Details

analyze22.0s (16.9%)

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)

sample53.4s (40.9%)

Results

19.4s	1661×	body	4096	valid
11.4s	1490×	body	2048	valid
10.4s	1684×	body	1024	valid
5.6s	76×	body	8192	exit
3.0s	721×	body	512	valid
2.4s	2319×	body	128	valid
1.0s	381×	body	256	valid

Compiler

Compiled 524 to 380 computations (27.5% saved)

simplify23.0ms (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

53.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	54.2b	(.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)))
	56.0b	(.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

▶

54.2b

(*.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)))

56.0b

(*.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)

localize49.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	16.2b	(/.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))
✓	23.2b	(-.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)))))))))
✓	26.9b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	27.0b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

series17.2s (13.2%)

Counts

4 → 132

Calls

4 calls:

17.0s	(-.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)))))))))
162.0ms	(/.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))
5.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite82.0ms (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:

76.0ms	(/.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))
76.0ms	(-.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)))))))))
76.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
76.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

simplify1.6s (1.2%)

Algorithm

1×	egg-herbie

Rules

977×	`fma-def_binary64`
1×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4317	282855

Stop Event

1×	node limit

Counts

210 → 185

prune9.5s (7.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	423	12	435
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	424	13	437

Error

44.5b

Counts

437 → 13

Alt Table

Status	Error	Program
	54.9b	(.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 (log1p.f64 (expm1.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)))
	54.5b	(.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 (.f64 1/180 (.f64 angle (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)))
	53.7b	(.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 (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)))
	58.1b	(.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)))
	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)))
	61.4b	(.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)))
	53.7b	(.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 (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 (.f64 1/180 (.f64 angle (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)))
▶	50.4b	(.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)))
	56.9b	(.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)))
	60.8b	(.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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) 3) 1/3) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	61.0b	(.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)))
	55.9b	(.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)) (cbrt.f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 (.f64 (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))) a) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 y-scale -2)) 3))) (.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)))
	56.0b	(.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 342739 to 240638 computations (29.8% saved)

localize54.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	26.9b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
	27.0b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	27.2b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
✓	27.4b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series8.0ms (0%)

Counts

2 → 8

Calls

2 calls:

5.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
3.0ms	(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	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
37.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

simplify31.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	216
1	159	212
2	536	206
3	2808	206

Stop Event

1×	node limit

Counts

44 → 51

prune1.9s (1.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	188	9	197
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	191	19	210

Error

43.5b

Counts

210 → 19

Alt Table

Status	Error	Program
	58.1b	(.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)))
	52.4b	(.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 (cbrt.f64 (pow.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) 3)) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) y-scale)))) (PI.f64)))
	61.4b	(.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)))
▶	49.5b	(.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)))
	51.1b	(.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 (expm1.f64 (log1p.f64 (cos.f64 (.f64 (.f64 angle 1/180) (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 (/.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 (.f64 1/180 (.f64 angle (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)))
	54.9b	(.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 (log1p.f64 (expm1.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)))
	54.5b	(.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 (.f64 1/180 (.f64 angle (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)))
	61.0b	(.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)))
	51.1b	(.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 (.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64)))) 2) (cbrt.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)))
	54.9b	(.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 (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)))
	56.0b	(.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)))
	50.4b	(.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 1 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)))
	58.4b	(.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 (exp.f64 (log.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)))
	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)))
	53.8b	(.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 (-.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)))
	60.8b	(.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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) 3) 1/3) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	50.2b	(.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)))
	55.9b	(.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)) (cbrt.f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 (.f64 (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))) a) (.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) b)) 2) (pow.f64 y-scale -2)) 3))) (.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)))

Compiler

Compiled 29368 to 20007 computations (31.9% saved)

localize52.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	22.9b	(/.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))
	27.0b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
	27.2b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	27.4b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series1.2s (1%)

Counts

1 → 60

Calls

1 calls:

1.2s

(/.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))

rewrite38.0ms (0%)

Algorithm

1×	batch-egg-rewrite

Rules

440×	`log1p-expm1-u_binary64`
440×	`expm1-log1p-u_binary64`
415×	`pow1_binary64`
157×	`log-prod_binary64`
125×	`prod-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	153
1	1005	147

Stop Event

1×	node limit

Counts

1 → 18

Calls

1 calls:

