Details

analyze12.7s (19.6%)

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)

sample45.2s (69.9%)

Results

12.2s	1512×	body	4096	valid
8.6s	1767×	body	2048	valid
6.5s	796×	body	4096	invalid
5.7s	1142×	body	2048	invalid
3.0s	904×	body	1024	valid
2.6s	3468×	body	128	valid
2.3s	696×	body	1024	invalid
1.1s	66×	body	8192	valid
859.0ms	394×	body	512	valid
694.0ms	1026×	body	128	invalid
635.0ms	296×	body	512	invalid
508.0ms	30×	body	8192	invalid
196.0ms	145×	body	256	valid
161.0ms	124×	body	256	invalid

Compiler

Compiled 344 to 251 computations (27% saved)

simplify19.0ms (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

prune12.0ms (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

42.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	47.7b	(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)))
▶	42.4b	(-.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 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

47.7b

(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)))

▶

42.4b

(-.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 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)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.3b	(.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))
✓	29.0b	(-.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 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)))
✓	30.9b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	31.4b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

series2.5s (3.8%)

Counts

4 → 144

Calls

4 calls:

1.9s	(-.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)))
604.0ms	(.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)))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite80.0ms (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:

74.0ms	(.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))
74.0ms	(-.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)))
74.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
74.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

simplify172.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

465×	`times-frac_binary64`
357×	`associate-/l*_binary64`
343×	`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 → 160

prune1.1s (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	297	10	307
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	299	10	309

Error

22.8b

Counts

309 → 10

Alt Table

Status	Error	Program
	42.6b	(-.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)))) 1) 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)))
	47.2b	(-.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 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 x-scale x-scale)) (.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (*.f64 angle 1/180))) 2) y-scale) (/.f64 (pow.f64 a 4) y-scale)) 4)))
	42.3b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 a a) (/.f64 (/.f64 (.f64 x-scale x-scale) (.f64 b b)) (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4))) (fma.f64 8 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 x-scale x-scale)) (.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 (.f64 a b) (.f64 a b)))) (/.f64 (.f64 (.f64 4 (.f64 (.f64 a b) (.f64 a b))) (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4)) (.f64 x-scale x-scale)))) (.f64 y-scale y-scale)))
	42.4b	(/.f64 (neg.f64 (fma.f64 4 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4) (.f64 y-scale y-scale)) (.f64 (.f64 a b) (.f64 a b))) (fma.f64 4 (.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4))) (.f64 8 (/.f64 (.f64 (.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 b b)) (.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 a a))) (.f64 y-scale y-scale)))))) (*.f64 x-scale x-scale))
	44.1b	(-.f64 (.f64 4 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (/.f64 (.f64 x-scale x-scale) (pow.f64 b 4))))) (fma.f64 8 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 y-scale y-scale)) (.f64 (/.f64 (.f64 a a) x-scale) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 b b)) x-scale))) (.f64 4 (+.f64 (.f64 (/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (.f64 b b))) (/.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4) (.f64 x-scale x-scale))) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4) (.f64 x-scale x-scale)) (/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (.f64 b b))) (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (/.f64 (*.f64 x-scale x-scale) (pow.f64 b 4)))))))))
	33.7b	(.f64 -4 (.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (*.f64 b b)))
	41.9b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	43.2b	(.f64 (.f64 a a) (neg.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 (PI.f64) (.f64 angle 1/180))) 4)) (fma.f64 8 (.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 b b)) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 x-scale x-scale))) (.f64 4 (.f64 (.f64 (/.f64 b x-scale) (/.f64 b x-scale)) (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4) (.f64 y-scale y-scale))))))))
▶	30.3b	0
	42.5b	(-.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 4 (/.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 b b) (.f64 a (.f64 a (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2)))) (/.f64 (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale)) (fma.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (*.f64 b b)))))))

Compiler

Compiled 39280 to 26767 computations (31.9% saved)

localize0.0ms (0%)

prune26.0ms (0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	9	9
Picked	1	1
Done	0	0
Total	10	10

