Details

analyze12.6s (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
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)

sample48.1s (59.8%)

Results

12.7s	1426×	body	4096	valid
9.1s	1768×	body	2048	valid
7.2s	863×	body	4096	invalid
6.1s	1161×	body	2048	invalid
3.2s	926×	body	1024	valid
2.9s	3539×	body	128	valid
2.5s	708×	body	1024	invalid
1.2s	68×	body	8192	valid
871.0ms	376×	body	512	valid
747.0ms	1084×	body	128	invalid
666.0ms	292×	body	512	invalid
627.0ms	36×	body	8192	invalid
212.0ms	153×	body	256	valid
186.0ms	132×	body	256	invalid

Compiler

Compiled 344 to 251 computations (27% saved)

simplify40.0ms (0%)

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)

localize39.0ms (0%)

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)))

series3.7s (4.6%)

Counts

4 → 144

Calls

4 calls:

2.8s	(-.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)))
905.0ms	(.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))
4.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
3.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite82.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

87× egg-rr

Counts

4 → 87

Calls

2 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))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.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)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	238
1	914	226
2	5200	226
0	0	0
1	0	0

simplify304.0ms (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

231 → 155

Iterations

Useful iterations: 1 (0.0ms)

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

prune1.1s (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	284	9	293
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	286	9	295

Error

24.2b

Counts

295 → 9

Alt Table

Status	Error	Program
	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)))
	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))))
	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))))))))
	41.5b	(-.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)))
	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))))))))
	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)))))
▶	28.0b	0
	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)))
	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)))) 1) 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 37980 to 25897 computations (31.8% saved)

localize0.0ms (0%)

prune31.0ms (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
▶	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)))
	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))))
	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))))))))
	41.5b	(-.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)))
	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))))))))
	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)))))
✓	28.0b	0
	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)))
	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)))) 1) 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 1856 to 1280 computations (31% saved)

localize35.0ms (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))))

series1.7s (2.1%)

Counts

4 → 92

Calls

4 calls:

1.7s	(/.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))
11.0ms	(.f64 (.f64 a a) (*.f64 b b))
5.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
3.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

rewrite75.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

61× egg-rr

Counts

4 → 61

Calls

2 calls:

74.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	153
1	801	138
2	4864	138
3	4959	138
0	0	0
1	0	0

simplify163.0ms (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

153 → 93

Iterations

Useful iterations: 2 (0.0ms)

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

prune392.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	137	9	146

Error

22.7b

Counts

146 → 9

Alt Table

Status	Error	Program
	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)))
	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)))
▶	35.2b	(neg.f64 (pow.f64 (/.f64 (.f64 y-scale y-scale) (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)))))) -1))
	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)))) 1) 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)))
	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))
	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

Compiler

Compiled 12791 to 7001 computations (45.3% saved)

localize37.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
✓	18.1b	(/.f64 (.f64 y-scale y-scale) (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))))))
	26.1b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	26.2b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series5.4s (6.7%)

Counts

2 → 108

Calls

2 calls:

5.2s

(/.f64 (*.f64 y-scale y-scale) (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))))))

200.0ms

(/.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))

rewrite44.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

35× egg-rr

Counts

2 → 35

Calls

2 calls:

42.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	136
1	781	136
2	5383	136
0	0	0
1	0	0

simplify139.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

916×	`associate-/l*_binary64`
595×	`associate-/r*_binary64`
331×	`fma-def_binary64`
269×	`unswap-sqr_binary64`
212×	`associate-*l/_binary64`

Counts

143 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	8302
1	320	8158
2	1317	7340
3	5146	7340

prune582.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	140	11	151

Error

20.8b

Counts

151 → 11

Alt Table

Status	Error	Program
✓	28.0b	0
	37.5b	(neg.f64 (pow.f64 (/.f64 (.f64 y-scale y-scale) (.f64 (.f64 b b) (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)))))) -1))
	35.3b	(neg.f64 (pow.f64 (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 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)))))) -1))
	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)))) 1) 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)))
	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))
	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))))))
	29.9b	(neg.f64 (pow.f64 (pow.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 (.f64 a b) 2) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (.f64 8 (.f64 (pow.f64 x-scale -2) (pow.f64 (.f64 (.f64 a (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2))))) (.f64 y-scale y-scale)) -1) -1))
	29.9b	(neg.f64 (pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 y-scale y-scale) (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 (.f64 a b) 2) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (.f64 8 (.f64 (pow.f64 x-scale -2) (pow.f64 (.f64 (.f64 a (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2))))))) 2) -1))
	37.8b	(neg.f64 (pow.f64 (/.f64 (pow.f64 y-scale 2) (.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))))))) -1))

Compiler

Compiled 12183 to 7887 computations (35.3% saved)

regimes2.2s (2.8%)

Accuracy

Total 5.6b remaining (21%)

Threshold costs 0b (0%)

Counts

53 → 5

Compiler

Compiled 43964 to 30443 computations (30.8% saved)

bsearch3.3s (4.2%)

Steps

Iters	Range		Point
10	6.181985499258908e+46	2.360926834084748e+60	8.820974121076705e+56
7	1.2554971273801964e-150	3.0655792825731447e-148	1.8991933952856355e-150
10	-2.987988986991748e-56	-1.5258259993586639e-69	-1.5508134181418592e-69
8	-8.505198692469966e+126	-2.4256685579998474e+124	-4.542722851914629e+125

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	261
1	74	261
2	78	261
3	80	261
4	80	261

end452.0ms (0.6%)

Compiler: Compiled 1087 to 770 computations (29.2% saved)

Details

analyze12.6s (15.6%)

sample48.1s (59.8%)

simplify40.0ms (0%)

prune11.0ms (0%)

localize39.0ms (0%)

series3.7s (4.6%)

rewrite82.0ms (0.1%)

simplify304.0ms (0.4%)

prune1.1s (1.3%)

localize0.0ms (0%)

prune31.0ms (0%)

localize35.0ms (0%)

series1.7s (2.1%)

rewrite75.0ms (0.1%)

simplify163.0ms (0.2%)

prune392.0ms (0.5%)

localize37.0ms (0%)

series5.4s (6.7%)

rewrite44.0ms (0.1%)

simplify139.0ms (0.2%)

prune582.0ms (0.7%)

regimes2.2s (2.8%)

bsearch3.3s (4.2%)

simplify8.0ms (0%)

end452.0ms (0.6%)

Profiling