Details

analyze22.0s (18.8%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
5.3%	94.5%	0.2%	11
6.1%	93.6%	0.2%	12
9.2%	90.6%	0.2%	13
13.8%	85.9%	0.2%	14

Compiler

Compiled 175 to 127 computations (27.4% saved)

sample54.3s (46.4%)

Results

19.5s	1705×	body	4096	valid
11.5s	1495×	body	2048	valid
10.2s	1641×	body	1024	valid
6.2s	83×	body	8192	exit
3.1s	751×	body	512	valid
3.0s	2347×	body	128	valid
828.0ms	317×	body	256	valid

Compiler

Compiled 524 to 380 computations (27.5% saved)

simplify22.0ms (0%)

Algorithm

1×	egg-herbie

Rules

637×	`times-frac_binary64`
293×	`associate-/l/_binary64`
243×	`div-sub_binary64`
198×	`fma-def_binary64`
174×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	273
1	115	265
2	345	265
3	1608	265

Stop Event

1×	node limit

Counts

1 → 2

prune16.0ms (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

52.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	53.3b	(.f64 180 (/.f64 (atan.f64 (.f64 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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	56.1b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.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) (/.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)) (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 (.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) 2)))) (/.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))) (PI.f64)))

Status

Error

Program

▶

53.3b

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

56.1b

(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.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) (/.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)) (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 (*.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) 2)))) (/.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))) (PI.f64)))

Compiler

Compiled 1024 to 708 computations (30.9% saved)

localize48.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	15.2b	(/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))
✓	25.0b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	25.5b	(-.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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))
✓	25.6b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

series16.5s (14.1%)

Counts

4 → 132

Calls

4 calls:

16.4s	(-.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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))
160.0ms	(/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))
3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite83.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

444×	`log1p-expm1-u_binary64`
444×	`expm1-log1p-u_binary64`
411×	`pow1_binary64`
147×	`unpow-prod-down_binary64`
145×	`log-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	271
1	917	254

Stop Event

1×	node limit

Counts

4 → 78

Calls

4 calls:

77.0ms	(/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (*.f64 x-scale x-scale))
77.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
77.0ms	(-.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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))
77.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

simplify1.5s (1.3%)

Algorithm

1×	egg-herbie

Rules

979×	`fma-def_binary64`
1×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4322	282855

Stop Event

1×	node limit

Counts

210 → 185

prune9.2s (7.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	424	11	435
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	425	12	437

Error

44.2b

Counts

437 → 12

Alt Table

Status	Error	Program
▶	50.9b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 b 2) (sqrt.f64 (fma.f64 2 (.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)))) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 4) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))))))) (pow.f64 x-scale 2))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	59.5b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (sqrt.f64 (fma.f64 (pow.f64 b 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (fma.f64 2 (.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 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 a 4)))))) (pow.f64 y-scale 2)) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	59.6b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 y-scale 2)) (+.f64 (sqrt.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 x-scale 4)) (fma.f64 3 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 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 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 y-scale 4)))) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2))))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 x-scale 2)))) (pow.f64 b 2)) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	54.1b	(.f64 180 (/.f64 (atan.f64 (.f64 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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 1 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	52.8b	(.f64 180 (/.f64 (atan.f64 (.f64 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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (-.f64 1 (.f64 1/64800 (.f64 (pow.f64 angle 2) (pow.f64 (PI.f64) 2)))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	55.3b	(.f64 180 (/.f64 (atan.f64 (.f64 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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (-.f64 1 (.f64 1/64800 (.f64 (pow.f64 angle 2) (pow.f64 (PI.f64) 2)))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	56.1b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.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) (/.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)) (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 (.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) 2)))) (/.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))) (PI.f64)))
	55.7b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (-.f64 (.f64 1/180 (.f64 angle (PI.f64))) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 (PI.f64) 3))))) 2)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	54.2b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (fma.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64)))) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 y-scale -2) (neg.f64 (fma.f64 (pow.f64 (hypot.f64 (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) a) (.f64 (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 x-scale -2) (hypot.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) a) (.f64 (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 x-scale -2)) (.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64)))) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 y-scale -2))) (/.f64 (.f64 (/.f64 2 y-scale) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 x-scale (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	54.1b	(.f64 180 (/.f64 (atan.f64 (.f64 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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 1 (.f64 1/64800 (.f64 (pow.f64 angle 2) (pow.f64 (PI.f64) 2))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	61.5b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 (pow.f64 a 2) (-.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 y-scale 2)) (+.f64 (sqrt.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 x-scale 4)) (fma.f64 3 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 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 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 y-scale 4)))) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2))))) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 x-scale 2))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	60.4b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64)))) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 y-scale -2)) (fma.f64 (pow.f64 (hypot.f64 (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) a) (.f64 (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 x-scale -2) (hypot.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) a) (.f64 (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 x-scale -2)) (.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64)))) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 y-scale -2))) (/.f64 (.f64 (/.f64 2 y-scale) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 x-scale (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64)))))))) 3) 1/3) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))