Error

22.8b

Counts

10 → 10

Alt Table

Status	Error	Program
	42.6b	(-.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)))) 1) 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)))
	47.2b	(-.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 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 x-scale x-scale)) (.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (*.f64 angle 1/180))) 2) y-scale) (/.f64 (pow.f64 a 4) y-scale)) 4)))
	42.3b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 a a) (/.f64 (/.f64 (.f64 x-scale x-scale) (.f64 b b)) (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4))) (fma.f64 8 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 x-scale x-scale)) (.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 (.f64 a b) (.f64 a b)))) (/.f64 (.f64 (.f64 4 (.f64 (.f64 a b) (.f64 a b))) (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4)) (.f64 x-scale x-scale)))) (.f64 y-scale y-scale)))
	42.4b	(/.f64 (neg.f64 (fma.f64 4 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4) (.f64 y-scale y-scale)) (.f64 (.f64 a b) (.f64 a b))) (fma.f64 4 (.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4))) (.f64 8 (/.f64 (.f64 (.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 b b)) (.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 a a))) (.f64 y-scale y-scale)))))) (*.f64 x-scale x-scale))
	44.1b	(-.f64 (.f64 4 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (/.f64 (.f64 x-scale x-scale) (pow.f64 b 4))))) (fma.f64 8 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 y-scale y-scale)) (.f64 (/.f64 (.f64 a a) x-scale) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 b b)) x-scale))) (.f64 4 (+.f64 (.f64 (/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (.f64 b b))) (/.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4) (.f64 x-scale x-scale))) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4) (.f64 x-scale x-scale)) (/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (.f64 b b))) (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (/.f64 (*.f64 x-scale x-scale) (pow.f64 b 4)))))))))
▶	33.7b	(.f64 -4 (.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (*.f64 b b)))
	41.9b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	43.2b	(.f64 (.f64 a a) (neg.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 (PI.f64) (.f64 angle 1/180))) 4)) (fma.f64 8 (.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 b b)) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 x-scale x-scale))) (.f64 4 (.f64 (.f64 (/.f64 b x-scale) (/.f64 b x-scale)) (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 4) (.f64 y-scale y-scale))))))))
✓	30.3b	0
	42.5b	(-.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 4 (/.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 b b) (.f64 a (.f64 a (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2)))) (/.f64 (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale)) (fma.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 (PI.f64) (.f64 angle 1/180))) 2) (*.f64 b b)))))))

Compiler

Compiled 1550 to 1030 computations (33.5% saved)

localize11.0ms (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))
✓	16.8b	(/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale)))
✓	21.4b	(.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (.f64 b b))

series388.0ms (0.6%)

Counts

4 → 156

Calls

4 calls:

156.0ms	(.f64 -4 (.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (*.f64 b b)))
139.0ms	(.f64 (/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale))) (.f64 b b))
83.0ms	(/.f64 (.f64 a a) (.f64 (.f64 x-scale y-scale) (.f64 x-scale y-scale)))
9.0ms	(.f64 (.f64 x-scale y-scale) (*.f64 x-scale y-scale))

rewrite59.0ms (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:

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

simplify59.0ms (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

prune150.0ms (0.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	103	15	118
Fresh	8	0	8
Picked	1	0	1
Done	0	1	1
Total	112	16	128

Error

2.7b

Counts

128 → 16

Alt Table

Status	Error	Program
	4.7b	(pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2) -4)) 3)
	25.0b	(.f64 -4 (/.f64 (.f64 (.f64 (/.f64 a x-scale) (/.f64 a y-scale)) (.f64 b b)) (*.f64 x-scale y-scale)))
	29.1b	(.f64 -4 (.f64 (.f64 (/.f64 a (pow.f64 (.f64 x-scale y-scale) 2)) a) (*.f64 b b)))
	18.8b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (*.f64 x-scale y-scale) 2)))
	28.8b	(.f64 -4 (.f64 (.f64 (/.f64 a x-scale) (/.f64 a (.f64 y-scale (.f64 x-scale y-scale)))) (.f64 b b)))
	33.5b	(.f64 -4 (/.f64 (.f64 b b) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a a))))
	18.7b	(.f64 -4 (cbrt.f64 (pow.f64 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2) 3)))
	26.7b	(.f64 (.f64 b (.f64 (.f64 b (/.f64 a y-scale)) (/.f64 a y-scale))) (/.f64 -4 (*.f64 x-scale x-scale)))
▶	4.4b	(.f64 -4 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2))
✓	30.3b	0
	19.4b	(.f64 -4 (pow.f64 (pow.f64 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2) 3) 1/3))
	27.2b	(.f64 -4 (/.f64 (.f64 a (.f64 b b)) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) a)))
	14.3b	(.f64 -4 (/.f64 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 x-scale y-scale)) (.f64 x-scale y-scale)))
	21.5b	(.f64 -4 (/.f64 (/.f64 (pow.f64 (.f64 a b) 2) x-scale) (.f64 y-scale (.f64 x-scale y-scale))))
	19.0b	(.f64 -4 (/.f64 1 (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (pow.f64 (*.f64 a b) 2))))
	4.7b	(.f64 -4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2)) 3))

Compiler

Compiled 2564 to 1385 computations (46% saved)

localize7.0ms (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))
✓	0.3b	(pow.f64 (.f64 b (/.f64 a (.f64 x-scale y-scale))) 2)
✓	4.9b	(.f64 b (/.f64 a (.f64 x-scale y-scale)))
✓	5.3b	(/.f64 a (*.f64 x-scale y-scale))

series322.0ms (0.5%)

Counts

4 → 164

Calls

4 calls:

241.0ms	(.f64 -4 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2))
40.0ms	(pow.f64 (.f64 b (/.f64 a (.f64 x-scale y-scale))) 2)
26.0ms	(.f64 b (/.f64 a (.f64 x-scale y-scale)))
15.0ms	(/.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))

simplify60.0ms (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

prune184.0ms (0.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	124	7	131
Fresh	4	10	14
Picked	1	0	1
Done	1	0	1
Total	130	17	147