37.0ms

(/.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 1 (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a))))) y-scale))

simplify118.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

708×	`times-frac_binary64`
409×	`associate-/l*_binary64`
380×	`associate-/r*_binary64`
260×	`fma-def_binary64`
254×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	473	12140
1	1614	11321

Stop Event

1×	node limit

Counts

78 → 51

prune808.0ms (0.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	221	5	226
Fresh	11	7	18
Picked	1	0	1
Done	0	0	0
Total	233	12	245

Error

17.9b

Counts

245 → 12

Alt Table

Status	Error	Program
	36.9b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 x-scale x-scale)) (neg.f64 (/.f64 y-scale (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))))))) (PI.f64)))
	50.4b	(.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 1 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)))
	54.9b	(.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 (log1p.f64 (expm1.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)))
	54.5b	(.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 (.f64 1/180 (.f64 angle (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)))
	37.3b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 y-scale (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64))))) (pow.f64 x-scale 2)))) (PI.f64)))
	56.0b	(.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)))
	36.7b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 -1 (/.f64 (.f64 y-scale (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (.f64 (pow.f64 x-scale 2) (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64))))))))) (PI.f64)))
	58.4b	(.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 (exp.f64 (log.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)))
	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)))
	60.8b	(.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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))))))) (/.f64 (.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))) 3) 1/3) (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) y-scale)))) (PI.f64)))
	57.2b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (exp.f64 (log.f64 (sin.f64 (.f64 angle (.f64 (PI.f64) 1/180))))) 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)))
▶	35.9b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))))) (PI.f64)))

Compiler

Compiled 32084 to 21227 computations (33.8% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.1b	(.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))
✓	9.1b	(/.f64 y-scale (*.f64 x-scale x-scale))
✓	14.8b	(.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64))))))
	27.2b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series114.0ms (0.1%)

Counts

3 → 96

Calls

3 calls:

61.0ms

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

30.0ms

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

22.0ms

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

rewrite52.0ms (0%)

Algorithm

1×	batch-egg-rewrite

Rules

357×	`prod-diff_binary64`
243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`
134×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	270	48
2	3523	48

Stop Event

1×	node limit

Counts

3 → 78

Calls

3 calls:

51.0ms

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

51.0ms

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

51.0ms

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

simplify51.0ms (0%)

Algorithm

1×	egg-herbie

Rules

560×	`fma-neg_binary64`
414×	`distribute-rgt-neg-in_binary64`
359×	`associate-r_binary64`
333×	`times-frac_binary64`
302×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	60	1682
1	185	1674
2	635	1670
3	3745	1670

Stop Event

1×	node limit

Counts

174 → 100

prune209.0ms (0.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	114	12	126
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	120	18	138

Error

13.1b

Counts

138 → 18

Alt Table

Status	Error	Program
	44.6b	(.f64 180 (/.f64 (atan.f64 (fma.f64 1/180 (.f64 (.f64 angle (PI.f64)) (/.f64 y-scale x-scale)) (.f64 (/.f64 y-scale x-scale) (.f64 (.f64 (pow.f64 angle 3) (pow.f64 (PI.f64) 3)) -1/34992000)))) (PI.f64)))
	36.9b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 x-scale x-scale)) (neg.f64 (/.f64 y-scale (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))))))) (PI.f64)))
	50.4b	(.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 1 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)))
	33.8b	(.f64 180 (/.f64 (atan.f64 (.f64 1/180 (.f64 (.f64 angle (PI.f64)) (/.f64 y-scale x-scale)))) (PI.f64)))
	58.4b	(.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 (exp.f64 (log.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)))
	38.5b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (sqrt.f64 (/.f64 (.f64 y-scale y-scale) (pow.f64 x-scale 4))) (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))))) (PI.f64)))
	33.1b	(.f64 180 (/.f64 (atan.f64 (.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (/.f64 y-scale x-scale))) (PI.f64)))
	41.7b	(.f64 180 (/.f64 (atan.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (/.f64 x-scale (/.f64 (*.f64 x-scale x-scale) y-scale))) 3) 1/3)) (PI.f64)))
	43.5b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (.f64 angle (.f64 (PI.f64) 1/180))))))))) (PI.f64)))
	36.7b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 -1 (/.f64 (.f64 y-scale (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (.f64 (pow.f64 x-scale 2) (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64))))))))) (PI.f64)))
	34.2b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 y-scale (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) x-scale)) (PI.f64)))
	39.2b	(.f64 180 (/.f64 (atan.f64 (sqrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) (/.f64 x-scale (/.f64 (*.f64 x-scale x-scale) y-scale))) 2))) (PI.f64)))
	39.5b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (sqrt.f64 (pow.f64 (sin.f64 (.f64 angle (.f64 (PI.f64) 1/180))) 2))))) (PI.f64)))
	36.8b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (pow.f64 (pow.f64 (.f64 y-scale (pow.f64 x-scale -2)) 3) 1/3) (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))))) (PI.f64)))
	35.1b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (.f64 (/.f64 y-scale (.f64 x-scale x-scale)) (expm1.f64 (log1p.f64 (sin.f64 (.f64 angle (.f64 (PI.f64) 1/180)))))))) (PI.f64)))
	57.2b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (/.f64 (.f64 -1 (/.f64 (fma.f64 (pow.f64 a 2) (pow.f64 (exp.f64 (log.f64 (sin.f64 (.f64 angle (.f64 (PI.f64) 1/180))))) 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)))
	43.6b	(.f64 180 (/.f64 (atan.f64 (.f64 x-scale (exp.f64 (log.f64 (.f64 (.f64 y-scale (pow.f64 x-scale -2)) (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))))))) (PI.f64)))
	56.0b	(.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 4024 to 2545 computations (36.8% saved)

