Details

analyze19.1s (18.1%)

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
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)

sample50.0s (47.3%)

Results

13.3s	1525×	body	4096	valid
9.0s	1685×	body	2048	valid
8.2s	876×	body	4096	invalid
6.5s	1146×	body	2048	invalid
3.1s	902×	body	1024	valid
3.0s	3547×	body	128	valid
2.2s	653×	body	1024	invalid
1.1s	58×	body	8192	valid
905.0ms	366×	body	512	valid
794.0ms	1072×	body	128	invalid
634.0ms	275×	body	512	invalid
595.0ms	36×	body	8192	invalid
247.0ms	173×	body	256	valid
225.0ms	122×	body	256	invalid

Compiler

Compiled 344 to 251 computations (27% saved)

simplify37.0ms (0%)

Algorithm

1×	egg-herbie

Rules

600×	`associate-/l/_binary64`
529×	`associate-/r/_binary64`
282×	`div-sub_binary64`
263×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	175
1	104	173
2	316	173
3	1431	170
4	4673	170
5	5335	170

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

41.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	41.6b	(-.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)))) (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)))
	46.1b	(fma.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 (+.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) (.f64 (.f64 (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 x-scale y-scale)) (/.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64))) (.f64 x-scale y-scale))) (.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))))))))

Status

Error

Program

▶

41.6b

(-.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)))) (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)))

46.1b

(fma.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 (+.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) (*.f64 (*.f64 (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 x-scale y-scale)) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) (*.f64 x-scale y-scale))) (*.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))))))))

Compiler

Compiled 670 to 459 computations (31.5% saved)

localize38.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	14.0b	(.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))
✓	27.7b	(-.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)))
✓	29.2b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	29.6b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

series4.1s (3.9%)

Counts

4 → 144

Calls

4 calls:

3.2s	(-.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)))
902.0ms	(.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))
3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
3.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite80.0ms (0.1%)

Algorithm

2×	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`

Counts

4 → 87

Calls

4 calls:

73.0ms	(.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))
73.0ms	(-.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)))
73.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
73.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	238
1	914	226
2	5200	226
0	0	0
1	0	0

simplify286.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

465×	`times-frac_binary64`
431×	`fma-neg_binary64`
357×	`associate-/l*_binary64`
342×	`associate-r_binary64`
277×	`associate-/r*_binary64`

Counts

231 → 155

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	297	18027
1	1020	16993
2	4866	16993
3	5195	16993

prune979.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	286	7	293
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	288	7	295

Error

27.1b

Counts

295 → 7

Alt Table

Status	Error	Program
	42.1b	(-.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 (pow.f64 (cbrt.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 3)) 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)))
	40.0b	(neg.f64 (.f64 (.f64 a a) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (*.f64 x-scale x-scale))))))))
	41.8b	(-.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 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 3)) 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)))
▶	30.7b	0
	39.0b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale)))
	38.7b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale)))
	42.9b	(-.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (pow.f64 a 2) (pow.f64 b 2))) (*.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2))))))))

Compiler

Compiled 37424 to 25493 computations (31.9% saved)

localize0.0ms (0%)

prune23.0ms (0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

27.1b

Counts

7 → 7

Alt Table

Status	Error	Program
	42.1b	(-.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 (pow.f64 (cbrt.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 3)) 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)))
	40.0b	(neg.f64 (.f64 (.f64 a a) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (*.f64 x-scale x-scale))))))))
	41.8b	(-.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 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 3)) 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)))
✓	30.7b	0
	39.0b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 x-scale x-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 x-scale x-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 x-scale x-scale))))) (.f64 y-scale y-scale)))
▶	38.7b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale)))
	42.9b	(-.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (pow.f64 a 2) (pow.f64 b 2))) (*.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2))))))))

Compiler

Compiled 1300 to 876 computations (32.6% saved)

localize38.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	17.0b	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (*.f64 y-scale y-scale))
✓	20.3b	(/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale))
✓	29.2b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
✓	29.4b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series2.8s (2.6%)

Counts

4 → 116

Calls

4 calls:

