Details

analyze12.7s (18.9%)

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
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)

sample46.3s (68.7%)

Results

12.4s	1505×	body	4096	valid
8.8s	1753×	body	2048	valid
7.0s	851×	body	4096	invalid
5.9s	1175×	body	2048	invalid
3.1s	911×	body	1024	valid
2.7s	3493×	body	128	valid
2.3s	695×	body	1024	invalid
986.0ms	57×	body	8192	valid
857.0ms	374×	body	512	valid
680.0ms	987×	body	128	invalid
641.0ms	293×	body	512	invalid
481.0ms	27×	body	8192	invalid
232.0ms	163×	body	256	valid
179.0ms	131×	body	256	invalid

Compiler

Compiled 344 to 251 computations (27% saved)

simplify20.0ms (0%)

Algorithm

1×	egg-herbie

Rules

545×	`associate-/l/_binary64`
526×	`associate-/r/_binary64`
263×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`
157×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	175
1	104	173
2	339	173
3	1688	170

Stop Event

1×	node limit

Counts

1 → 2

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

44.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	47.5b	(fma.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 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 x-scale x-scale)) -4) (.f64 (/.f64 (/.f64 (.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)))))) (.f64 y-scale (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))))) x-scale) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) 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))) (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

47.5b

(fma.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 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) -4) (*.f64 (/.f64 (/.f64 (*.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)))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) x-scale) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) 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))) (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 462 computations (31% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.4b	(.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))
✓	27.9b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	28.0b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	32.1b	(-.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)))

series2.6s (3.9%)

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)))
632.0ms	(.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale))
4.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
3.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite84.0ms (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`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	238
1	918	226

Stop Event

1×	node limit

Counts

4 → 87

Calls

4 calls:

77.0ms	(.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))
77.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
77.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
77.0ms	(-.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)))

simplify170.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

465×	`times-frac_binary64`
357×	`associate-/l*_binary64`
342×	`associate-r_binary64`
277×	`associate-/r*_binary64`
263×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	297	18027
1	1275	17004

Stop Event

1×	node limit

Counts

231 → 157

prune913.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	288	7	295
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	289	8	297

Error

22.6b

Counts

297 → 8

Alt Table

Status	Error	Program
	38.4b	(/.f64 (neg.f64 (fma.f64 4 (.f64 (.f64 (/.f64 a x-scale) (/.f64 a x-scale)) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (fma.f64 4 (.f64 (/.f64 (.f64 (.f64 a a) (.f64 b b)) x-scale) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale)) (.f64 (/.f64 8 x-scale) (/.f64 (.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 a a))) x-scale))))) (*.f64 y-scale y-scale))
	38.6b	(/.f64 (neg.f64 (fma.f64 4 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 y-scale (.f64 b b)))) (fma.f64 4 (.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) 8) (/.f64 (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 y-scale (.f64 b b))) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))))) (.f64 x-scale x-scale))
	32.7b	(.f64 -4 (.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (*.f64 b b)))
	40.7b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	41.3b	(.f64 (fma.f64 4 (.f64 (/.f64 (.f64 b b) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (fma.f64 8 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 y-scale y-scale)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)) (.f64 x-scale x-scale))) (.f64 4 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (/.f64 (.f64 y-scale y-scale) b) (/.f64 (.f64 x-scale x-scale) b)))))) (neg.f64 (.f64 a a)))
✓	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))) (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)))
	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 (.f64 4 (.f64 a a)) (.f64 b b)) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))))
▶	29.3b	0

Compiler

Compiled 37300 to 25300 computations (32.2% saved)

localize0.0ms (0%)

prune16.0ms (0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	1	1
Total	8	8

Error

22.6b

Counts

8 → 8

Alt Table

Status	Error	Program
	38.4b	(/.f64 (neg.f64 (fma.f64 4 (.f64 (.f64 (/.f64 a x-scale) (/.f64 a x-scale)) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (fma.f64 4 (.f64 (/.f64 (.f64 (.f64 a a) (.f64 b b)) x-scale) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale)) (.f64 (/.f64 8 x-scale) (/.f64 (.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 a a))) x-scale))))) (*.f64 y-scale y-scale))
	38.6b	(/.f64 (neg.f64 (fma.f64 4 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 y-scale (.f64 b b)))) (fma.f64 4 (.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) 8) (/.f64 (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 y-scale (.f64 b b))) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))))) (.f64 x-scale x-scale))
▶	32.7b	(.f64 -4 (.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (*.f64 b b)))
	40.7b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	41.3b	(.f64 (fma.f64 4 (.f64 (/.f64 (.f64 b b) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (fma.f64 8 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 y-scale y-scale)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)) (.f64 x-scale x-scale))) (.f64 4 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (/.f64 (.f64 y-scale y-scale) b) (/.f64 (.f64 x-scale x-scale) b)))))) (neg.f64 (.f64 a a)))
✓	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))) (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)))
	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 (.f64 4 (.f64 a a)) (.f64 b b)) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))))
✓	29.3b	0

