Details

analyze12.8s (16.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
6.2%	93.5%	0.2%	11
6.2%	93.5%	0.2%	12
7.8%	92%	0.2%	13
8.6%	91.2%	0.2%	14

Compiler

Compiled 115 to 84 computations (27% saved)

sample50.6s (64.6%)

Results

12.9s	1490×	body	4096	valid
9.3s	1756×	body	2048	valid
7.8s	847×	body	4096	invalid
7.1s	1255×	body	2048	invalid
3.2s	911×	body	1024	valid
3.1s	3500×	body	128	valid
2.4s	657×	body	1024	invalid
1.2s	68×	body	8192	valid
828.0ms	365×	body	512	valid
753.0ms	1043×	body	128	invalid
741.0ms	301×	body	512	invalid
556.0ms	31×	body	8192	invalid
292.0ms	166×	body	256	valid
168.0ms	117×	body	256	invalid

Compiler

Compiled 344 to 251 computations (27% saved)

simplify42.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

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

prune11.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

43.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	47.6b	(fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) -4) (.f64 (.f64 (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 x-scale y-scale)) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 x-scale y-scale))) (.f64 4 (.f64 (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))))
▶	44.0b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

Status

Error

Program

47.6b

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

▶

44.0b

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

Compiler

Compiled 670 to 459 computations (31.5% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.1b	(.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))
✓	28.4b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	28.6b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	33.1b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

series2.7s (3.4%)

Counts

4 → 144

Calls

4 calls:

2.0s	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
647.0ms	(.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))
3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite86.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

429×	`log1p-expm1-u_binary64`
429×	`expm1-log1p-u_binary64`
413×	`add-log-exp_binary64`
398×	`pow1_binary64`
152×	`log-prod_binary64`

Counts

4 → 91

Calls

4 calls:

78.0ms	(.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))
78.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
78.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
78.0ms	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify291.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

235 → 159

Iterations

Useful iterations: 1 (0.0ms)

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

prune1.1s (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	291	12	303
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	293	12	305

Error

27.0b

Counts

305 → 12

Alt Table

Status	Error	Program
	44.2b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	40.2b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	47.2b	(-.f64 (pow.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2) (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (*.f64 y-scale y-scale))))
	46.1b	(-.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale)))) (fma.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 4 (+.f64 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 y-scale y-scale)) (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (.f64 x-scale x-scale)) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))))))))
	49.2b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (fma.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 (PI.f64) 4)) 1) (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 (PI.f64) 2))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
▶	33.2b	0
	45.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (/.f64 (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) y-scale)) y-scale))
	44.0b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cbrt.f64 (pow.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) 3))) 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)))
	44.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (cbrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) 3))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	44.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (log.f64 (exp.f64 (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)))
	40.1b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale)))
	40.3b	(neg.f64 (.f64 (.f64 a a) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (*.f64 x-scale x-scale))))))))

Compiler

Compiled 39468 to 26910 computations (31.8% saved)

localize0.0ms (0%)

prune41.0ms (0.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	11	11
Picked	1	1
Done	0	0
Total	12	12

Error

27.0b

Counts

12 → 12

Alt Table

Status	Error	Program
	44.2b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	40.2b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	47.2b	(-.f64 (pow.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) 2) (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (*.f64 y-scale y-scale))))
	46.1b	(-.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale)))) (fma.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 4 (+.f64 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 y-scale y-scale)) (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (.f64 x-scale x-scale)) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))))))))
	49.2b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (fma.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 (PI.f64) 4)) 1) (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 (PI.f64) 2))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
✓	33.2b	0
	45.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (/.f64 (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) y-scale)) y-scale))
	44.0b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cbrt.f64 (pow.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) 3))) 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)))
	44.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (cbrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) 3))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	44.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (log.f64 (exp.f64 (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)))
▶	40.1b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale)))
	40.3b	(neg.f64 (.f64 (.f64 a a) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (*.f64 x-scale x-scale))))))))

Compiler

Compiled 2288 to 1558 computations (31.9% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	16.9b	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (*.f64 y-scale y-scale))
✓	20.5b	(/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale))
✓	28.4b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
✓	28.8b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series1.3s (1.6%)

Counts

4 → 116

Calls

4 calls:

