Details

analyze13.2s (14.9%)

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
24.9%	74.8%	0.2%	6
24.9%	74.8%	0.2%	7
24.9%	74.8%	0.2%	8
24.9%	74.8%	0.2%	9
37.4%	62.3%	0.2%	10
56.1%	43.6%	0.2%	11
56.1%	43.6%	0.2%	12
56.1%	43.6%	0.2%	13
56.1%	43.6%	0.2%	14

Compiler

Compiled 115 to 84 computations (27% saved)

sample55.2s (62.5%)

Results

22.7s	1562×	body	4096	valid
17.8s	1930×	body	2048	valid
6.4s	1062×	body	1024	valid
3.9s	3003×	body	128	valid
2.0s	68×	body	8192	valid
1.7s	444×	body	512	valid
448.0ms	187×	body	256	valid

Compiler

Compiled 344 to 251 computations (27% saved)

simplify74.0ms (0.1%)

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

prune22.0ms (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

45.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	48.0b	(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))))))))
▶	45.7b	(-.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)))

Status

Error

Program

48.0b

(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))))))))

▶

45.7b

(-.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)))

Compiler

Compiled 670 to 459 computations (31.5% saved)

localize78.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	9.2b	(/.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)
✓	29.9b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	30.4b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	38.1b	(-.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 (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)))

series5.5s (6.2%)

Counts

4 → 132

Calls

4 calls:

5.1s	(-.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)))
358.0ms	(/.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)
16.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
6.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite72.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
15×	`associate-*r/_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`

Counts

4 → 80

Calls

4 calls:

41.0ms	(-.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)))
12.0ms	(/.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)
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
1.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

simplify551.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

421×	`associate-r_binary64`
313×	`associate-l_binary64`
311×	`associate-/l*_binary64`
292×	`times-frac_binary64`
265×	`fma-def_binary64`

Counts

212 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	428	21239
1	1306	19706
2	5249	19706

prune2.2s (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	331	10	341
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	333	10	343

Error

22.4b

Counts

343 → 10

Alt Table

Status	Error	Program
	45.2b	(-.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 4 (/.f64 (.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (/.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) 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)))
	47.4b	(fma.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 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)) (.f64 x-scale x-scale)) (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)) (.f64 y-scale y-scale)))))
	48.5b	(-.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))) (fma.f64 1/180 (.f64 angle (PI.f64)) (.f64 (.f64 (pow.f64 angle 3) (pow.f64 (PI.f64) 3)) -1/34992000))) (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)))
	40.6b	0
	45.0b	(/.f64 (-.f64 (.f64 x-scale (.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) x-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) x-scale) y-scale))) (.f64 y-scale (.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)) (.f64 y-scale y-scale)) (.f64 4 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)) x-scale))))) (*.f64 y-scale x-scale))
	43.5b	(-.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))) (.f64 1/180 (.f64 angle (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)))
▶	34.0b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	39.1b	(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))))))))
	44.6b	(fma.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) (neg.f64 (.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))))
	38.1b	(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)))

Compiler

Compiled 43628 to 30269 computations (30.6% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
✓	13.3b	(/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))
✓	14.1b	(*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))
✓	18.1b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series803.0ms (0.9%)

Counts

4 → 60

Calls

4 calls:

390.0ms	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
365.0ms	(/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))
24.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
23.0ms	(*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))

rewrite143.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

650×	`add-exp-log_binary64`
479×	`prod-exp_binary64`
252×	`pow-exp_binary64`
252×	`pow-to-exp_binary64`
200×	`div-exp_binary64`

Counts

4 → 352

Calls

4 calls:

18.0ms	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
15.0ms	(/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))
12.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
10.0ms	(*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))

simplify382.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

460×	`fma-def_binary64`
331×	`associate-/r/_binary64`
314×	`associate-/l/_binary64`
283×	`unswap-sqr_binary64`
252×	`times-frac_binary64`

Counts

412 → 270

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	9211
1	438	8177
2	2019	7939
3	4366	7330
4	5053	7330

prune1.0s (1.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	255	15	270
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	261	19	280