Compiler

Compiled 874 to 559 computations (36% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (*.f64 b b)))
✓	0.2b	(.f64 (.f64 x-scale y-scale) (*.f64 x-scale y-scale))
✓	17.1b	(/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale)))
✓	18.0b	(.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (.f64 b b))

series431.0ms (0.6%)

Counts

4 → 156

Calls

4 calls:

170.0ms	(.f64 -4 (.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (*.f64 b b)))
155.0ms	(.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (.f64 b b))
95.0ms	(/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale)))
12.0ms	(.f64 (.f64 x-scale y-scale) (*.f64 x-scale y-scale))

rewrite60.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

237×	`expm1-udef_binary64`
237×	`log1p-udef_binary64`
219×	`log-pow_binary64`
141×	`associate-r_binary64`
136×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	61
1	278	46
2	3865	46

Stop Event

1×	node limit

Counts

4 → 106

Calls

4 calls:

58.0ms	(.f64 -4 (.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (*.f64 b b)))
58.0ms	(.f64 (.f64 x-scale y-scale) (*.f64 x-scale y-scale))
58.0ms	(/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale)))
58.0ms	(.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (.f64 b b))

simplify61.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

780×	`associate-r_binary64`
759×	`associate-l_binary64`
615×	`associate-/l/_binary64`
451×	`associate-/r/_binary64`
292×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	3072
1	56	3072
2	203	3072
3	1664	3072

Stop Event

1×	node limit

Counts

262 → 118

prune174.0ms (0.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	105	13	118
Fresh	4	1	5
Picked	1	0	1
Done	1	1	2
Total	111	15	126

Error

3.9b

Counts

126 → 15

Alt Table

Status	Error	Program
	24.8b	(.f64 -4 (.f64 (.f64 (.f64 (/.f64 a x-scale) (/.f64 a y-scale)) (/.f64 1 (.f64 x-scale y-scale))) (.f64 b b)))
	19.0b	(.f64 -4 (/.f64 1 (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (pow.f64 (*.f64 a b) 2))))
	7.2b	(pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2) -4)) 3)
	38.6b	(/.f64 (neg.f64 (fma.f64 4 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 y-scale (.f64 b b)))) (fma.f64 4 (.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) 8) (/.f64 (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 y-scale (.f64 b b))) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))))) (.f64 x-scale x-scale))
▶	6.9b	(.f64 -4 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2))
	21.2b	(.f64 -4 (/.f64 (/.f64 (pow.f64 (.f64 a b) 2) x-scale) (.f64 y-scale (.f64 x-scale y-scale))))
	22.3b	(.f64 (.f64 b (.f64 (.f64 b (/.f64 a y-scale)) (/.f64 a y-scale))) (/.f64 -4 (*.f64 x-scale x-scale)))
	7.2b	(.f64 -4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2)) 3))
	18.9b	(/.f64 (.f64 (pow.f64 (.f64 a b) 2) -4) (pow.f64 (*.f64 x-scale y-scale) 2))
	21.4b	(.f64 -4 (cbrt.f64 (pow.f64 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2) 3)))
	20.8b	(.f64 -4 (.f64 (pow.f64 (/.f64 a (.f64 x-scale y-scale)) 2) (.f64 b b)))
	24.6b	(.f64 -4 (/.f64 (.f64 (.f64 (/.f64 a x-scale) (/.f64 a y-scale)) (.f64 b b)) (*.f64 x-scale y-scale)))
	15.8b	(.f64 -4 (/.f64 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 x-scale y-scale)) (.f64 x-scale y-scale)))
✓	29.3b	0
	23.0b	(.f64 -4 (/.f64 (.f64 a (.f64 b b)) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) a)))

Compiler

Compiled 2654 to 1423 computations (46.4% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2))
✓	0.2b	(pow.f64 (.f64 b (/.f64 a (.f64 x-scale y-scale))) 2)
✓	6.1b	(.f64 b (/.f64 a (.f64 x-scale y-scale)))
✓	7.5b	(/.f64 a (*.f64 x-scale y-scale))

series265.0ms (0.4%)

Counts

4 → 164

Calls

4 calls:

172.0ms	(.f64 -4 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2))
46.0ms	(pow.f64 (.f64 b (/.f64 a (.f64 x-scale y-scale))) 2)
28.0ms	(.f64 b (/.f64 a (.f64 x-scale y-scale)))
18.0ms	(/.f64 a (*.f64 x-scale y-scale))

rewrite59.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

638×	`log-prod_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
193×	`log-pow_binary64`
122×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	253	46
2	3170	46

Stop Event

1×	node limit

Counts

4 → 122

Calls

4 calls:

