Details

analyze6.2s (12.8%)

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)

sample29.4s (60.6%)

Infinites

33.4% of outputs are infinite.

Results

12.1s	1530×	body	4096	valid
9.2s	1913×	body	2048	valid
3.6s	1130×	body	1024	valid
2.1s	2969×	body	128	valid
1.1s	67×	body	8192	valid
950.0ms	461×	body	512	valid
248.0ms	186×	body	256	valid

Compiler

Compiled 344 to 251 computations (27% saved)

simplify39.0ms (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

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

48.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	48.8b	(-.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 (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)))
	50.7b	(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

▶

48.8b

(-.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 (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)))

50.7b

(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)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	10.0b	(/.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)
✓	28.8b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	28.8b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	38.5b	(-.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 (.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)))

series3.0s (6.2%)

Counts

4 → 132

Calls

4 calls:

2.8s	(-.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)))
181.0ms	(/.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)
4.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
3.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite53.0ms (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:

30.0ms	(-.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)))
8.0ms	(/.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)
3.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

simplify269.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

416×	`associate-r_binary64`
311×	`associate-l_binary64`
311×	`associate-/l*_binary64`
292×	`times-frac_binary64`
261×	`fma-def_binary64`

Counts

212 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	426	21239
1	1300	19706
2	5218	19706

prune1.1s (2.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	326	15	341
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	328	15	343

Error

22.8b

Counts

343 → 15

Alt Table

Status	Error	Program
	48.3b	(-.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 (hypot.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (/.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) y-scale)) y-scale)))
	41.3b	(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))))))))
	47.5b	(-.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))) (log.f64 (exp.f64 (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)))
	48.3b	(-.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)))
	43.3b	0
	56.7b	(-.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 (hypot.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (sqrt.f64 y-scale)) (/.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (sqrt.f64 y-scale))) y-scale)))
	57.3b	(/.f64 (-.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) (/.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)) (.f64 x-scale y-scale)) (.f64 (.f64 y-scale y-scale) (.f64 (.f64 4 (/.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)) (/.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)))) (.f64 (.f64 y-scale y-scale) (.f64 x-scale y-scale)))
	57.0b	(-.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 (exp.f64 (-.f64 (log.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))) (log.f64 y-scale))) y-scale)))
	48.8b	(-.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)))) (expm1.f64 (log1p.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)))
	61.8b	(/.f64 (-.f64 (.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 (/.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 (.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)) (.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)))) (+.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))))
	46.5b	(-.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)))
	40.5b	(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)))
	47.8b	(/.f64 (.f64 y-scale (-.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 (/.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)) 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 (*.f64 y-scale x-scale)))
	52.6b	(/.f64 (.f64 y-scale (-.f64 (.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 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 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)) 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)) (.f64 x-scale x-scale))))))) (pow.f64 y-scale 3))
▶	36.9b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))

Compiler

Compiled 45280 to 31440 computations (30.6% saved)

localize10.0ms (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))))
✓	14.5b	(/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))
✓	14.8b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
✓	17.6b	(*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))

series417.0ms (0.9%)

Counts

4 → 60

Calls

4 calls:

207.0ms	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
187.0ms	(/.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 y-scale 2) (pow.f64 x-scale 2))
11.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite86.0ms (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:

13.0ms	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
9.0ms	(/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2)))
6.0ms	(*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))
6.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

simplify208.0ms (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

prune784.0ms (1.6%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	254	16	270
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	262	23	285

