Details

analyze18.0s (16.7%)

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
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 189 to 125 computations (33.9% saved)

sample2.6s (2.4%)

Algorithm

1×

intervals

Results

1.2s	117×	body	4096	valid
882.0ms	48×	body	8192	valid
306.0ms	53×	body	2048	valid
81.0ms	25×	body	1024	valid
18.0ms	9×	body	512	valid
12.0ms	2×	body	2048	invalid
4.0ms	3×	body	256	valid
1.0ms	1×	body	128	invalid
1.0ms	1×	body	128	valid

Compiler

Compiled 382 to 254 computations (33.5% saved)

simplify27.0ms (0%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
606×	`associate-l_binary64`
593×	`associate-r_binary64`
303×	`associate-/r*_binary64`
262×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	292
1	154	287
2	560	287
3	5065	287

prune25.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

63.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))

Status

Error

Program

▶

63.9b

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

Compiler

Compiled 555 to 354 computations (36.2% saved)

localize93.0ms (0.1%)

Local error

Found 4 expressions with local error:

25.8b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
25.8b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
25.8b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
36.5b	(-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))

rewrite666.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

63.9b

Rules

18×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`cancel-sign-sub-inv_binary64`
9×	`add-log-exp_binary64`
7×	`sqrt-prod_binary64`

Counts

4 → 53

Calls

4 calls:

280.0ms	(-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 13849 to 8490 computations (38.7% saved)

series2.9s (2.7%)

Error

63.1b

Counts

4 → 24

Calls

4 calls:

2.7s	(-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))
27.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
26.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
24.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 18024 to 12061 computations (33.1% saved)

simplify382.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

298×	`unswap-sqr_binary64`
257×	`cancel-sign-sub-inv_binary64`
177×	`times-frac_binary64`
163×	`associate-/l*_binary64`
151×	`sub-neg_binary64`

Counts

77 → 60

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	15493
1	855	14979
2	3160	14592
3	4779	14592
4	4976	14592

prune558.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	54	6	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	7	61

Error

63.0b

Counts

61 → 7

Alt Table

Status	Error	Program
	63.7b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 x-scale x-scale)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (pow.f64 x-scale 4)) (+.f64 (/.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 x-scale 4)))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.7b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 (-.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)))))))) (.f64 x-scale x-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 (/.f64 (pow.f64 a 4) (.f64 x-scale x-scale)) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (.f64 x-scale x-scale)) (.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) 2))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
▶	63.6b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (.f64 (.f64 b b) (-.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))) (sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)))) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.8b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (pow.f64 y-scale 4)) (+.f64 (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 y-scale 4)))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (.f64 (.f64 a a) (-.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)))))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
✓	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))

Compiler

Compiled 13201 to 7670 computations (41.9% saved)

localize79.0ms (0.1%)

Local error

Found 4 expressions with local error:

25.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.5b	(-.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))) (sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)))) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))

rewrite1.2s (1.1%)

Algorithm

1×	rewrite-expression-head

Error

63.0b

Rules

47×	`frac-add_binary64`
36×	`associate-*r/_binary64`
33×	`frac-sub_binary64`
33×	`sqrt-div_binary64`
23×	`flip-+_binary64`

Counts

4 → 77

Calls

4 calls:

158.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))) (sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)))) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 18621 to 10276 computations (44.8% saved)

series653.0ms (0.6%)

Error

61.6b

Counts

4 → 18

Calls

4 calls:

553.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))) (sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)))) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))
21.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
19.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
19.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 4397 to 2487 computations (43.4% saved)

simplify385.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

571×	`associate-l_binary64`
507×	`associate-r_binary64`
234×	`distribute-rgt-in_binary64`
226×	`distribute-lft-in_binary64`
154×	`*-commutative_binary64`

Counts

95 → 59

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	20195
1	1071	18922
2	4813	18886
3	5038	18886

prune730.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	59	7	66

Error

63.0b

Counts

66 → 7

Alt Table

Status	Error	Program
	63.7b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 x-scale x-scale)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (pow.f64 x-scale 4)) (+.f64 (/.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 x-scale 4)))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.7b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 (-.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)))))))) (.f64 x-scale x-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
▶	63.6b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (.f64 (.f64 b b) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (-.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)))) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 (/.f64 (pow.f64 a 4) (.f64 x-scale x-scale)) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (.f64 x-scale x-scale)) (.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) 2))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
	63.8b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (pow.f64 y-scale 4)) (+.f64 (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 y-scale 4)))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (.f64 (.f64 a a) (-.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)))))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
✓	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))

Compiler

Compiled 15322 to 8708 computations (43.2% saved)

localize79.0ms (0.1%)

Local error

Found 4 expressions with local error:

25.4b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite315.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

63.0b

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

4 → 28

Calls

4 calls:

3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 3785 to 1915 computations (49.4% saved)

series101.0ms (0.1%)

Error

63.0b

Counts

4 → 12

Calls

4 calls:

21.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
21.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
19.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
18.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 3853 to 2219 computations (42.4% saved)

simplify206.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1392×	`sqr-pow_binary64`
724×	`unswap-sqr_binary64`
592×	`cube-prod_binary64`
500×	`fabs-mul_binary64`
470×	`pow-sqr_binary64`

