Details

analyze12.5s (16.1%)

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
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 115 to 84 computations (27% saved)

sample49.7s (63.9%)

Results

12.5s	1426×	body	4096	valid
9.4s	1768×	body	2048	valid
7.5s	863×	body	4096	invalid
6.7s	1161×	body	2048	invalid
3.5s	926×	body	1024	valid
2.8s	3539×	body	128	valid
2.5s	708×	body	1024	invalid
1.3s	68×	body	8192	valid
837.0ms	376×	body	512	valid
745.0ms	1084×	body	128	invalid
689.0ms	36×	body	8192	invalid
664.0ms	292×	body	512	invalid
211.0ms	153×	body	256	valid
173.0ms	132×	body	256	invalid

Compiler

Compiled 344 to 251 computations (27% saved)

simplify67.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

600×	`associate-/l/_binary64`
529×	`associate-/r/_binary64`
282×	`div-sub_binary64`
263×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	175
1	104	173
2	316	173
3	1431	170
4	4673	170
5	5335	170

prune11.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

40.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	43.1b	(fma.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 (+.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) (.f64 (.f64 (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 x-scale y-scale)) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 x-scale y-scale))) (.f64 4 (.f64 (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))))
▶	41.3b	(-.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)))

Status

Error

Program

43.1b

(fma.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 (+.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) (*.f64 (*.f64 (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 x-scale y-scale)) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 x-scale y-scale))) (*.f64 4 (*.f64 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))))

▶

41.3b

(-.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)))

Compiler

Compiled 670 to 459 computations (31.5% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.9b	(.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))
✓	26.1b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	26.4b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	32.2b	(-.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)))

series4.2s (5.4%)

Counts

4 → 144

Calls

4 calls:

3.3s	(-.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)))
891.0ms	(.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))
5.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
3.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite246.0ms (0.3%)

Algorithm

4×	egg-rewrite

Rules

47×	`egg`
20×	`egg`
18×	`egg`
18×	`egg`

Counts

4 → 103

Calls

4 calls:

77.0ms	(.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))
74.0ms	(-.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)))
45.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
43.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	133
1	914	127
2	5200	127
0	7	10
1	148	10
2	1736	10
3	4953	10
0	7	10
1	148	10
2	1736	10
3	4953	10
0	30	85
1	665	79
2	4959	79
3	5002	79

simplify302.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

465×	`times-frac_binary64`
431×	`fma-neg_binary64`
357×	`associate-/l*_binary64`
342×	`associate-r_binary64`
277×	`associate-/r*_binary64`

Counts

247 → 169

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	297	18027
1	1020	16993
2	4866	16993
3	5195	16993

prune1.5s (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	316	9	325
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	318	9	327

Error

24.2b

Counts

327 → 9

Alt Table

Status	Error	Program
	44.8b	(+.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2) (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 y-scale y-scale)))) (fma.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 y-scale y-scale))))) (sqrt.f64 (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 y-scale y-scale)))) (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (*.f64 y-scale y-scale)))))
	37.1b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale)))
	41.5b	(-.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))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 3)) (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)))
	37.4b	(neg.f64 (.f64 (.f64 a a) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (*.f64 x-scale x-scale))))))))
	41.0b	(-.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 b 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (pow.f64 a 2) (pow.f64 b 2))) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))) (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 b 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))))))
	41.5b	(-.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)))) (sqrt.f64 (pow.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) 2))) 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)))
	37.6b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	43.6b	(-.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))) (.f64 1/180 (.f64 angle (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)))
▶	28.0b	0

Compiler

Compiled 41640 to 28467 computations (31.6% saved)

localize0.0ms (0%)

prune32.0ms (0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

24.2b

Counts

9 → 9

Alt Table

Status	Error	Program
	44.8b	(+.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2) (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 y-scale y-scale)))) (fma.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 y-scale y-scale))))) (sqrt.f64 (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 y-scale y-scale)))) (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (*.f64 y-scale y-scale)))))
▶	37.1b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale)))
	41.5b	(-.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))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 3)) (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)))
	37.4b	(neg.f64 (.f64 (.f64 a a) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (*.f64 x-scale x-scale))))))))
	41.0b	(-.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 b 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (pow.f64 a 2) (pow.f64 b 2))) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))) (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 b 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))))))
	41.5b	(-.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)))) (sqrt.f64 (pow.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) 2))) 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)))
	37.6b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	43.6b	(-.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))) (.f64 1/180 (.f64 angle (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)))
✓	28.0b	0

