Details

analyze12.8s (15.6%)

Algorithm

1×

Search

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

Compiler

Compiled 115 to 84 computations (27% saved)

sample49.2s (59.7%)

Results

13.2s	1497×	body	4096	valid
9.1s	1720×	body	2048	valid
7.3s	841×	body	4096	invalid
6.1s	1192×	body	2048	invalid
3.0s	903×	body	1024	valid
2.9s	3544×	body	128	valid
2.4s	682×	body	1024	invalid
1.5s	81×	body	8192	valid
1.0s	352×	body	512	valid
821.0ms	1059×	body	128	invalid
713.0ms	284×	body	512	invalid
631.0ms	35×	body	8192	invalid
218.0ms	159×	body	256	valid
183.0ms	130×	body	256	invalid

Compiler

Compiled 344 to 251 computations (27% saved)

simplify40.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

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

prune11.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

41.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	43.3b	(fma.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale) (.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale) -4) (.f64 (.f64 (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 x-scale y-scale)) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 x-scale y-scale))) (.f64 4 (.f64 (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64))))))))
▶	41.5b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

Status

Error

Program

43.3b

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

▶

41.5b

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

localize38.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.2b	(.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))
✓	27.1b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	27.3b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	27.5b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (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)))

series2.6s (3.1%)

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)))
628.0ms	(.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)))

rewrite89.0ms (0.1%)

Algorithm

1×	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:

82.0ms	(.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))
82.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
82.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
82.0ms	(-.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: 1 (0.0ms)

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

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

prune923.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	294	9	303
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	296	9	305

Error

27.1b

Counts

305 → 9

Alt Table

Status	Error	Program
	41.5b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	41.3b	(-.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 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.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 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (pow.f64 a 2) (pow.f64 b 2))) (*.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2))))))))
	41.4b	(-.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))
	41.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 3)) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	37.7b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale)))
	38.3b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	37.8b	(neg.f64 (.f64 (.f64 a a) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (*.f64 x-scale x-scale))))))))
	41.7b	(-.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)))) (.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (cbrt.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)))
▶	31.6b	0

Compiler

Compiled 38818 to 26502 computations (31.7% saved)

localize0.0ms (0%)

prune29.0ms (0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

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

Error

27.1b

Counts

9 → 9

Alt Table

Status	Error	Program
	41.5b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	41.3b	(-.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 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.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 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (pow.f64 a 2) (pow.f64 b 2))) (*.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2))))))))
	41.4b	(-.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))
	41.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 3)) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
▶	37.7b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale)))
	38.3b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	37.8b	(neg.f64 (.f64 (.f64 a a) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (*.f64 x-scale x-scale))))))))
	41.7b	(-.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)))) (.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (cbrt.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)))
✓	31.6b	0

Compiler

Compiled 1638 to 1150 computations (29.8% saved)

localize36.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	15.7b	(.f64 (.f64 a a) (*.f64 b b))
✓	19.9b	(/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale))
✓	27.0b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
✓	27.3b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series1.1s (1.4%)

Counts

4 → 92

Calls

4 calls:

1.1s	(/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale))
10.0ms	(.f64 (.f64 a a) (*.f64 b b))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))
2.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))

rewrite77.0ms (0.1%)

Algorithm

1×	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 → 63

Calls

4 calls:

75.0ms	(.f64 (.f64 a a) (*.f64 b b))
75.0ms	(/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale))
75.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
74.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

Iterations

Useful iterations: 1 (0.0ms)

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

simplify158.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

155 → 95

Iterations

Useful iterations: 2 (0.0ms)

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

prune360.0ms (0.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	139	11	150

Error

25.1b

Counts

150 → 11

Alt Table

Status	Error	Program
	41.5b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	36.1b	(neg.f64 (exp.f64 (log.f64 (.f64 (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))) (pow.f64 y-scale -2)))))
	38.6b	(neg.f64 (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (fma.f64 4 (.f64 (/.f64 (.f64 b b) x-scale) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 x-scale x-scale))))))
	41.4b	(-.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))
	37.7b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 3) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale)))
	38.3b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	37.5b	(neg.f64 (/.f64 (fma.f64 8 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))) (.f64 x-scale x-scale)) (.f64 (/.f64 4 x-scale) (+.f64 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) x-scale) (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) x-scale)))) (.f64 y-scale y-scale)))
	37.0b	(neg.f64 (/.f64 (fma.f64 4 (.f64 (/.f64 (.f64 a a) x-scale) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 x-scale x-scale)))) (/.f64 (.f64 y-scale y-scale) (*.f64 b b))))
	41.7b	(-.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)))) (.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (cbrt.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)))
✓	31.6b	0
▶	35.7b	(neg.f64 (pow.f64 (/.f64 (.f64 y-scale y-scale) (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2)))))) -1))

Compiler

Compiled 13537 to 7401 computations (45.3% saved)

localize37.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.8b	(.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))
✓	19.2b	(/.f64 (.f64 y-scale y-scale) (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 x-scale -2))))))
	27.0b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	27.3b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series3.1s (3.8%)