Error

0.0b

Counts

147 → 17

Alt Table

Status	Error	Program
	4.7b	(pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2) -4)) 3)
	25.0b	(.f64 -4 (/.f64 (.f64 (.f64 (/.f64 a x-scale) (/.f64 a y-scale)) (.f64 b b)) (*.f64 x-scale y-scale)))
	14.3b	(.f64 -4 (/.f64 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 x-scale y-scale)) (.f64 x-scale y-scale)))
	6.3b	(.f64 -4 (pow.f64 (/.f64 (.f64 (/.f64 a x-scale) b) y-scale) 2))
	7.8b	(.f64 -4 (pow.f64 (.f64 b (*.f64 (/.f64 1 x-scale) (/.f64 a y-scale))) 2))
	28.8b	(.f64 -4 (.f64 (.f64 (/.f64 a x-scale) (/.f64 a (.f64 y-scale (.f64 x-scale y-scale)))) (.f64 b b)))
	33.5b	(.f64 -4 (/.f64 (.f64 b b) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a a))))
	4.7b	(.f64 -4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2)) 3))
	8.5b	(.f64 -4 (.f64 (/.f64 (/.f64 a x-scale) y-scale) (.f64 b (.f64 (/.f64 (/.f64 a x-scale) y-scale) b))))
	17.0b	(.f64 -4 (sqrt.f64 (pow.f64 (.f64 (/.f64 (/.f64 a x-scale) y-scale) b) 4)))
	4.8b	(.f64 -4 (pow.f64 (/.f64 (.f64 a b) (*.f64 y-scale x-scale)) 2))
	27.2b	(.f64 -4 (/.f64 (.f64 a (.f64 b b)) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) a)))
	11.7b	(.f64 -4 (/.f64 (.f64 (.f64 a b) (.f64 (/.f64 (/.f64 a x-scale) y-scale) b)) (*.f64 x-scale y-scale)))
	21.5b	(.f64 -4 (/.f64 (/.f64 (pow.f64 (.f64 a b) 2) x-scale) (.f64 y-scale (.f64 x-scale y-scale))))
	29.1b	(.f64 -4 (.f64 (.f64 (/.f64 a (pow.f64 (.f64 x-scale y-scale) 2)) a) (*.f64 b b)))
	26.7b	(.f64 (.f64 b (.f64 (.f64 b (/.f64 a y-scale)) (/.f64 a y-scale))) (/.f64 -4 (*.f64 x-scale x-scale)))
	8.8b	(.f64 -4 (.f64 b (.f64 (/.f64 (/.f64 a x-scale) y-scale) (.f64 (/.f64 (/.f64 a x-scale) y-scale) b))))

Compiler

Compiled 2468 to 1219 computations (50.6% saved)

regimes1.3s (2%)

Accuracy

Total 4.2b remaining (97.4%)

Threshold costs 0b (0%)

Counts

82 → 2

Compiler

Compiled 36272 to 25735 computations (29% saved)

bsearch8.0ms (0%)

Compiler: Compiled 114 to 83 computations (27.2% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

29×	`*-commutative_binary64`
17×	`+-commutative_binary64`
15×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	215
1	83	215
2	103	215
3	117	215
4	132	215
5	150	215
6	168	215
7	178	215
8	182	215

Stop Event

1×

saturated

end234.0ms (0.4%)

Compiler: Compiled 619 to 433 computations (30% saved)

Iter	Nodes	Cost
0	57	215
1	83	215
2	103	215
3	117	215
4	132	215
5	150	215
6	168	215
7	178	215
8	182	215

Iter	Nodes	Cost
0	57	215
1	83	215
2	103	215
3	117	215
4	132	215
5	150	215
6	168	215
7	178	215
8	182	215

Details

analyze12.7s (19.6%)

sample45.2s (69.9%)

simplify19.0ms (0%)

prune12.0ms (0%)

localize36.0ms (0.1%)

series2.5s (3.8%)

rewrite80.0ms (0.1%)

simplify172.0ms (0.3%)

prune1.1s (1.7%)

localize0.0ms (0%)

prune26.0ms (0%)

localize11.0ms (0%)

series388.0ms (0.6%)

rewrite59.0ms (0.1%)

simplify59.0ms (0.1%)

prune150.0ms (0.2%)

localize7.0ms (0%)

series322.0ms (0.5%)

rewrite59.0ms (0.1%)

simplify60.0ms (0.1%)

prune184.0ms (0.3%)

regimes1.3s (2%)

bsearch8.0ms (0%)

simplify9.0ms (0%)

end234.0ms (0.4%)

Profiling

Iter	Nodes	Cost
0	57	215
1	83	215
2	103	215
3	117	215
4	132	215
5	150	215
6	168	215
7	178	215
8	182	215