Compiler

Compiled 1872 to 1292 computations (31% saved)

localize37.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	18.1b	(.f64 (.f64 a a) (*.f64 b b))
✓	19.2b	(/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale))
✓	26.1b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
✓	26.2b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series2.3s (3%)

Counts

4 → 92

Calls

4 calls:

2.3s	(/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale))
12.0ms	(.f64 (.f64 a a) (*.f64 b b))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
3.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

rewrite213.0ms (0.3%)

Algorithm

4×	egg-rewrite

Rules

62×	`egg`
22×	`egg`
22×	`egg`
22×	`egg`

Counts

4 → 128

Calls

4 calls:

75.0ms	(/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale))
45.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
45.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
44.0ms	(.f64 (.f64 a a) (*.f64 b b))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	140	10
2	1576	10
3	5161	10
0	7	10
1	140	10
2	1576	10
3	5162	10
0	37	123
1	801	111
2	4864	111
3	4959	111
0	6	10
1	123	7
2	1348	7
3	5084	7

simplify182.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-def_binary64`
445×	`unswap-sqr_binary64`
292×	`cancel-sign-sub-inv_binary64`
275×	`fma-neg_binary64`
238×	`associate-r_binary64`

Counts

220 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	7450
1	557	7298
2	2277	6763
3	4782	6763
4	4980	6763

prune656.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	209	7	216
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	215	10	225

Error

22.0b

Counts

225 → 10

Alt Table

Status	Error	Program
	36.6b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 b (.f64 a (.f64 a b)))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale)))
▶	31.4b	(neg.f64 (/.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))) y-scale) y-scale))
	38.5b	(neg.f64 (/.f64 (fma.f64 4 (.f64 (/.f64 (.f64 a a) x-scale) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 x-scale x-scale)))) (/.f64 (.f64 y-scale y-scale) (*.f64 b b))))
	37.6b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	38.8b	(neg.f64 (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (fma.f64 4 (.f64 (/.f64 (.f64 b b) x-scale) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 x-scale x-scale))))))
✓	28.0b	0
	37.8b	(neg.f64 (/.f64 (.f64 (pow.f64 a 2) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale 2))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 2)) (pow.f64 x-scale 2))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (pow.f64 x-scale 2)))))) (pow.f64 y-scale 2)))
	35.7b	(neg.f64 (pow.f64 (sqrt.f64 (.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))) (pow.f64 y-scale -2))) 2))
	35.2b	(neg.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))) (.f64 y-scale y-scale)))
	41.5b	(-.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)))) (sqrt.f64 (pow.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) 2))) 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)))

Compiler

Compiled 19744 to 10523 computations (46.7% saved)

localize35.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	14.1b	(.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64))))) 2))
✓	14.9b	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (*.f64 x-scale x-scale))
	26.1b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	26.2b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series351.0ms (0.5%)

Counts

2 → 84

Calls

2 calls:

214.0ms

(/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (pow.f64 (*.f64 a b) 2)) (*.f64 x-scale x-scale))

138.0ms

(*.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) a) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) 2))

rewrite206.0ms (0.3%)

Algorithm

2×	egg-rewrite

Rules

66×	`egg`
35×	`egg`

Counts

2 → 101

Calls

2 calls:

128.0ms

(*.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) a) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) 2))

76.0ms

(/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (pow.f64 (*.f64 a b) 2)) (*.f64 x-scale x-scale))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	378	25
2	4368	25
3	4990	25
0	16	31
1	329	31
2	3521	31
3	4919	31
4	4977	31
5	4906	31

simplify102.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-neg_binary64`
527×	`times-frac_binary64`
412×	`*-commutative_binary64`
367×	`associate-/l*_binary64`
314×	`unswap-sqr_binary64`