Compiler

Compiled 342383 to 240416 computations (29.8% saved)

localize58.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	24.8b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	25.0b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	25.6b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	25.6b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

series5.0ms (0%)

Counts

2 → 8

Calls

2 calls:

3.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
2.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

rewrite38.0ms (0%)

Algorithm

1×	batch-egg-rewrite

Rules

677×	`log1p-expm1-u_binary64`
677×	`expm1-log1p-u_binary64`
324×	`prod-diff_binary64`
144×	`log1p-udef_binary64`
80×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	159	20
2	1850	20

Stop Event

1×	node limit

Counts

2 → 36

Calls

2 calls:

37.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
37.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

simplify28.0ms (0%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-neg_binary64`
606×	`distribute-rgt-neg-in_binary64`
600×	`distribute-lft-neg-in_binary64`
422×	`associate-r_binary64`
387×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	216
1	159	212
2	536	206
3	2802	206

Stop Event

1×	node limit

Counts

44 → 51

prune1.8s (1.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	192	5	197
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	194	15	209

Error

44.1b

Counts

209 → 15

Alt Table

Status	Error	Program
	51.3b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 b 2) (sqrt.f64 (fma.f64 2 (.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)))) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 4) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))))))) (pow.f64 x-scale 2))) (/.f64 (.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	59.5b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (sqrt.f64 (fma.f64 (pow.f64 b 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (fma.f64 2 (.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 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 a 4)))))) (pow.f64 y-scale 2)) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	59.6b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 y-scale 2)) (+.f64 (sqrt.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 x-scale 4)) (fma.f64 3 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 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 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 y-scale 4)))) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2))))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 x-scale 2)))) (pow.f64 b 2)) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	51.9b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 b 2) (sqrt.f64 (fma.f64 2 (.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)))) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 4) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))))))) (pow.f64 x-scale 2))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 1 (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	54.1b	(.f64 180 (/.f64 (atan.f64 (.f64 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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 1 (.f64 1/64800 (.f64 (pow.f64 angle 2) (pow.f64 (PI.f64) 2))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	61.5b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 (pow.f64 a 2) (-.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 y-scale 2)) (+.f64 (sqrt.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 x-scale 4)) (fma.f64 3 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 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 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 y-scale 4)))) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2))))) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 x-scale 2))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
▶	51.3b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 b 2) (sqrt.f64 (fma.f64 2 (.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)))) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 4) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))))))) (pow.f64 x-scale 2))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	54.1b	(.f64 180 (/.f64 (atan.f64 (.f64 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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 1 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	52.8b	(.f64 180 (/.f64 (atan.f64 (.f64 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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (-.f64 1 (.f64 1/64800 (.f64 (pow.f64 angle 2) (pow.f64 (PI.f64) 2)))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	55.8b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 b 2) (sqrt.f64 (fma.f64 2 (.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)))) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 4) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))))))) (pow.f64 x-scale 2))) (/.f64 (.f64 (log.f64 (exp.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	56.1b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.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) (/.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)) (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 (.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) 2)))) (/.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))) (PI.f64)))
	55.7b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (-.f64 (.f64 1/180 (.f64 angle (PI.f64))) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 (PI.f64) 3))))) 2)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	54.2b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (fma.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64)))) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 y-scale -2) (neg.f64 (fma.f64 (pow.f64 (hypot.f64 (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) a) (.f64 (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 x-scale -2) (hypot.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) a) (.f64 (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 x-scale -2)) (.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64)))) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 y-scale -2))) (/.f64 (.f64 (/.f64 2 y-scale) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 x-scale (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	53.7b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 b 2) (sqrt.f64 (fma.f64 2 (.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)))) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 4) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))))))) (pow.f64 x-scale 2))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (-.f64 1 (.f64 1/64800 (.f64 (pow.f64 angle 2) (pow.f64 (PI.f64) 2)))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	60.4b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64)))) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 y-scale -2)) (fma.f64 (pow.f64 (hypot.f64 (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) a) (.f64 (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 x-scale -2) (hypot.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) a) (.f64 (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 x-scale -2)) (.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64)))) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 y-scale -2))) (/.f64 (.f64 (/.f64 2 y-scale) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 x-scale (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64)))))))) 3) 1/3) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))