Counts

40 → 4

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	585
1	31	501
2	40	501
3	47	501
4	54	501
5	69	501
6	106	501
7	207	501
8	551	501
9	1147	501
10	1286	501
11	1549	501
12	1854	501
13	2148	501
14	2550	501
15	2904	501
16	3087	501
17	3344	501
18	3483	501
19	3562	501
20	3642	501
21	4400	501
22	4802	501

prune82.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	4	7	11

Error

63.0b

Counts

11 → 7

Alt Table

Status	Error	Program
	63.7b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 x-scale x-scale)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (pow.f64 x-scale 4)) (+.f64 (/.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 x-scale 4)))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
▶	63.6b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (.f64 (.f64 b b) (+.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 3)) 2) (.f64 x-scale x-scale)) (-.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)))) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.7b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 (-.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)))))))) (.f64 x-scale x-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 (/.f64 (pow.f64 a 4) (.f64 x-scale x-scale)) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (.f64 x-scale x-scale)) (.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) 2))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
	63.8b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (pow.f64 y-scale 4)) (+.f64 (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 y-scale 4)))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (.f64 (.f64 a a) (-.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)))))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
✓	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))

Compiler

Compiled 2404 to 1389 computations (42.2% saved)

localize79.0ms (0.1%)

Local error

Found 4 expressions with local error:

25.4b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite326.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

63.0b

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

4 → 28

Calls

4 calls:

3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 3869 to 1999 computations (48.3% saved)

series112.0ms (0.1%)

Error

63.0b

Counts

4 → 12

Calls

4 calls:

22.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
22.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
20.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
20.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 3940 to 2306 computations (41.5% saved)

simplify211.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1392×	`sqr-pow_binary64`
724×	`unswap-sqr_binary64`
592×	`cube-prod_binary64`
500×	`fabs-mul_binary64`
470×	`pow-sqr_binary64`

Counts

40 → 4

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	585
1	31	501
2	40	501
3	47	501
4	54	501
5	69	501
6	106	501
7	207	501
8	551	501
9	1147	501
10	1286	501
11	1549	501
12	1854	501
13	2148	501
14	2550	501
15	2904	501
16	3087	501
17	3344	501
18	3483	501
19	3562	501
20	3642	501
21	4400	501
22	4802	501

prune80.0ms (0.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	4	7	11

Error

63.0b

Counts

11 → 7

Alt Table

Status	Error	Program
	63.7b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 x-scale x-scale)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (pow.f64 x-scale 4)) (+.f64 (/.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 x-scale 4)))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.6b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (.f64 (.f64 b b) (+.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 3)) 2) (.f64 x-scale x-scale)) (-.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)))) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.7b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 (-.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)))))))) (.f64 x-scale x-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 (/.f64 (pow.f64 a 4) (.f64 x-scale x-scale)) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (.f64 x-scale x-scale)) (.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) 2))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
	63.8b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (pow.f64 y-scale 4)) (+.f64 (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 y-scale 4)))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (.f64 (.f64 a a) (-.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (.f64 2 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)))))))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))
	63.9b	(.f64 -1/4 (.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 x-scale y-scale)) 2))))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2)))

Compiler

Compiled 1571 to 905 computations (42.4% saved)

regimes1.5s (1.4%)

Accuracy

Total -1.4b remaining (-2.3%)

Threshold costs -1.4b (-2.3%)

Compiler

Compiled 47624 to 28954 computations (39.2% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

45×	`distribute-rgt-neg-in_binary64`
33×	`distribute-lft-neg-in_binary64`
24×	`*-commutative_binary64`
22×	`neg-sub0_binary64`
22×	`neg-mul-1_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	75
1	39	75
2	48	75
3	63	75
4	84	71
5	99	71
6	134	71
7	163	71
8	188	71
9	199	71
10	201	71
11	195	71

end1.0ms (0%)

Compiler: Compiled 52 to 28 computations (46.2% saved)

sample1.3min (70.8%)

Algorithm

1×

intervals

Results

33.7s	3689×	body	4096	valid
27.8s	1526×	body	8192	valid
10.2s	1823×	body	2048	valid
2.0s	583×	body	1024	valid
495.0ms	227×	body	512	valid
223.0ms	36×	body	2048	invalid
144.0ms	102×	body	256	valid
107.0ms	30×	body	1024	invalid
49.0ms	23×	body	512	invalid
33.0ms	50×	body	128	valid
25.0ms	2×	body	4096	invalid
11.0ms	7×	body	256	invalid
8.0ms	12×	body	128	invalid

Compiler

Compiled 1276 to 772 computations (39.5% saved)

Iter	Nodes	Cost
0	25	75
1	39	75
2	48	75
3	63	75
4	84	71
5	99	71
6	134	71
7	163	71
8	188	71
9	199	71
10	201	71
11	195	71

Iter	Nodes	Cost
0	25	75
1	39	75
2	48	75
3	63	75
4	84	71
5	99	71
6	134	71
7	163	71
8	188	71
9	199	71
10	201	71
11	195	71

Details

analyze18.0s (16.7%)

sample2.6s (2.4%)

simplify27.0ms (0%)

prune25.0ms (0%)

localize93.0ms (0.1%)

rewrite666.0ms (0.6%)

series2.9s (2.7%)

simplify382.0ms (0.4%)

prune558.0ms (0.5%)

localize79.0ms (0.1%)

rewrite1.2s (1.1%)

series653.0ms (0.6%)

simplify385.0ms (0.4%)

prune730.0ms (0.7%)

localize79.0ms (0.1%)

rewrite315.0ms (0.3%)

series101.0ms (0.1%)

simplify206.0ms (0.2%)

prune82.0ms (0.1%)

localize79.0ms (0.1%)

rewrite326.0ms (0.3%)

series112.0ms (0.1%)

simplify211.0ms (0.2%)

prune80.0ms (0.1%)

regimes1.5s (1.4%)

simplify10.0ms (0%)

end1.0ms (0%)

sample1.3min (70.8%)

Profiling

Iter	Nodes	Cost
0	25	75
1	39	75
2	48	75
3	63	75
4	84	71
5	99	71
6	134	71
7	163	71
8	188	71
9	199	71
10	201	71
11	195	71