1.6s	(/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale))
1.2s	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (*.f64 y-scale y-scale))
4.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
4.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

rewrite77.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

363×	`log1p-expm1-u_binary64`
363×	`expm1-log1p-u_binary64`
359×	`add-log-exp_binary64`
358×	`add-exp-log_binary64`
347×	`pow1_binary64`

Counts

4 → 65

Calls

4 calls:

75.0ms	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (*.f64 y-scale y-scale))
75.0ms	(/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale))
75.0ms	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
75.0ms	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	174
1	801	159
2	4864	159
3	4959	159
0	0	0
1	0	0

simplify211.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-def_binary64`
448×	`unswap-sqr_binary64`
311×	`cancel-sign-sub-inv_binary64`
279×	`fma-neg_binary64`
251×	`associate-r_binary64`

Counts

181 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	8612
1	601	8451
2	2471	8017
3	4680	8017
4	4873	8017

prune737.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	143	11	154

Error

25.5b

Counts

154 → 11

Alt Table

Status	Error	Program
	38.4b	(neg.f64 (/.f64 (fma.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))) (.f64 y-scale y-scale)) (.f64 (/.f64 4 y-scale) (+.f64 (/.f64 (.f64 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) y-scale) (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) y-scale)))) (.f64 x-scale x-scale)))
	38.7b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 3)) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale)))
	42.1b	(-.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 (pow.f64 (cbrt.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 3)) 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)))
	40.0b	(neg.f64 (.f64 (.f64 a a) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (*.f64 x-scale x-scale))))))))
	38.4b	(neg.f64 (/.f64 (fma.f64 4 (pow.f64 (/.f64 (.f64 y-scale y-scale) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2))) -1) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale)))
✓	30.7b	0
▶	37.2b	(neg.f64 (pow.f64 (/.f64 (.f64 x-scale x-scale) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 y-scale -2)))))) -1))
	37.7b	(neg.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 y-scale -2))))) (pow.f64 x-scale -2))) 3))
	38.6b	(neg.f64 (/.f64 (fma.f64 4 (exp.f64 (log.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)))) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale)))
	40.3b	(neg.f64 (/.f64 (fma.f64 4 (pow.f64 (pow.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) 3) 1/3) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale)))
	39.9b	(neg.f64 (/.f64 (fma.f64 4 (.f64 (/.f64 (.f64 a a) y-scale) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) y-scale) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) y-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 y-scale y-scale)))) (/.f64 (.f64 x-scale x-scale) (*.f64 b b))))

Compiler

Compiled 14256 to 7710 computations (45.9% saved)

localize37.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	17.0b	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (*.f64 y-scale y-scale))
✓	19.4b	(/.f64 (.f64 x-scale x-scale) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 y-scale -2))))))
	29.2b	(cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))
	29.4b	(sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))

series10.5s (10%)

Counts

2 → 108

Calls

2 calls:

10.2s

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

387.0ms

(/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (pow.f64 (*.f64 a b) 2)) (*.f64 y-scale y-scale))

rewrite87.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

358×	`log1p-expm1-u_binary64`
358×	`expm1-log1p-u_binary64`
351×	`add-cbrt-cube_binary64`
347×	`add-log-exp_binary64`
346×	`add-exp-log_binary64`

Counts

2 → 35

Calls

2 calls:

84.0ms

(/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (pow.f64 (*.f64 a b) 2)) (*.f64 y-scale y-scale))

83.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	136
1	789	136
2	5452	136
0	0	0
1	0	0

simplify277.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

914×	`associate-/l*_binary64`
595×	`associate-/r*_binary64`
277×	`fma-def_binary64`
267×	`unswap-sqr_binary64`
207×	`associate-/r/_binary64`

Counts

143 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	8162
1	313	8014
2	1294	7532
3	5067	7532

prune1.1s (1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	135	8	143
Fresh	5	4	9
Picked	1	0	1
Done	0	1	1
Total	141	13	154