Compiler

Compiled 28354 to 19281 computations (32% saved)

localize56.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	22.1b	(/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 b 2) (sqrt.f64 (fma.f64 2 (.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)))) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 4) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))))))) (pow.f64 x-scale 2))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale))
	24.8b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	25.6b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	25.6b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

series1.4s (1.2%)

Counts

1 → 60

Calls

1 calls:

1.4s

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

rewrite42.0ms (0%)

Algorithm

1×	batch-egg-rewrite

Rules

446×	`log1p-expm1-u_binary64`
446×	`expm1-log1p-u_binary64`
422×	`pow1_binary64`
162×	`log-prod_binary64`
129×	`exp-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	165
1	993	159

Stop Event

1×	node limit

Counts

1 → 18

Calls

1 calls:

40.0ms

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

simplify137.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

805×	`times-frac_binary64`
446×	`associate-/l*_binary64`
428×	`associate-/r*_binary64`
283×	`*-commutative_binary64`
263×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	498	13152
1	1739	12008

Stop Event

1×	node limit

Counts

78 → 46

prune856.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	238	8	246
Fresh	10	4	14
Picked	1	0	1
Done	0	0	0
Total	249	12	261

Error

19.0b

Counts

261 → 12

Alt Table

Status	Error	Program
	56.1b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.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) (/.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)) (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 (.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) 2)))) (/.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))) (PI.f64)))
	35.9b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 y-scale (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (.f64 (pow.f64 x-scale 2) (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))))))) (PI.f64)))
	54.1b	(.f64 180 (/.f64 (atan.f64 (.f64 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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 1 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	51.8b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 b 2) (sqrt.f64 (fma.f64 2 (.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)))) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 4) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))))))) (pow.f64 x-scale 2))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sqrt.f64 (pow.f64 (cos.f64 (.f64 angle (.f64 (PI.f64) 1/180))) 2)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	52.8b	(.f64 180 (/.f64 (atan.f64 (.f64 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)) (.f64 y-scale y-scale)) (+.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (hypot.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) (.f64 x-scale x-scale)) (/.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)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 y-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (-.f64 (.f64 b b) (.f64 a a))) (/.f64 x-scale (-.f64 1 (.f64 1/64800 (.f64 (pow.f64 angle 2) (pow.f64 (PI.f64) 2)))))))))) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	51.3b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 b 2) (sqrt.f64 (fma.f64 2 (.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)))) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 4) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))))))) (pow.f64 x-scale 2))) (/.f64 (.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	49.4b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (neg.f64 (.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) b) 2) (sqrt.f64 (fma.f64 2 (.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)) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) b) 4) (pow.f64 (.f64 a (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 4)))))) (pow.f64 x-scale -2))) (/.f64 1 (/.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) (/.f64 y-scale (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))))))))) (PI.f64)))
	59.4b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (-.f64 (+.f64 (.f64 1/32400 (/.f64 (.f64 y-scale (.f64 angle (.f64 (pow.f64 (PI.f64) 2) (pow.f64 b 2)))) (-.f64 (.f64 1/180 (.f64 (pow.f64 x-scale 2) (.f64 (PI.f64) (pow.f64 b 2)))) (.f64 1/180 (.f64 (pow.f64 x-scale 2) (.f64 (PI.f64) (pow.f64 a 2))))))) (.f64 1/8748000 (/.f64 (.f64 y-scale (.f64 (pow.f64 x-scale 2) (.f64 angle (.f64 (pow.f64 (PI.f64) 3) (.f64 (pow.f64 a 2) (pow.f64 b 2)))))) (pow.f64 (-.f64 (.f64 1/180 (.f64 (pow.f64 x-scale 2) (.f64 (PI.f64) (pow.f64 b 2)))) (.f64 1/180 (.f64 (pow.f64 x-scale 2) (.f64 (PI.f64) (pow.f64 a 2))))) 2)))) (+.f64 (.f64 1/8748000 (/.f64 (.f64 y-scale (.f64 (pow.f64 x-scale 2) (.f64 angle (.f64 (pow.f64 (PI.f64) 3) (pow.f64 b 4))))) (pow.f64 (-.f64 (.f64 1/180 (.f64 (pow.f64 x-scale 2) (.f64 (PI.f64) (pow.f64 b 2)))) (.f64 1/180 (.f64 (pow.f64 x-scale 2) (.f64 (PI.f64) (pow.f64 a 2))))) 2))) (+.f64 (/.f64 (.f64 y-scale (pow.f64 b 2)) (.f64 angle (-.f64 (.f64 1/180 (.f64 (pow.f64 x-scale 2) (.f64 (PI.f64) (pow.f64 b 2)))) (.f64 1/180 (.f64 (pow.f64 x-scale 2) (.f64 (PI.f64) (pow.f64 a 2))))))) (.f64 1/32400 (/.f64 (.f64 y-scale (.f64 angle (.f64 (pow.f64 a 2) (pow.f64 (PI.f64) 2)))) (-.f64 (.f64 1/180 (.f64 (pow.f64 x-scale 2) (.f64 (PI.f64) (pow.f64 b 2)))) (.f64 1/180 (.f64 (pow.f64 x-scale 2) (*.f64 (PI.f64) (pow.f64 a 2)))))))))))) (PI.f64)))
▶	35.8b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (/.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))))))) (PI.f64)))
	38.7b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (.f64 x-scale x-scale)) (neg.f64 (/.f64 y-scale (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))))))) (PI.f64)))
	38.1b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 -1 (/.f64 (.f64 y-scale (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (.f64 (pow.f64 x-scale 2) (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64))))))))) (PI.f64)))
	53.4b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (exp.f64 (log.f64 (.f64 (/.f64 (neg.f64 (.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) b) 2) (sqrt.f64 (fma.f64 2 (.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)) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) b) 4) (pow.f64 (.f64 a (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 4)))))) (pow.f64 x-scale -2))) (.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))))) y-scale))))) (PI.f64)))

