Details

analyze23.6s (15.7%)

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
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 189 to 125 computations (33.9% saved)

sample36.5s (24.3%)

Results

12.8s	1917×	body	1024	valid
6.5s	967×	body	1024	invalid
4.7s	4688×	body	128	valid
4.4s	1002×	body	512	valid
2.3s	515×	body	512	invalid
2.0s	1982×	body	128	invalid
2.0s	205×	body	2048	valid
1.1s	444×	body	256	valid
681.0ms	246×	body	256	invalid

Compiler

Compiled 378 to 250 computations (33.9% saved)

preprocess60.0ms (0%)

Algorithm

2×	egg-herbie

Rules

544×	`associate-r_binary64`
492×	`associate-l_binary64`
171×	`times-frac_binary64`
170×	`associate-/l*_binary64`
138×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	410	3212
1	1268	3033
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 188 to 124 computations (34% saved)

simplify19.0ms (0%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
668×	`associate-l_binary64`
301×	`associate-/r*_binary64`
262×	`associate-/l*_binary64`
190×	`associate-*l/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	292
1	160	279
2	643	279

Stop Event

1×	node limit

Counts

1 → 2

prune11.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

62.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	62.8b	(.f64 (/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (/.f64 (.f64 (.f64 b (neg.f64 a)) 8) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a (.f64 (neg.f64 a) (.f64 b b)))))) (+.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)) (hypot.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)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 (/.f64 x-scale (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (/.f64 y-scale (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))))) (.f64 a (.f64 (.f64 b b) (.f64 a -4)))) (neg.f64 (pow.f64 (.f64 x-scale y-scale) 2)))

Status

Error

Program

▶

62.8b

(*.f64 (/.f64 (sqrt.f64 (*.f64 b (*.f64 (*.f64 a (/.f64 (*.f64 (*.f64 b (neg.f64 a)) 8) (/.f64 (pow.f64 (*.f64 x-scale y-scale) 2) (*.f64 a (*.f64 (neg.f64 a) (*.f64 b b)))))) (+.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)) (hypot.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)) (*.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale))) (*.f64 (/.f64 2 (/.f64 x-scale (-.f64 (*.f64 b b) (*.f64 a a)))) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (/.f64 y-scale (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))))))))) (*.f64 a (*.f64 (*.f64 b b) (*.f64 a -4)))) (neg.f64 (pow.f64 (*.f64 x-scale y-scale) 2)))

Compiler

Compiled 723 to 466 computations (35.5% saved)

localize62.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	22.2b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	22.4b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	37.8b	(/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (/.f64 (.f64 (.f64 b (neg.f64 a)) 8) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a (.f64 (neg.f64 a) (.f64 b b)))))) (+.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)) (hypot.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)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 (/.f64 x-scale (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (/.f64 y-scale (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))))) (.f64 a (.f64 (.f64 b b) (.f64 a -4))))
✓	41.2b	(.f64 (/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (/.f64 (.f64 (.f64 b (neg.f64 a)) 8) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a (.f64 (neg.f64 a) (.f64 b b)))))) (+.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)) (hypot.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)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 (/.f64 x-scale (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (/.f64 y-scale (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))))) (.f64 a (.f64 (.f64 b b) (.f64 a -4)))) (neg.f64 (pow.f64 (.f64 x-scale y-scale) 2)))

series1.5min (59.8%)

Calls

6 calls:

19.7s	(.f64 (/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (/.f64 (.f64 (.f64 b (neg.f64 a)) 8) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a (.f64 (neg.f64 a) (.f64 b b)))))) (+.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)) (hypot.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)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 (/.f64 x-scale (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (/.f64 y-scale (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))))) (.f64 a (.f64 (.f64 b b) (.f64 a -4)))) (neg.f64 (pow.f64 (.f64 x-scale y-scale) 2)))	a	0
16.7s	(.f64 (/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (/.f64 (.f64 (.f64 b (neg.f64 a)) 8) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a (.f64 (neg.f64 a) (.f64 b b)))))) (+.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)) (hypot.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)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 (/.f64 x-scale (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (/.f64 y-scale (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))))) (.f64 a (.f64 (.f64 b b) (.f64 a -4)))) (neg.f64 (pow.f64 (.f64 x-scale y-scale) 2)))	b	0
15.1s	(.f64 (/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (/.f64 (.f64 (.f64 b (neg.f64 a)) 8) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a (.f64 (neg.f64 a) (.f64 b b)))))) (+.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)) (hypot.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)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 (/.f64 x-scale (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (/.f64 y-scale (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))))) (.f64 a (.f64 (.f64 b b) (.f64 a -4)))) (neg.f64 (pow.f64 (.f64 x-scale y-scale) 2)))	b	-inf
14.8s	(.f64 (/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (/.f64 (.f64 (.f64 b (neg.f64 a)) 8) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a (.f64 (neg.f64 a) (.f64 b b)))))) (+.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)) (hypot.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)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 (/.f64 x-scale (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (/.f64 y-scale (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))))) (.f64 a (.f64 (.f64 b b) (.f64 a -4)))) (neg.f64 (pow.f64 (.f64 x-scale y-scale) 2)))	b	inf
14.7s	(.f64 (/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (/.f64 (.f64 (.f64 b (neg.f64 a)) 8) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a (.f64 (neg.f64 a) (.f64 b b)))))) (+.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)) (hypot.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)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale))) (.f64 (/.f64 2 (/.f64 x-scale (-.f64 (.f64 b b) (.f64 a a)))) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (/.f64 y-scale (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))))))))) (.f64 a (.f64 (.f64 b b) (.f64 a -4)))) (neg.f64 (pow.f64 (.f64 x-scale y-scale) 2)))	a	inf

Details

analyze23.6s (15.7%)

sample36.5s (24.3%)

preprocess60.0ms (0%)

simplify19.0ms (0%)

prune11.0ms (0%)

localize62.0ms (0%)

series1.5min (59.8%)

Profiling