1.1s	(/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale))
167.0ms	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (*.f64 y-scale y-scale))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
3.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

rewrite77.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

363×	`log1p-expm1-u_binary64`
363×	`expm1-log1p-u_binary64`
359×	`add-log-exp_binary64`
358×	`add-exp-log_binary64`
347×	`pow1_binary64`

Counts

4 → 68

Calls

4 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	174
1	801	159
2	4864	159
3	4959	159
0	0	0
1	0	0

simplify179.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-def_binary64`
448×	`unswap-sqr_binary64`
311×	`cancel-sign-sub-inv_binary64`
279×	`fma-neg_binary64`
251×	`associate-r_binary64`

Counts

184 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	8612
1	601	8451
2	2471	8017
3	4680	8017
4	4873	8017

prune444.0ms (0.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	145	7	152
Fresh	4	6	10
Picked	1	0	1
Done	0	1	1
Total	150	14	164

Error

25.6b

Counts

164 → 14

Alt Table

Status	Error	Program
	40.0b	(neg.f64 (/.f64 (fma.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))) (.f64 y-scale y-scale)) (.f64 (/.f64 4 y-scale) (+.f64 (/.f64 (.f64 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) y-scale) (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) y-scale)))) (.f64 x-scale x-scale)))
	49.2b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (fma.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 (PI.f64) 4)) 1) (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 (PI.f64) 2))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	39.9b	(neg.f64 (/.f64 (fma.f64 4 (pow.f64 (cbrt.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale))) 3) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale)))
✓	33.2b	0
	38.0b	(neg.f64 (pow.f64 (sqrt.f64 (.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 y-scale -2))))) (pow.f64 x-scale -2))) 2))
	45.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (/.f64 (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) y-scale)) y-scale))
	38.1b	(neg.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 y-scale -2))))) (pow.f64 x-scale -2))) 3))
	44.0b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cbrt.f64 (pow.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) 3))) 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)))
	44.2b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	40.2b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	44.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (cbrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) 3))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
▶	38.0b	(neg.f64 (.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 y-scale -2))))) (pow.f64 x-scale -2)))
	40.6b	(neg.f64 (/.f64 (fma.f64 4 (.f64 (/.f64 (.f64 a a) y-scale) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) y-scale) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) y-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 y-scale y-scale)))) (/.f64 (.f64 x-scale x-scale) (*.f64 b b))))
	39.7b	(neg.f64 (/.f64 (.f64 (+.f64 (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (pow.f64 y-scale 2))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 a 2)) (pow.f64 y-scale 2))) (.f64 4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 y-scale 2))))) (pow.f64 b 2)) (pow.f64 x-scale 2)))

Compiler

Compiled 15284 to 8455 computations (44.7% saved)

localize34.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	16.9b	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (*.f64 y-scale y-scale))
✓	20.4b	(.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 y-scale -2))))) (pow.f64 x-scale -2))
	28.4b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	28.8b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series1.6s (2%)

Counts

2 → 108

Calls

2 calls:

1.4s

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

173.0ms

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

rewrite41.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

356×	`log1p-expm1-u_binary64`
356×	`expm1-log1p-u_binary64`
348×	`add-cbrt-cube_binary64`
344×	`add-log-exp_binary64`
343×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

40.0ms

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

39.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	136
1	785	136
2	5409	136
0	0	0
1	0	0

simplify144.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-def_binary64`
436×	`associate-*l/_binary64`
406×	`unswap-sqr_binary64`
346×	`associate-/r/_binary64`
216×	`times-frac_binary64`

Counts

140 → 56

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	8396
1	482	8239
2	2060	7535
3	5195	7535

prune534.0ms (0.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	142	6	148
Fresh	4	8	12
Picked	1	0	1
Done	0	1	1
Total	147	15	162