Error

22.9b

Counts

154 → 13

Alt Table

Status	Error	Program
	40.0b	(neg.f64 (.f64 (.f64 a a) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (.f64 y-scale y-scale) (.f64 x-scale x-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 (.f64 y-scale y-scale) (*.f64 x-scale x-scale))))))))
	36.4b	(neg.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 x-scale x-scale) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2) (pow.f64 y-scale -2)))))) 3)) -1))
	42.1b	(-.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 (pow.f64 (cbrt.f64 (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 3)) 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)))
	32.9b	(neg.f64 (pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 x-scale x-scale) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2) (pow.f64 y-scale -2))))))) 2) -1))
	39.9b	(neg.f64 (/.f64 (fma.f64 4 (.f64 (/.f64 (.f64 a a) y-scale) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) y-scale) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) y-scale))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 y-scale y-scale)))) (/.f64 (.f64 x-scale x-scale) (*.f64 b b))))
	37.2b	(neg.f64 (pow.f64 (/.f64 (.f64 x-scale x-scale) (fma.f64 4 (pow.f64 (/.f64 (.f64 y-scale y-scale) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2))) -1) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) 2) (pow.f64 (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2)) (pow.f64 y-scale -2)))))) -1))
✓	30.7b	0
	33.0b	(neg.f64 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 x-scale x-scale) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2) (pow.f64 y-scale -2))))))) 2) (cbrt.f64 (/.f64 (.f64 x-scale x-scale) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))))) 2) (pow.f64 y-scale -2)))))))) -1))
	32.9b	(neg.f64 (pow.f64 (.f64 (.f64 x-scale x-scale) (/.f64 1 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))))) 2) (pow.f64 y-scale -2))))))) -1))
	38.7b	(neg.f64 (/.f64 (fma.f64 4 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 3)) 4) (.f64 (.f64 a a) (.f64 b b))) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (.f64 a a) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 y-scale y-scale)) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) (.f64 y-scale y-scale))))) (.f64 x-scale x-scale)))
	33.4b	(neg.f64 (pow.f64 (exp.f64 (log.f64 (/.f64 (.f64 x-scale x-scale) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2) (pow.f64 y-scale -2)))))))) -1))
	38.5b	(neg.f64 (pow.f64 (/.f64 (.f64 x-scale x-scale) (.f64 (.f64 a a) (fma.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 y-scale y-scale)) (.f64 (/.f64 4 y-scale) (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 b b)) y-scale) (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) y-scale)))))) -1))
	36.6b	(neg.f64 (pow.f64 (pow.f64 (pow.f64 (/.f64 (.f64 x-scale x-scale) (fma.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 (.f64 a b) 2)) (.f64 y-scale y-scale)) (fma.f64 4 (/.f64 (.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 y-scale y-scale)) (.f64 8 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) a) (.f64 b (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))))) 2) (pow.f64 y-scale -2)))))) 3) 1/3) -1))

Compiler

Compiled 12590 to 7767 computations (38.3% saved)

regimes7.1s (6.8%)

Accuracy

Total 3.4b remaining (12.9%)

Threshold costs 0b (0%)

Counts

149 → 5

Compiler

Compiled 114300 to 80432 computations (29.6% saved)

bsearch7.0s (6.6%)

Steps

Iters	Range		Point
10	4.8289711566502535e+135	2.0126216025952726e+154	4.144448978699342e+153
9	1.0340750904346658e-144	1.5991582118538626e-137	1.0490117072824621e-144
12	-4.3558419591338245e-147	-4.096522804581416e-191	-1.2055991195742165e-154
7	-5.272398230964545e+159	-2.5371053510437917e+158	-1.1813850436860082e+159

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	256
1	76	256
2	80	256
3	82	256
4	81	256

end1.0s (1%)

Compiler: Compiled 1413 to 934 computations (33.9% saved)

Details

analyze19.1s (18.1%)

sample50.0s (47.3%)

simplify37.0ms (0%)

prune11.0ms (0%)

localize38.0ms (0%)

series4.1s (3.9%)

rewrite80.0ms (0.1%)

simplify286.0ms (0.3%)

prune979.0ms (0.9%)

localize0.0ms (0%)

prune23.0ms (0%)

localize38.0ms (0%)

series2.8s (2.6%)

rewrite77.0ms (0.1%)

simplify211.0ms (0.2%)

prune737.0ms (0.7%)

localize37.0ms (0%)

series10.5s (10%)

rewrite87.0ms (0.1%)

simplify277.0ms (0.3%)

prune1.1s (1%)

regimes7.1s (6.8%)

bsearch7.0s (6.6%)

simplify13.0ms (0%)

end1.0s (1%)

Profiling