Error

9.1b

Counts

280 → 19

Alt Table

Status	Error	Program
	45.2b	(-.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 4 (/.f64 (.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (/.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) 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)))
	34.0b	(/.f64 (.f64 -4 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))
	44.6b	(fma.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) (neg.f64 (.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))))
	58.4b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 a) 2) (log.f64 (pow.f64 b 2))) (+.f64 (.f64 (log.f64 y-scale) 2) (.f64 (log.f64 x-scale) 2)))))
	48.5b	(-.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))) (fma.f64 1/180 (.f64 angle (PI.f64)) (.f64 (.f64 (pow.f64 angle 3) (pow.f64 (PI.f64) 3)) -1/34992000))) (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)))
	40.6b	0
	45.9b	(.f64 -4 (exp.f64 (fma.f64 2 (log.f64 (/.f64 a y-scale)) (.f64 2 (log.f64 (/.f64 b x-scale))))))
	34.0b	(.f64 -4 (.f64 (/.f64 (pow.f64 a 2) (pow.f64 y-scale 2)) (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2))))
	60.0b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 a) 2) (.f64 (log.f64 b) 2)) (+.f64 (.f64 (log.f64 y-scale) 2) (*.f64 (log.f64 x-scale) 2)))))
▶	24.9b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	27.2b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 y-scale (.f64 x-scale (*.f64 x-scale y-scale)))))
	46.3b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 a 2)) (log.f64 (pow.f64 b 2))) (+.f64 (log.f64 (pow.f64 y-scale 2)) (.f64 (log.f64 x-scale) 2)))))
	26.3b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (pow.f64 (*.f64 y-scale x-scale) 2)))
	31.0b	(.f64 -4 (/.f64 (.f64 (.f64 (pow.f64 a 2) b) b) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	58.4b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 a 2)) (.f64 (log.f64 b) 2)) (+.f64 (.f64 (log.f64 y-scale) 2) (.f64 (log.f64 x-scale) 2)))))
	47.9b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 a) 2) (log.f64 (pow.f64 b 2))) (+.f64 (log.f64 (pow.f64 y-scale 2)) (log.f64 (pow.f64 x-scale 2))))))
	57.7b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 a) 2) (.f64 (log.f64 b) 2)) (+.f64 (.f64 (log.f64 y-scale) 2) (log.f64 (pow.f64 x-scale 2))))))
	32.9b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 (pow.f64 (.f64 (cbrt.f64 y-scale) (cbrt.f64 y-scale)) 2) (*.f64 (pow.f64 (cbrt.f64 y-scale) 2) (pow.f64 x-scale 2)))))
	26.4b	(.f64 -4 (/.f64 (.f64 (.f64 a (.f64 a b)) b) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))

Compiler

Compiled 8018 to 5535 computations (31% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
✓	0.2b	(pow.f64 (*.f64 a b) 2)
✓	13.3b	(/.f64 (pow.f64 (.f64 a b) 2) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))
	14.1b	(*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))

series909.0ms (1%)

Counts

3 → 120

Calls

3 calls:

546.0ms	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
348.0ms	(/.f64 (pow.f64 (.f64 a b) 2) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))
14.0ms	(pow.f64 (*.f64 a b) 2)

rewrite84.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

232×	`add-exp-log_binary64`
134×	`prod-exp_binary64`
90×	`pow-exp_binary64`
80×	`div-exp_binary64`
69×	`pow-to-exp_binary64`

Counts

3 → 157

Calls

3 calls:

48.0ms	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
13.0ms	(/.f64 (pow.f64 (.f64 a b) 2) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))
5.0ms	(pow.f64 (*.f64 a b) 2)

simplify410.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-*l/_binary64`
631×	`associate-*r/_binary64`
307×	`fma-def_binary64`
283×	`log-div_binary64`
263×	`*-commutative_binary64`

Counts

277 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	5982
1	289	5243
2	1055	5159
3	4042	4993
4	4960	4993
5	5101	4993

prune1.0s (1.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	209	18	227
Fresh	11	7	18
Picked	1	0	1
Done	0	0	0
Total	221	25	246

