Details

analyze22.9s (15.3%)

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)

sample1.5min (60.2%)

Results

39.8s	3785×	body	4096	valid
34.5s	1608×	body	8192	valid
11.8s	1815×	body	2048	valid
2.7s	642×	body	1024	valid
671.0ms	238×	body	512	valid
291.0ms	40×	body	2048	invalid
227.0ms	117×	body	256	valid
192.0ms	42×	body	1024	invalid
49.0ms	18×	body	512	invalid
48.0ms	51×	body	128	valid
47.0ms	4×	body	4096	invalid
14.0ms	8×	body	256	invalid
10.0ms	9×	body	128	invalid

Compiler

Compiled 378 to 250 computations (33.9% saved)

preprocess61.0ms (0%)

Algorithm

2×	egg-herbie

Rules

461×	`associate-r_binary64`
408×	`associate-l_binary64`
290×	`*-commutative_binary64`
171×	`times-frac_binary64`
170×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	410	3212
1	1203	3033
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 188 to 124 computations (34% saved)

simplify28.0ms (0%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
587×	`associate-l_binary64`
580×	`associate-r_binary64`
299×	`associate-/r*_binary64`
262×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	292
1	155	279
2	603	279

Stop Event

1×	node limit

Counts

1 → 2

prune12.0ms (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

63.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (.f64 a (.f64 (neg.f64 b) (/.f64 (.f64 8 (.f64 b a)) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 b (neg.f64 a))))))) (+.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 (+.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)) (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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) x-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) y-scale)))))))) (.f64 (.f64 a (neg.f64 a)) (.f64 b b))) (pow.f64 (.f64 x-scale y-scale) 2)))

Status

Error

Program

▶

63.9b

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

Compiler

Compiled 723 to 468 computations (35.3% saved)

localize59.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	27.3b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	27.3b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	27.6b	(/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (.f64 a (.f64 (neg.f64 b) (/.f64 (.f64 8 (.f64 b a)) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 b (neg.f64 a))))))) (+.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 (+.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)) (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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) x-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) y-scale)))))))) (.f64 (.f64 a (neg.f64 a)) (*.f64 b b)))
✓	27.6b	(-.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)) (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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) x-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) y-scale))))

series36.6s (24.4%)

Calls

17 calls:

17.8s	(/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (.f64 a (.f64 (neg.f64 b) (/.f64 (.f64 8 (.f64 b a)) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 b (neg.f64 a))))))) (+.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 (+.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)) (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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) x-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) y-scale)))))))) (.f64 (.f64 a (neg.f64 a)) (*.f64 b b)))	b	0
6.3s	(/.f64 (sqrt.f64 (.f64 b (.f64 (.f64 a (.f64 a (.f64 (neg.f64 b) (/.f64 (.f64 8 (.f64 b a)) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 b (neg.f64 a))))))) (+.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 (+.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)) (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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) x-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) y-scale)))))))) (.f64 (.f64 a (neg.f64 a)) (*.f64 b b)))	b	inf
2.0s	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale)) (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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) x-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) y-scale))))	angle	0
1.2s	(-.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)) (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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) x-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) y-scale))))	b	0
1.2s	(-.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)) (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 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) x-scale) (/.f64 (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) y-scale))))	a	0

Details

analyze22.9s (15.3%)

sample1.5min (60.2%)

preprocess61.0ms (0%)

simplify28.0ms (0%)

prune12.0ms (0%)

localize59.0ms (0%)

series36.6s (24.4%)

Profiling