Details

analyze24.1s (16.1%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
5.3%	94.5%	0.2%	11
6.1%	93.6%	0.2%	12
9.2%	90.6%	0.2%	13
13.8%	85.9%	0.2%	14

Compiler

Compiled 175 to 127 computations (27.4% saved)

sample57.8s (38.5%)

Results

21.2s	1689×	body	4096	valid
11.7s	1446×	body	2048	valid
11.6s	1701×	body	1024	valid
6.3s	83×	body	8192	exit
3.3s	687×	body	512	valid
2.6s	2392×	body	128	valid
997.0ms	341×	body	256	valid

Compiler

Compiled 524 to 380 computations (27.5% saved)

simplify46.0ms (0%)

Algorithm

1×	egg-herbie

Rules

873×	`div-sub_binary64`
637×	`times-frac_binary64`
295×	`associate-/l/_binary64`
206×	`fma-neg_binary64`
198×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	273
1	115	265
2	319	265
3	1421	265
4	4671	265
5	6224	265

prune16.0ms (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

53.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	53.1b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) x-scale) x-scale)) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 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)) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale))) (PI.f64)))
	53.7b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.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) (/.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)) (sqrt.f64 (+.f64 (pow.f64 (-.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 (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)) 2) (pow.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) 2)))) (/.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))) (PI.f64)))

Status

Error

Program

▶

53.1b

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

53.7b

(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.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) (/.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)) (sqrt.f64 (+.f64 (pow.f64 (-.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 (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)) 2) (pow.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) 2)))) (/.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))) (PI.f64)))

Compiler

Compiled 1024 to 714 computations (30.3% saved)

localize44.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	17.8b	(-.f64 (-.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) x-scale) x-scale)) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 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)) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale)))
✓	23.0b	(/.f64 (-.f64 (-.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) x-scale) x-scale)) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 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)) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))
✓	25.7b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	25.9b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

series54.4s (36.3%)

Counts

4 → 144

Calls

4 calls:

38.1s	(/.f64 (-.f64 (-.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) x-scale) x-scale)) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 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)) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))
16.3s	(-.f64 (-.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) x-scale) x-scale)) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 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)) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale)))
3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
3.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite127.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

458×	`log1p-expm1-u_binary64`
458×	`expm1-log1p-u_binary64`
424×	`pow1_binary64`
298×	`prod-diff_binary64`
152×	`log-prod_binary64`

Counts

4 → 85

Calls

4 calls:

118.0ms	(-.f64 (-.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) x-scale) x-scale)) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 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)) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale)))
118.0ms	(/.f64 (-.f64 (-.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 2)) x-scale) x-scale)) (hypot.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) b) 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)) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))
118.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
118.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	487
1	946	463
2	4953	463
3	5301	463

simplify3.8s (2.6%)

Algorithm

1×	egg-herbie

Counts

229 → 182

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10900	677483

prune9.6s (6.4%)

Compiler: Compiled 393740 to 277266 computations (29.6% saved)

Details

analyze24.1s (16.1%)

sample57.8s (38.5%)

simplify46.0ms (0%)

prune16.0ms (0%)

localize44.0ms (0%)

series54.4s (36.3%)

rewrite127.0ms (0.1%)

simplify3.8s (2.6%)

prune9.6s (6.4%)

Profiling