Error

4.5b

Counts

246 → 25

Alt Table

Status	Error	Program
	24.9b	(/.f64 (.f64 -4 (pow.f64 (.f64 a b) 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))
	58.4b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 a 2)) (.f64 (log.f64 b) 2)) (+.f64 (.f64 (log.f64 y-scale) 2) (.f64 (log.f64 x-scale) 2)))))
▶	13.9b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (*.f64 x-scale y-scale) 2)))
	29.4b	(.f64 -4 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 a b) 2) 3)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	40.0b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 (.f64 y-scale (pow.f64 (sqrt.f64 x-scale) 2)) (*.f64 y-scale (pow.f64 (sqrt.f64 x-scale) 2)))))
	48.8b	(.f64 -4 (exp.f64 (-.f64 (.f64 (log.f64 (.f64 a b)) 2) (+.f64 (log.f64 (pow.f64 y-scale 2)) (.f64 (log.f64 x-scale) 2)))))
	47.9b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 a) 2) (log.f64 (pow.f64 b 2))) (+.f64 (log.f64 (pow.f64 y-scale 2)) (log.f64 (pow.f64 x-scale 2))))))
	45.2b	(-.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 4 (/.f64 (.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (/.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) 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)))
	24.5b	(.f64 -4 (/.f64 (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 y-scale 2)) (pow.f64 x-scale 2)))
	39.9b	(.f64 -4 (exp.f64 (-.f64 (log.f64 (pow.f64 (.f64 a b) 2)) (+.f64 (*.f64 (log.f64 y-scale) 2) (log.f64 (pow.f64 x-scale 2))))))
	47.6b	(.f64 -4 (exp.f64 (-.f64 (.f64 (log.f64 (.f64 a b)) 2) (+.f64 (.f64 (log.f64 y-scale) 2) (log.f64 (pow.f64 x-scale 2))))))
	44.6b	(fma.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) (neg.f64 (.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))))
	20.9b	(.f64 -4 (/.f64 (.f64 a b) (/.f64 (.f64 y-scale y-scale) (/.f64 (.f64 a b) (*.f64 x-scale x-scale)))))
	45.0b	(.f64 -4 (exp.f64 (.f64 2 (-.f64 (log.f64 (/.f64 (*.f64 a b) y-scale)) (log.f64 x-scale)))))
	20.9b	(.f64 -4 (.f64 (/.f64 (.f64 a b) (pow.f64 y-scale 2)) (/.f64 (.f64 a b) (pow.f64 x-scale 2))))
	25.0b	(.f64 -4 (.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))) (cbrt.f64 (/.f64 (pow.f64 (.f64 a b) 2) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))))
	22.4b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 y-scale (.f64 y-scale (pow.f64 x-scale 2)))))
	40.6b	0
	45.9b	(.f64 -4 (exp.f64 (fma.f64 2 (log.f64 (/.f64 a y-scale)) (.f64 2 (log.f64 (/.f64 b x-scale))))))
	25.0b	(.f64 (.f64 (cbrt.f64 -4) (cbrt.f64 -4)) (.f64 (cbrt.f64 -4) (/.f64 (pow.f64 (.f64 a b) 2) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))))
	22.9b	(.f64 -4 (/.f64 (.f64 a b) (/.f64 (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)) (.f64 a b))))
	15.4b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 y-scale (.f64 x-scale (*.f64 x-scale y-scale)))))
	27.2b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 y-scale (.f64 x-scale (*.f64 x-scale y-scale)))))
	41.4b	(.f64 -4 (exp.f64 (-.f64 (log.f64 (pow.f64 (.f64 a b) 2)) (+.f64 (log.f64 (pow.f64 y-scale 2)) (*.f64 (log.f64 x-scale) 2)))))
	57.7b	(.f64 -4 (exp.f64 (-.f64 (.f64 (+.f64 (log.f64 a) (log.f64 b)) 2) (+.f64 (*.f64 (log.f64 y-scale) 2) (log.f64 (pow.f64 x-scale 2))))))

Compiler

Compiled 6459 to 4190 computations (35.1% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (*.f64 x-scale y-scale) 2)))
	0.2b	(pow.f64 (*.f64 a b) 2)
✓	0.2b	(pow.f64 (*.f64 x-scale y-scale) 2)
✓	13.3b	(/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (.f64 x-scale y-scale) 2))

series637.0ms (0.7%)

Counts

3 → 120

Calls

3 calls:

332.0ms	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (*.f64 x-scale y-scale) 2)))
295.0ms	(/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (.f64 x-scale y-scale) 2))
10.0ms	(pow.f64 (*.f64 x-scale y-scale) 2)

rewrite71.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`add-exp-log_binary64`
81×	`times-frac_binary64`
49×	`add-sqr-sqrt_binary64`
40×	`associate-r_binary64`
34×	`pow-exp_binary64`

Counts

3 → 181

Calls

3 calls:

25.0ms	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (*.f64 x-scale y-scale) 2)))
10.0ms	(/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (.f64 x-scale y-scale) 2))
5.0ms	(pow.f64 (*.f64 x-scale y-scale) 2)

simplify303.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

758×	`associate-l_binary64`
697×	`associate-r_binary64`
538×	`associate-/l/_binary64`
305×	`associate-/r/_binary64`
152×	`associate-/l*_binary64`