Error

9.3b

Counts

285 → 23

Alt Table

Status	Error	Program
	56.7b	(-.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 (hypot.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (sqrt.f64 y-scale)) (/.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (sqrt.f64 y-scale))) y-scale)))
▶	25.8b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (pow.f64 (*.f64 y-scale x-scale) 2)))
	54.8b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 a 2)) (.f64 (log.f64 b) 2)) (+.f64 (*.f64 (log.f64 y-scale) 2) (log.f64 (pow.f64 x-scale 2))))))
	56.5b	(.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)))))
	47.5b	(-.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))) (log.f64 (exp.f64 (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)))
	48.3b	(-.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)))
	43.3b	0
	36.7b	(.f64 -4 (/.f64 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (pow.f64 y-scale 2)) (pow.f64 x-scale 2)))
	56.3b	(.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))))))
	46.5b	(-.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)))
	38.0b	(.f64 -4 (.f64 (/.f64 (pow.f64 a 2) (pow.f64 y-scale 2)) (/.f64 (pow.f64 b 2) (pow.f64 x-scale 2))))
	47.3b	(.f64 -4 (exp.f64 (fma.f64 2 (log.f64 (/.f64 a y-scale)) (.f64 2 (log.f64 (/.f64 b x-scale))))))
	48.6b	(.f64 -4 (exp.f64 (-.f64 (log.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 (log.f64 y-scale) 2) (log.f64 (pow.f64 x-scale 2))))))
	29.1b	(.f64 -4 (/.f64 (.f64 (.f64 a (.f64 a b)) b) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	28.1b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	52.6b	(/.f64 (.f64 y-scale (-.f64 (.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 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 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)) 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)) (.f64 x-scale x-scale))))))) (pow.f64 y-scale 3))
	31.9b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 y-scale (.f64 y-scale (pow.f64 x-scale 2)))))
	57.0b	(-.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 (exp.f64 (-.f64 (log.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))) (log.f64 y-scale))) y-scale)))
	45.3b	(.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))))))
	46.5b	(.f64 -4 (exp.f64 (-.f64 (log.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (log.f64 (pow.f64 y-scale 2)) (*.f64 (log.f64 x-scale) 2)))))
	33.0b	(.f64 -4 (/.f64 (.f64 a (.f64 a (pow.f64 b 2))) (.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	46.6b	(.f64 -4 (/.f64 (.f64 (pow.f64 (sqrt.f64 a) 2) (.f64 a (.f64 b b))) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
	28.0b	(.f64 -4 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 y-scale (.f64 x-scale (*.f64 x-scale y-scale)))))

Compiler

Compiled 8750 to 6057 computations (30.8% saved)

localize9.0ms (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)) (pow.f64 (*.f64 y-scale x-scale) 2)))
✓	0.2b	(pow.f64 (*.f64 y-scale x-scale) 2)
✓	14.5b	(/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (pow.f64 (.f64 y-scale x-scale) 2))
	14.8b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series462.0ms (1%)

Counts

3 → 120

Calls

3 calls:

237.0ms

(/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (pow.f64 (*.f64 y-scale x-scale) 2))

218.0ms

(*.f64 -4 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (pow.f64 (*.f64 y-scale x-scale) 2)))

7.0ms

(pow.f64 (*.f64 y-scale x-scale) 2)

rewrite35.0ms (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:

9.0ms

(*.f64 -4 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (pow.f64 (*.f64 y-scale x-scale) 2)))

6.0ms

(/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (pow.f64 (*.f64 y-scale x-scale) 2))

2.0ms

(pow.f64 (*.f64 y-scale x-scale) 2)

simplify436.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

435×	`associate-/l/_binary64`
317×	`fma-neg_binary64`
312×	`associate-/r/_binary64`
288×	`*-commutative_binary64`
259×	`log-prod_binary64`

Counts

277 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	5984
1	298	5245
2	1182	5161
3	3186	4926
4	4869	4926
5	5156	4926

prune401.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	216	9	225
Fresh	19	3	22
Picked	1	0	1
Done	0	0	0
Total	236	12	248