Counts

185 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	3172
1	260	3168
2	992	3122
3	4310	3122
4	5028	3122

prune921.0ms (1.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	227	8	235
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	230	15	245

Error

19.5b

Counts

245 → 15

Alt Table

Status	Error	Program
	41.5b	(-.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)))) (sqrt.f64 (pow.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) 2))) 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)))
	25.5b	(neg.f64 (/.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))))) 2) (pow.f64 x-scale -2))))) y-scale) y-scale))
	38.5b	(neg.f64 (/.f64 (fma.f64 4 (.f64 (/.f64 (.f64 a a) x-scale) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 x-scale x-scale)))) (/.f64 (.f64 y-scale y-scale) (*.f64 b b))))
	37.6b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	38.8b	(neg.f64 (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (fma.f64 4 (.f64 (/.f64 (.f64 b b) x-scale) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 x-scale x-scale))))))
	31.1b	(neg.f64 (/.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 (.f64 a b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) x-scale) 2)) 3) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))) y-scale) y-scale))
✓	28.0b	0
	37.8b	(neg.f64 (/.f64 (.f64 (pow.f64 a 2) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale 2))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 2)) (pow.f64 x-scale 2))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (pow.f64 x-scale 2)))))) (pow.f64 y-scale 2)))
	35.2b	(neg.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))) (.f64 y-scale y-scale)))
	25.5b	(neg.f64 (/.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))))) 2)) 3) (pow.f64 x-scale -2))))) y-scale) y-scale))
	26.9b	(neg.f64 (/.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))))) 2) 3) 1/3) (pow.f64 x-scale -2))))) y-scale) y-scale))
	36.6b	(neg.f64 (/.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (cbrt.f64 (pow.f64 x-scale 4))) (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (cbrt.f64 x-scale) 2))) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))) y-scale) y-scale))
	31.4b	(neg.f64 (/.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (exp.f64 (log.f64 (pow.f64 (/.f64 (.f64 (.f64 a b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) x-scale) 2))) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))) y-scale) y-scale))
	31.1b	(neg.f64 (/.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (.f64 (.f64 (.f64 a b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (.f64 (.f64 (.f64 a b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (pow.f64 x-scale -2))) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))) y-scale) y-scale))
	31.4b	(neg.f64 (/.f64 (/.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (pow.f64 (.f64 a b) 2)) x-scale) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))) y-scale) y-scale))

Compiler

Compiled 19709 to 12686 computations (35.6% saved)

regimes2.1s (2.7%)

Accuracy

Total 5.2b remaining (20.7%)

Threshold costs 0b (0%)

Counts

95 → 3

Compiler

Compiled 70578 to 49251 computations (30.2% saved)

bsearch1.3s (1.7%)

Steps

Iters	Range		Point
10	6.181985499258908e+46	2.360926834084748e+60	3.2690170656138226e+59
6	-1.2341836887308364e+212	-2.0224123572580359e+211	-2.3171389343851727e+211

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	124
1	61	124
2	67	124
3	72	124
4	75	124
5	76	124
6	76	124

end623.0ms (0.8%)

Compiler: Compiled 1246 to 885 computations (29% saved)

Details

analyze12.5s (16.1%)

sample49.7s (63.9%)

simplify67.0ms (0.1%)

prune11.0ms (0%)

localize40.0ms (0.1%)

series4.2s (5.4%)

rewrite246.0ms (0.3%)

simplify302.0ms (0.4%)

prune1.5s (2%)

localize0.0ms (0%)

prune32.0ms (0%)

localize37.0ms (0%)

series2.3s (3%)

rewrite213.0ms (0.3%)

simplify182.0ms (0.2%)

prune656.0ms (0.8%)

localize35.0ms (0%)

series351.0ms (0.5%)

rewrite206.0ms (0.3%)

simplify102.0ms (0.1%)

prune921.0ms (1.2%)

regimes2.1s (2.7%)

bsearch1.3s (1.7%)

simplify6.0ms (0%)

end623.0ms (0.8%)

Profiling