Compiler

Compiled 35593 to 23382 computations (34.3% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.5b	(/.f64 y-scale (*.f64 x-scale x-scale))
✓	14.0b	(.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (/.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (cos.f64 (.f64 1/180 (*.f64 angle (PI.f64)))))))
	24.8b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	25.6b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series100.0ms (0.1%)

Counts

2 → 60

Calls

2 calls:

76.0ms

(*.f64 x-scale (*.f64 (/.f64 y-scale (*.f64 x-scale x-scale)) (/.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))))

23.0ms

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

rewrite60.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

375×	`prod-diff_binary64`
163×	`add-sqr-sqrt_binary64`
159×	`associate-r_binary64`
151×	`add-log-exp_binary64`
151×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	321	29
2	4474	29

Stop Event

1×	node limit

Counts

2 → 59

Calls

2 calls:

58.0ms

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

58.0ms

(*.f64 x-scale (*.f64 (/.f64 y-scale (*.f64 x-scale x-scale)) (/.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))))

simplify52.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1014×	`fma-def_binary64`
416×	`unswap-sqr_binary64`
288×	`associate-r_binary64`
284×	`associate-/r/_binary64`
266×	`associate-*l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	50	1240
1	148	1240
2	423	1240
3	2069	1226
4	3991	1216

Stop Event

1×	node limit

Counts

119 → 72

prune233.0ms (0.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	111	12	123
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	118	17	135