Error

0.5b

Counts

248 → 12

Alt Table

Status	Error	Program
	54.8b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 a 2)) (.f64 (log.f64 b) 2)) (+.f64 (*.f64 (log.f64 y-scale) 2) (log.f64 (pow.f64 x-scale 2))))))
	56.7b	(-.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 (hypot.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (sqrt.f64 y-scale)) (/.f64 (hypot.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (sqrt.f64 y-scale))) y-scale)))
	46.4b	(.f64 -4 (exp.f64 (.f64 2 (-.f64 (log.f64 (.f64 a b)) (log.f64 (.f64 y-scale x-scale))))))
	21.3b	(.f64 -4 (/.f64 (.f64 a (.f64 a (.f64 b b))) (pow.f64 (*.f64 y-scale x-scale) 2)))
	15.1b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (*.f64 y-scale x-scale) 2)))
	25.9b	(.f64 -4 (/.f64 (.f64 (.f64 (.f64 a a) (.f64 (cbrt.f64 (.f64 b b)) (cbrt.f64 (.f64 b b)))) (cbrt.f64 (pow.f64 b 2))) (pow.f64 (.f64 y-scale x-scale) 2)))
	45.1b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 a 2)) (.f64 (log.f64 b) 2)) (log.f64 (pow.f64 (*.f64 y-scale x-scale) 2)))))
	24.4b	(.f64 (.f64 -4 (/.f64 (pow.f64 a 2) (.f64 y-scale x-scale))) (/.f64 (pow.f64 b 2) (.f64 y-scale x-scale)))
	24.2b	(.f64 -4 (/.f64 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 y-scale x-scale)) (.f64 y-scale x-scale)))
▶	4.4b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale)))))
	46.5b	(-.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)))
	56.5b	(.f64 -4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 a) 2) (log.f64 (pow.f64 b 2))) (*.f64 (+.f64 (log.f64 y-scale) (log.f64 x-scale)) 2))))

Compiler

Compiled 5799 to 3670 computations (36.7% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale)))))
✓	0.2b	(.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (*.f64 (/.f64 a y-scale) (/.f64 b x-scale))))
✓	9.7b	(*.f64 (/.f64 a y-scale) (/.f64 b x-scale))

series97.0ms (0.2%)

Counts

3 → 144

Calls

3 calls:

43.0ms

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

29.0ms

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

24.0ms

(*.f64 (fabs.f64 (*.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (*.f64 (/.f64 a y-scale) (/.f64 b x-scale))))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`fabs-div_binary64`
38×	`associate-*r/_binary64`
37×	`add-sqr-sqrt_binary64`
35×	`frac-times_binary64`
23×	`associate-*l/_binary64`

Counts

3 → 135

Calls

3 calls:

8.0ms

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

7.0ms

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

4.0ms

(*.f64 (fabs.f64 (*.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (*.f64 (/.f64 a y-scale) (/.f64 b x-scale))))

simplify137.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

663×	`associate-/l*_binary64`
512×	`times-frac_binary64`
277×	`associate-r_binary64`
248×	`associate-/l/_binary64`
246×	`associate-l_binary64`

Counts

279 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	4769
1	501	4416
2	1907	4338
3	4993	4332
4	4980	4332

prune518.0ms (1.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	283	12	295
Fresh	9	2	11
Picked	0	1	1
Done	0	0	0
Total	292	15	307

