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)))) (pow.f64 (*.f64 x-scale y-scale) 2))
34.0ms	(/.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))))
31.0ms	(.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))
11.0ms	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0)

series31.0ms (0%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(.f64 (/.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)))) (pow.f64 (*.f64 x-scale y-scale) 2))
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))))
8.0ms	(.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)

simplify173.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

398 → 398

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4715	2605
1	4715	2605

prune510.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	397	1	398
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	399	3	402

Error

41.5b

Counts

402 → 3

Compiler

Compiled 9640 to 4430 computations (54% 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

prune9.0ms (0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	0	0
Total	3	3

Error

41.5b

Counts

3 → 3

Compiler

Compiled 233 to 147 computations (36.9% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

14.2b	(/.f64 (.f64 a a) (.f64 y-scale y-scale))
15.8b	(.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
30.1b	(.f64 (/.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))) (.f64 2 (/.f64 (.f64 a a) (.f64 y-scale y-scale)))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
35.3b	(/.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))) (.f64 2 (/.f64 (.f64 a a) (.f64 y-scale y-scale)))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a))))

rewrite159.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

244×	`add-exp-log_binary64`
144×	`prod-exp_binary64`
100×	`add-cbrt-cube_binary64`
52×	`cbrt-unprod_binary64`
49×	`div-exp_binary64`
30×	`associate-l_binary64`
27×	`times-frac_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`pow1_binary64` `pow-exp_binary64`
19×	`*-un-lft-identity_binary64` `cbrt-undiv_binary64` `add-cube-cbrt_binary64`
13×	`pow-prod-down_binary64`
11×	`pow-to-exp_binary64`
7×	`associate-r_binary64`
5×	`unpow2_binary64` `associate-r/_binary64` `sqr-pow_binary64` `associate-/l_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `unpow-prod-down_binary64` `div-inv_binary64`
3×	`associate-/l/_binary64` `distribute-rgt-neg-out_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64` `sqrt-div_binary64`
2×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`
1×	`frac-times_binary64`

Counts

4 → 182

Calls

4 calls:

49.0ms	(/.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))) (.f64 2 (/.f64 (.f64 a a) (.f64 y-scale y-scale)))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a))))
47.0ms	(.f64 (/.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))) (.f64 2 (/.f64 (.f64 a a) (.f64 y-scale y-scale)))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
16.0ms	(.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
7.0ms	(/.f64 (.f64 a a) (.f64 y-scale y-scale))

series225.0ms (0.2%)

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))))
55.0ms	(/.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))) (.f64 2 (/.f64 (.f64 a a) (.f64 y-scale y-scale)))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a))))
32.0ms	(.f64 (/.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))) (.f64 2 (/.f64 (.f64 a a) (.f64 y-scale y-scale)))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
20.0ms	(/.f64 (.f64 a a) (.f64 y-scale y-scale))

simplify112.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4964	7256
1	4964	7256

prune382.0ms (0.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	186	8	194
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	187	10	197

Error

37.5b

Counts

197 → 10

Compiler

Compiled 10432 to 3933 computations (62.3% saved)

regimes1.3s (1.1%)

Accuracy

Total 5.2b remaining (12.3%)

Threshold costs 0b (0%)

Compiler

Compiled 21336 to 13850 computations (35.1% saved)

bsearch955.0ms (0.8%)

Steps

Iters	Range		Point
9	8.118014839616776e-213	4.980557417614125e-207	6.425263427286898e-208
9	5.956810933050399e-268	4.075245114934005e-263	1.3968060922336803e-264

Compiler

Compiled 3 to 7 computations (-133.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	30
1	25	30

end0.0ms (0%)

sample1.3min (66.9%)

Algorithm

1×

intervals

Results

33.1s	3630×	body	4096	valid
28.9s	1554×	body	8192	valid
10.1s	1815×	body	2048	valid
2.1s	617×	body	1024	valid
501.0ms	225×	body	512	valid
190.0ms	33×	body	2048	invalid
165.0ms	110×	body	256	valid
144.0ms	40×	body	1024	invalid
38.0ms	49×	body	128	valid
20.0ms	9×	body	512	invalid
19.0ms	2×	body	4096	invalid
12.0ms	8×	body	256	invalid
7.0ms	11×	body	128	invalid

Compiler

Compiled 2823 to 1842 computations (34.8% saved)

Details

analyze18.0s (15.6%)

sample2.7s (2.4%)

simplify132.0ms (0.1%)

prune25.0ms (0%)

localize73.0ms (0.1%)

rewrite323.0ms (0.3%)

series11.9s (10.3%)

simplify136.0ms (0.1%)

prune820.0ms (0.7%)

localize23.0ms (0%)

rewrite219.0ms (0.2%)

series31.0ms (0%)

simplify173.0ms (0.1%)

prune510.0ms (0.4%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0%)

prune9.0ms (0%)

localize23.0ms (0%)

rewrite159.0ms (0.1%)

series225.0ms (0.2%)

simplify112.0ms (0.1%)

prune382.0ms (0.3%)

regimes1.3s (1.1%)

bsearch955.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3min (66.9%)

Profiling