Error

24.0b

Counts

162 → 15

Alt Table

Status	Error	Program
	32.2b	(neg.f64 (pow.f64 (sqrt.f64 (.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2) (pow.f64 y-scale -2))))) (pow.f64 x-scale -2))) 2))
	44.2b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	40.2b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	32.1b	(neg.f64 (.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2) (pow.f64 y-scale -2))))) (pow.f64 x-scale -2)))
	40.6b	(neg.f64 (/.f64 (fma.f64 4 (.f64 (/.f64 (.f64 a a) y-scale) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) y-scale) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) y-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 y-scale y-scale)))) (/.f64 (.f64 x-scale x-scale) (*.f64 b b))))
	50.1b	(neg.f64 (.f64 (fma.f64 4 (fma.f64 1/629856000 (/.f64 (.f64 (pow.f64 angle 4) (.f64 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 (PI.f64) 4))) (.f64 y-scale y-scale)) (fma.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (.f64 b b) (fma.f64 (/.f64 (.f64 (.f64 angle angle) (.f64 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 (PI.f64) 2))) (.f64 y-scale y-scale)) -1/16200 (.f64 (/.f64 (.f64 (pow.f64 angle 6) (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (PI.f64) 6)))) (.f64 y-scale y-scale)) -17/765275040000000)))) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 y-scale -2))))) (pow.f64 x-scale -2)))
	39.7b	(neg.f64 (/.f64 (.f64 (+.f64 (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (pow.f64 y-scale 2))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 a 2)) (pow.f64 y-scale 2))) (.f64 4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 y-scale 2))))) (pow.f64 b 2)) (pow.f64 x-scale 2)))
	49.2b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (fma.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 (PI.f64) 4)) 1) (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 (PI.f64) 2))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
✓	33.2b	0
	45.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (/.f64 (.f64 (.f64 4 (/.f64 (pow.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) (.f64 x-scale x-scale))) (/.f64 (pow.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))))) 2) y-scale)) y-scale))
	44.0b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cbrt.f64 (pow.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) 3))) 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)))
	44.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (cbrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) 3))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	38.1b	(neg.f64 (.f64 (fma.f64 4 (pow.f64 (cbrt.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale))) 3) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 y-scale -2))))) (pow.f64 x-scale -2)))
	32.2b	(neg.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2) (pow.f64 y-scale -2))))) (pow.f64 x-scale -2))) 3))
	41.3b	(neg.f64 (.f64 (/.f64 (.f64 a a) (.f64 x-scale x-scale)) (fma.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 y-scale y-scale)) (.f64 (/.f64 4 y-scale) (+.f64 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) y-scale) (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) y-scale))))))

Compiler

Compiled 12836 to 8188 computations (36.2% saved)

regimes2.2s (2.8%)

Accuracy

Total 5.1b remaining (18.6%)

Threshold costs 0b (0%)

Counts

67 → 4

Compiler

Compiled 62752 to 43039 computations (31.4% saved)

bsearch3.1s (3.9%)

Steps

Iters	Range	Point
10	4.617520012776859e-161	4.8216159733348804e-151	7.400822927420862e-155
10	-7.828262803921106e-124	-1.2966652660528904e-137	-1.320717690828003e-137
8	-1.8731898553074175e+172	-2.7912087138795753e+169	-2.8188140419137164e+169

Iters

Range

Point

4.617520012776859e-161

4.8216159733348804e-151

7.400822927420862e-155

-7.828262803921106e-124

-1.2966652660528904e-137

-1.320717690828003e-137

-1.8731898553074175e+172

-2.7912087138795753e+169

-2.8188140419137164e+169

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	240
1	66	240
2	74	240
3	79	240
4	81	240
5	81	240

end1.0s (1.3%)

Compiler: Compiled 1610 to 1114 computations (30.8% saved)

Details

analyze12.8s (16.4%)

sample50.6s (64.6%)

simplify42.0ms (0.1%)

prune11.0ms (0%)

localize42.0ms (0.1%)

series2.7s (3.4%)

rewrite86.0ms (0.1%)

simplify291.0ms (0.4%)

prune1.1s (1.4%)

localize0.0ms (0%)

prune41.0ms (0.1%)

localize40.0ms (0.1%)

series1.3s (1.6%)

rewrite77.0ms (0.1%)

simplify179.0ms (0.2%)

prune444.0ms (0.6%)

localize34.0ms (0%)

series1.6s (2%)

rewrite41.0ms (0.1%)

simplify144.0ms (0.2%)

prune534.0ms (0.7%)

regimes2.2s (2.8%)

bsearch3.1s (3.9%)

simplify8.0ms (0%)

end1.0s (1.3%)

Profiling