Error

14.1b

Counts

135 → 17

Alt Table

Status	Error	Program
	40.5b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (/.f64 (sqrt.f64 (pow.f64 (sin.f64 (.f64 angle (.f64 (PI.f64) 1/180))) 2)) (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))))))) (PI.f64)))
	33.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 y-scale (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (.f64 x-scale (cos.f64 (.f64 1/180 (*.f64 angle (PI.f64))))))) (PI.f64)))
	56.1b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.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) (/.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)) (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 (.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) 2)))) (/.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))) (PI.f64)))
	44.4b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (expm1.f64 (log1p.f64 (.f64 y-scale (pow.f64 x-scale -2)))) (/.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))))))) (PI.f64)))
	45.1b	(.f64 180 (/.f64 (atan.f64 (exp.f64 (log.f64 (.f64 (tan.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (/.f64 (.f64 x-scale y-scale) (.f64 x-scale x-scale)))))) (PI.f64)))
	41.1b	(.f64 180 (/.f64 (atan.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 y-scale) (pow.f64 x-scale -2)) (tan.f64 (.f64 1/180 (*.f64 angle (PI.f64))))) x-scale))) (PI.f64)))
	38.7b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (.f64 x-scale x-scale)) (neg.f64 (/.f64 y-scale (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))))))) (PI.f64)))
	36.0b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (/.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 1)))) (PI.f64)))
	38.1b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 -1 (/.f64 (.f64 y-scale (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (.f64 (pow.f64 x-scale 2) (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64))))))))) (PI.f64)))
	35.9b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (/.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (.f64 angle (.f64 (PI.f64) 1/180)))))))))) (PI.f64)))
	36.1b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (pow.f64 (cbrt.f64 (.f64 y-scale (pow.f64 x-scale -2))) 3) (/.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))))))) (PI.f64)))
	42.5b	(.f64 180 (/.f64 (atan.f64 (pow.f64 (pow.f64 (.f64 (tan.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (/.f64 (.f64 x-scale y-scale) (.f64 x-scale x-scale))) 3) 1/3)) (PI.f64)))
	31.1b	(.f64 180 (/.f64 (atan.f64 (.f64 1/180 (.f64 (/.f64 (.f64 y-scale (PI.f64)) x-scale) angle))) (PI.f64)))
	53.4b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (exp.f64 (log.f64 (.f64 (/.f64 (neg.f64 (.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) b) 2) (sqrt.f64 (fma.f64 2 (.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)) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) b) 4) (pow.f64 (.f64 a (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 4)))))) (pow.f64 x-scale -2))) (.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))))) y-scale))))) (PI.f64)))
	51.3b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (pow.f64 b 2) (sqrt.f64 (fma.f64 2 (.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)))) (fma.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 4) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))))))) (pow.f64 x-scale 2))) (/.f64 (.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	35.5b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 angle (.f64 (PI.f64) 1/180)))) 3) (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))))))) (PI.f64)))
	33.6b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 y-scale) 2) x-scale) (/.f64 (cbrt.f64 y-scale) x-scale)) (/.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))))))) (PI.f64)))

Compiler

Compiled 4465 to 2778 computations (37.8% saved)

regimes6.4s (5.4%)

Accuracy

Total 14.9b remaining (51%)

Threshold costs 0b (0%)

Counts

141 → 3

Compiler

Compiled 191950 to 133461 computations (30.5% saved)

bsearch1.5s (1.3%)

Steps

Iters	Range		Point
6	1.8740038994595344e-16	2.874187689648267e-15	2.9592549622702613e-16
10	-1.5968919011720093e+31	-45577076840550154000.0	-7.991062792573825e+26

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	117
1	57	117
2	65	117
3	81	117
4	92	117
5	100	117
6	103	117

Stop Event

1×

saturated

end454.0ms (0.4%)

Compiler: Compiled 982 to 714 computations (27.3% saved)

Details

analyze22.0s (18.8%)

sample54.3s (46.4%)

simplify22.0ms (0%)

prune16.0ms (0%)

localize48.0ms (0%)

series16.5s (14.1%)

rewrite83.0ms (0.1%)

simplify1.5s (1.3%)

prune9.2s (7.9%)

localize58.0ms (0%)

series5.0ms (0%)

rewrite38.0ms (0%)

simplify28.0ms (0%)

prune1.8s (1.5%)

localize56.0ms (0%)

series1.4s (1.2%)

rewrite42.0ms (0%)

simplify137.0ms (0.1%)

prune856.0ms (0.7%)

localize18.0ms (0%)

series100.0ms (0.1%)

rewrite60.0ms (0.1%)

simplify52.0ms (0%)

prune233.0ms (0.2%)

regimes6.4s (5.4%)

bsearch1.5s (1.3%)

simplify5.0ms (0%)

end454.0ms (0.4%)

Profiling