Error

0.0b

Counts

307 → 15

Alt Table

Status	Error	Program
	24.2b	(.f64 -4 (/.f64 (/.f64 (.f64 (pow.f64 a 2) (pow.f64 b 2)) (.f64 y-scale x-scale)) (.f64 y-scale x-scale)))
	6.4b	(.f64 -4 (.f64 (.f64 (cbrt.f64 (pow.f64 (fabs.f64 (/.f64 (.f64 a b) (.f64 x-scale y-scale))) 2)) (cbrt.f64 (pow.f64 (fabs.f64 (/.f64 (.f64 a b) (.f64 x-scale y-scale))) 2))) (cbrt.f64 (pow.f64 (fabs.f64 (/.f64 (.f64 a b) (*.f64 x-scale y-scale))) 2))))
	16.9b	(.f64 -4 (cbrt.f64 (pow.f64 (/.f64 (.f64 a b) (*.f64 x-scale y-scale)) 6)))
	15.1b	(.f64 -4 (/.f64 (pow.f64 (.f64 a b) 2) (pow.f64 (*.f64 y-scale x-scale) 2)))
✓	4.4b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale)))))
	4.6b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (.f64 (/.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) 1) (.f64 (/.f64 (cbrt.f64 a) y-scale) (/.f64 b x-scale))))))
	6.2b	(.f64 -4 (pow.f64 (fabs.f64 (/.f64 (.f64 a b) (*.f64 x-scale y-scale))) 2))
	32.4b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (.f64 (/.f64 (/.f64 a y-scale) (sqrt.f64 x-scale)) (/.f64 b (sqrt.f64 x-scale))))))
	4.6b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (.f64 (.f64 (/.f64 a y-scale) (.f64 (cbrt.f64 (/.f64 b x-scale)) (cbrt.f64 (/.f64 b x-scale)))) (cbrt.f64 (/.f64 b x-scale))))))
	5.1b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (.f64 (/.f64 (/.f64 a y-scale) (*.f64 (cbrt.f64 x-scale) (cbrt.f64 x-scale))) (/.f64 b (cbrt.f64 x-scale))))))
	5.8b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (/.f64 (.f64 (/.f64 a y-scale) b) x-scale))))
	21.4b	(.f64 -4 (/.f64 (.f64 (fabs.f64 (.f64 a b)) (fabs.f64 (.f64 a (/.f64 b x-scale)))) (.f64 (.f64 y-scale y-scale) (fabs.f64 x-scale))))
	4.6b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 y-scale) (cbrt.f64 y-scale))) (.f64 (/.f64 a (cbrt.f64 y-scale)) (/.f64 b x-scale))))))
	4.6b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a y-scale) (/.f64 b x-scale))) (fabs.f64 (.f64 (.f64 (cbrt.f64 (/.f64 a y-scale)) (cbrt.f64 (/.f64 a y-scale))) (.f64 (cbrt.f64 (/.f64 a y-scale)) (/.f64 b x-scale))))))
	10.3b	(.f64 (.f64 (fabs.f64 (/.f64 (.f64 a b) (.f64 x-scale y-scale))) -4) (fabs.f64 (*.f64 (/.f64 a y-scale) (/.f64 b x-scale))))

Compiler

Compiled 7716 to 1819 computations (76.4% saved)

regimes4.6s (9.4%)

Accuracy

Total 3.7b remaining (97.1%)

Threshold costs 0b (0%)

Counts

252 → 3

Compiler

Compiled 97904 to 68055 computations (30.5% saved)

bsearch17.0ms (0%)

Compiler: Compiled 8 to 7 computations (12.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
8×	`fabs-mul_binary64`
3×	`fabs-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	92
1	51	92
2	61	92
3	61	92

end201.0ms (0.4%)

Compiler: Compiled 540 to 320 computations (40.7% saved)

Details

analyze6.2s (12.8%)

sample29.4s (60.6%)

simplify39.0ms (0.1%)

prune12.0ms (0%)

localize39.0ms (0.1%)

series3.0s (6.2%)

rewrite53.0ms (0.1%)

simplify269.0ms (0.6%)

prune1.1s (2.3%)

localize10.0ms (0%)

series417.0ms (0.9%)

rewrite86.0ms (0.2%)

simplify208.0ms (0.4%)

prune784.0ms (1.6%)

localize9.0ms (0%)

series462.0ms (1%)

rewrite35.0ms (0.1%)

simplify436.0ms (0.9%)

prune401.0ms (0.8%)

localize8.0ms (0%)

series97.0ms (0.2%)

rewrite30.0ms (0.1%)

simplify137.0ms (0.3%)

prune518.0ms (1.1%)

regimes4.6s (9.4%)

bsearch17.0ms (0%)

simplify4.0ms (0%)

end201.0ms (0.4%)

Profiling