regimes12.0s (9.2%)

Accuracy

Total 19.8b remaining (56.9%)

Threshold costs 0b (0%)

Counts

223 → 15

Compiler

Compiled 287180 to 200982 computations (30% saved)

bsearch9.3s (7.1%)

Steps

Iters	Range		Point
7	2.7444597183409594e+119	1.8655953429776094e+121	7.22517356074486e+120
9	5.809826574893373e+27	1.1102540621234857e+35	1.8322237614678637e+34
9	1.5037525234504408e-39	7.325170831503081e-33	2.8859830434113404e-37
8	5.2126025053836554e-101	1.6016397698893554e-97	8.962533660054582e-101
10	8.838082681743427e-130	8.551752636810245e-119	1.4303173329051239e-126
7	3.016823682424392e-218	9.930680936144996e-217	8.191269321848878e-218
8	3.4157826416468544e-273	7.734368353321266e-269	5.147224452517122e-270
3	-1.7125623771851988e-307	4.3732322093334784e-306	1.6582340324706763e-307
1	-1.7945770109840678e-242	-2.0550088889159366e-243	-6.253184033580119e-243
7	-3.920591504545773e-196	-1.6576617689947377e-198	-4.8060553385269945e-197
8	-8.702931494623533e-97	-1.9760376432552133e-99	-5.6248734637854445e-99
4	-1.7725237665569725e-42	-1.0531645769417882e-42	-1.242420305716196e-42
9	-2.8945136551231654e+112	-6.5333789787075076e+106	-9.84452925613738e+111
8	-3.9724510242804825e+158	-3.1402523824286946e+154	-3.2116766629260986e+154

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify20.0ms (0%)

Algorithm

1×	egg-herbie

Rules

48×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	134	4294967295
1	183	4294967295
2	205	4294967295
3	232	4294967295
4	249	4294967295
5	260	4294967295
6	264	4294967295

Stop Event

1×

saturated

end614.0ms (0.5%)

Compiler: Compiled 1663 to 1147 computations (31% saved)

Details

analyze22.0s (16.9%)

sample53.4s (40.9%)

simplify23.0ms (0%)

prune16.0ms (0%)

localize49.0ms (0%)

series17.2s (13.2%)

rewrite82.0ms (0.1%)

simplify1.6s (1.2%)

prune9.5s (7.3%)

localize54.0ms (0%)

series8.0ms (0%)

rewrite38.0ms (0%)

simplify31.0ms (0%)

prune1.9s (1.4%)

localize52.0ms (0%)

series1.2s (1%)

rewrite38.0ms (0%)

simplify118.0ms (0.1%)

prune808.0ms (0.6%)

localize13.0ms (0%)

series114.0ms (0.1%)

rewrite52.0ms (0%)

simplify51.0ms (0%)

prune209.0ms (0.2%)

regimes12.0s (9.2%)

bsearch9.3s (7.1%)

simplify20.0ms (0%)

end614.0ms (0.5%)

Profiling