57.0ms	(.f64 -4 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2))
57.0ms	(pow.f64 (.f64 b (/.f64 a (.f64 x-scale y-scale))) 2)
57.0ms	(.f64 b (/.f64 a (.f64 x-scale y-scale)))
57.0ms	(/.f64 a (*.f64 x-scale y-scale))

simplify59.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

835×	`associate-r_binary64`
803×	`associate-l_binary64`
584×	`associate-/l/_binary64`
438×	`associate-/r/_binary64`
256×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	2876
1	74	2876
2	226	2876
3	1519	2876

Stop Event

1×	node limit

Counts

286 → 131

prune206.0ms (0.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	124	7	131
Fresh	6	7	13
Picked	1	0	1
Done	1	0	1
Total	132	14	146

Error

0.1b

Counts

146 → 14

Alt Table

Status	Error	Program
	9.9b	(.f64 -4 (.f64 b (.f64 (/.f64 (/.f64 a x-scale) y-scale) (.f64 (/.f64 (/.f64 a x-scale) y-scale) b))))
	38.6b	(/.f64 (neg.f64 (fma.f64 4 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 y-scale (.f64 b b)))) (fma.f64 4 (.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) 8) (/.f64 (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 y-scale (.f64 b b))) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))))) (.f64 x-scale x-scale))
	21.2b	(.f64 -4 (/.f64 (/.f64 (pow.f64 (.f64 a b) 2) x-scale) (.f64 y-scale (.f64 x-scale y-scale))))
	22.3b	(.f64 (.f64 b (.f64 (.f64 b (/.f64 a y-scale)) (/.f64 a y-scale))) (/.f64 -4 (*.f64 x-scale x-scale)))
	6.0b	(.f64 -4 (pow.f64 (/.f64 (.f64 (/.f64 a x-scale) b) y-scale) 2))
	7.2b	(.f64 -4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2)) 3))
	18.9b	(/.f64 (.f64 (pow.f64 (.f64 a b) 2) -4) (pow.f64 (*.f64 x-scale y-scale) 2))
	18.3b	(.f64 -4 (.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 a x-scale) y-scale) b)) 2) (cbrt.f64 (pow.f64 (.f64 (/.f64 (/.f64 a x-scale) y-scale) b) 4))))
	5.8b	(.f64 -4 (pow.f64 (/.f64 1 (/.f64 (.f64 x-scale y-scale) (*.f64 a b))) 2))
	23.0b	(.f64 -4 (/.f64 (.f64 a (.f64 b b)) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) a)))
	7.2b	(.f64 -4 (pow.f64 (.f64 b (*.f64 (/.f64 1 x-scale) (/.f64 a y-scale))) 2))
	24.8b	(.f64 -4 (.f64 (.f64 (.f64 (/.f64 a x-scale) (/.f64 a y-scale)) (/.f64 1 (.f64 x-scale y-scale))) (.f64 b b)))
	7.4b	(.f64 -4 (.f64 (.f64 (.f64 (/.f64 (/.f64 a x-scale) y-scale) b) (pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 a x-scale) y-scale) b)) 2)) (cbrt.f64 (.f64 (/.f64 (/.f64 a x-scale) y-scale) b))))
	23.8b	(.f64 -4 (.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 a x-scale) y-scale) b)) (.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 a x-scale) y-scale) b)) (.f64 (/.f64 (/.f64 a x-scale) y-scale) b))))

Compiler

Compiled 2507 to 1221 computations (51.3% saved)

regimes1.4s (2%)

Accuracy

Total 5.6b remaining (97.7%)

Threshold costs 0b (0%)

Counts

91 → 4

Compiler

Compiled 29616 to 20759 computations (29.9% saved)

bsearch1.6s (2.4%)

Steps

Iters

Range

Point

1.0245464157233097e-123

8.313157853364139e-123

2.5702775997100276e-123

1.4214653745063213e-185

7.110373637190948e-177

8.904505747878003e-182

-1.0565319868132318e-226

-3.4534878985471464e-230

-8.4656445169403e-227

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	86
1	60	86
2	78	86
3	90	86
4	96	86
5	97	86

Stop Event

1×

saturated

end207.0ms (0.3%)

Compiler: Compiled 502 to 319 computations (36.5% saved)

Details

analyze12.7s (18.9%)

sample46.3s (68.7%)

simplify20.0ms (0%)

prune11.0ms (0%)

localize42.0ms (0.1%)

series2.6s (3.9%)

rewrite84.0ms (0.1%)

simplify170.0ms (0.3%)

prune913.0ms (1.4%)

localize0.0ms (0%)

prune16.0ms (0%)

localize10.0ms (0%)

series431.0ms (0.6%)

rewrite60.0ms (0.1%)

simplify61.0ms (0.1%)

prune174.0ms (0.3%)

localize8.0ms (0%)

series265.0ms (0.4%)

rewrite59.0ms (0.1%)

simplify59.0ms (0.1%)

prune206.0ms (0.3%)

regimes1.4s (2%)

bsearch1.6s (2.4%)

simplify5.0ms (0%)

end207.0ms (0.3%)

Profiling