Counts

301 → 239

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	6175
1	411	5311
2	1438	5281
3	4956	5281
4	5009	5281

prune817.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	252	9	261
Fresh	16	8	24
Picked	1	0	1
Done	0	0	0
Total	269	17	286

Error

2.1b

Counts

286 → 17

Alt Table

Status	Error	Program
	10.0b	(.f64 (/.f64 -4 (.f64 x-scale y-scale)) (/.f64 (pow.f64 (.f64 a b) 2) (.f64 x-scale y-scale)))
	56.8b	(.f64 -4 (exp.f64 (-.f64 (.f64 (+.f64 (log.f64 a) (log.f64 b)) 2) (.f64 (log.f64 (.f64 x-scale y-scale)) 2))))
	45.2b	(-.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 4 (/.f64 (.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (/.f64 (hypot.f64 (.f64 a (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) 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)))
	11.5b	(.f64 (.f64 -4 (.f64 a b)) (/.f64 (.f64 a b) (pow.f64 (*.f64 x-scale y-scale) 2)))
	3.3b	(.f64 (.f64 -4 (/.f64 (.f64 a b) (.f64 x-scale y-scale))) (/.f64 (.f64 a b) (.f64 x-scale y-scale)))
	45.0b	(.f64 -4 (exp.f64 (.f64 2 (-.f64 (log.f64 (/.f64 (*.f64 a b) y-scale)) (log.f64 x-scale)))))
	20.9b	(.f64 -4 (.f64 (/.f64 (.f64 a b) (pow.f64 y-scale 2)) (/.f64 (.f64 a b) (pow.f64 x-scale 2))))
	10.0b	(.f64 -4 (/.f64 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 x-scale y-scale)) (.f64 x-scale y-scale)))
	22.4b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 y-scale (.f64 y-scale (pow.f64 x-scale 2)))))
	40.6b	0
	45.9b	(.f64 -4 (exp.f64 (fma.f64 2 (log.f64 (/.f64 a y-scale)) (.f64 2 (log.f64 (/.f64 b x-scale))))))
	10.2b	(.f64 -4 (.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 x-scale y-scale)) (/.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (.f64 x-scale y-scale))))
	40.0b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (.f64 (.f64 y-scale (pow.f64 (sqrt.f64 x-scale) 2)) (*.f64 y-scale (pow.f64 (sqrt.f64 x-scale) 2)))))
	14.0b	(.f64 (.f64 (cbrt.f64 -4) (cbrt.f64 -4)) (.f64 (cbrt.f64 -4) (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (*.f64 x-scale y-scale) 2))))
	11.6b	(.f64 -4 (/.f64 (.f64 a b) (/.f64 (pow.f64 (.f64 x-scale y-scale) 2) (.f64 a b))))
	57.7b	(.f64 -4 (exp.f64 (-.f64 (.f64 (+.f64 (log.f64 a) (log.f64 b)) 2) (+.f64 (*.f64 (log.f64 y-scale) 2) (log.f64 (pow.f64 x-scale 2))))))
	19.5b	(.f64 -4 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (*.f64 x-scale y-scale) 2)) 3)))

Compiler

Compiled 6145 to 3535 computations (42.5% saved)

regimes4.5s (5.1%)

Accuracy

Total 1.5b remaining (37.7%)

Threshold costs 0b (0%)

Counts

200 → 1

Compiler

Compiled 81561 to 59105 computations (27.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	15	25
2	15	25

end367.0ms (0.4%)

Compiler: Compiled 515 to 361 computations (29.9% saved)

Details

analyze13.2s (14.9%)

sample55.2s (62.5%)

simplify74.0ms (0.1%)

prune22.0ms (0%)

localize78.0ms (0.1%)

series5.5s (6.2%)

rewrite72.0ms (0.1%)

simplify551.0ms (0.6%)

prune2.2s (2.4%)

localize23.0ms (0%)

series803.0ms (0.9%)

rewrite143.0ms (0.2%)

simplify382.0ms (0.4%)

prune1.0s (1.2%)

localize20.0ms (0%)

series909.0ms (1%)

rewrite84.0ms (0.1%)

simplify410.0ms (0.5%)

prune1.0s (1.1%)

localize22.0ms (0%)

series637.0ms (0.7%)

rewrite71.0ms (0.1%)

simplify303.0ms (0.3%)

prune817.0ms (0.9%)

regimes4.5s (5.1%)

simplify2.0ms (0%)

end367.0ms (0.4%)

Profiling