Counts

2 → 96

Calls

2 calls:

3.0s

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

111.0ms

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

rewrite45.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

354×	`log1p-expm1-u_binary64`
354×	`expm1-log1p-u_binary64`
347×	`add-cbrt-cube_binary64`
343×	`add-log-exp_binary64`
342×	`add-exp-log_binary64`

Counts

2 → 33

Calls

2 calls:

43.0ms

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

43.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	139
1	781	139
2	5383	139

simplify134.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

892×	`times-frac_binary64`
673×	`associate-/l*_binary64`
468×	`fma-def_binary64`
410×	`unswap-sqr_binary64`
223×	`associate-r_binary64`

Counts

129 → 52

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	8222
1	373	8074
2	1465	7222
3	5541	7222

prune501.0ms (0.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	137	7	144
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	141	14	155

Error

21.7b

Counts

155 → 14

Alt Table

Status	Error	Program
	29.7b	(neg.f64 (pow.f64 (/.f64 (.f64 y-scale y-scale) (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 x-scale x-scale)) (.f64 8 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 a (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2)) 3) (pow.f64 x-scale -2)))))) -1))
	38.3b	(neg.f64 (pow.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)) (*.f64 (pow.f64 a 2) (pow.f64 b 2)))) -1))
	36.9b	(neg.f64 (pow.f64 (/.f64 (.f64 y-scale y-scale) (.f64 (.f64 b b) (fma.f64 4 (.f64 (/.f64 (.f64 a a) x-scale) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 x-scale x-scale)))))) -1))
	37.5b	(neg.f64 (/.f64 (fma.f64 8 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))) (.f64 x-scale x-scale)) (.f64 (/.f64 4 x-scale) (+.f64 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) x-scale) (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) x-scale)))) (.f64 y-scale y-scale)))
	35.0b	(neg.f64 (pow.f64 (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 y-scale (fma.f64 4 (.f64 (/.f64 (.f64 b b) x-scale) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (*.f64 x-scale x-scale)))))) -1))
	41.7b	(-.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)))) (.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (cbrt.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)))
	34.6b	(neg.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 y-scale y-scale) (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (.f64 8 (.f64 (pow.f64 x-scale -2) (pow.f64 (.f64 (.f64 a (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2)))))) 3)) -1))
	41.5b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	41.4b	(-.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))
	38.3b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	37.0b	(neg.f64 (/.f64 (fma.f64 4 (.f64 (/.f64 (.f64 a a) x-scale) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 x-scale x-scale)))) (/.f64 (.f64 y-scale y-scale) (*.f64 b b))))
✓	31.6b	0
	29.7b	(neg.f64 (pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 y-scale y-scale) (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (.f64 8 (.f64 (pow.f64 x-scale -2) (pow.f64 (.f64 (.f64 a (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2))))))) 2) -1))
	29.8b	(neg.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 y-scale y-scale) (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (fma.f64 4 (.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (pow.f64 x-scale -2)) (.f64 8 (.f64 (pow.f64 x-scale -2) (pow.f64 (.f64 (.f64 a (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2))))))) 3) -1))

Compiler

Compiled 12483 to 8070 computations (35.4% saved)

regimes6.5s (7.9%)

Accuracy

Total 4.6b remaining (17.5%)

Threshold costs 0b (0%)

Counts

171 → 5

Compiler

Compiled 157218 to 111055 computations (29.4% saved)

bsearch3.6s (4.3%)

Steps

Iters	Range		Point
7	2.460518880968122e+109	8.226168177440758e+110	7.39453938945273e+110
11	3.8089825748032663e-166	5.955762172186938e-136	7.474864398681438e-155
8	-3.278703971331098e-147	-9.66860462512823e-151	-9.808554852601608e-151
8	-2.1575832341673772e+133	-5.063812260947623e+130	-1.051336110722494e+131

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify40.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	258
1	77	258
2	81	258
3	83	258
4	83	258

end605.0ms (0.7%)

Compiler: Compiled 1360 to 957 computations (29.6% saved)

Details

analyze12.8s (15.6%)

sample49.2s (59.7%)

simplify40.0ms (0%)

prune11.0ms (0%)

localize38.0ms (0%)

series2.6s (3.1%)

rewrite89.0ms (0.1%)

simplify291.0ms (0.4%)

prune923.0ms (1.1%)

localize0.0ms (0%)

prune29.0ms (0%)

localize36.0ms (0%)

series1.1s (1.4%)

rewrite77.0ms (0.1%)

simplify158.0ms (0.2%)

prune360.0ms (0.4%)

localize37.0ms (0%)

series3.1s (3.8%)

rewrite45.0ms (0.1%)

simplify134.0ms (0.2%)

prune501.0ms (0.6%)

regimes6.5s (7.9%)

bsearch3.6s (4.3%)

simplify40.0ms (0%)

end605.0ms (0.7%)

Profiling