Details

analyze18.5s (23.5%)

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)

sample828.0ms (1.1%)

Algorithm

1×

intervals

Results

298.0ms	58×	body	1024	valid
128.0ms	26×	body	1024	invalid
113.0ms	33×	body	512	valid
106.0ms	145×	body	128	valid
38.0ms	55×	body	128	invalid
37.0ms	11×	body	512	invalid
33.0ms	5×	body	2048	valid
27.0ms	15×	body	256	valid
12.0ms	6×	body	256	invalid

Compiler

Compiled 382 to 254 computations (33.5% saved)

simplify58.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
686×	`associate-l_binary64`
303×	`associate-/r*_binary64`
262×	`associate-/l*_binary64`
190×	`associate-*l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	292
1	159	287
2	592	287
3	4709	283
4	5020	283

prune13.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

63.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	63.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))) (.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 (.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) 2))))))) (/.f64 (.f64 4 (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))

Status

Error

Program

▶

63.2b

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

Compiler

Compiled 559 to 368 computations (34.2% saved)

localize89.0ms (0.1%)

Local error

Found 4 expressions with local error:

25.7b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
25.7b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
25.7b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
47.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))) (.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 (.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) 2))))))) (/.f64 (.f64 4 (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))

rewrite2.9s (3.6%)

Algorithm

1×	rewrite-expression-head

Error

62.7b

Rules

198×	`times-frac_binary64`
130×	`add-exp-log_binary64`
63×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
58×	`prod-exp_binary64`
49×	`div-exp_binary64`

Counts

4 → 225

Calls

4 calls:

29.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))) (.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 (.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) 2))))))) (/.f64 (.f64 4 (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 67488 to 42888 computations (36.5% saved)

series14.2s (18.1%)

Error

47.3b

Counts

4 → 28

Calls

4 calls:

13.9s	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))) (.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 (.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) 2))))))) (/.f64 (.f64 4 (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
26.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
26.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
25.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 68669 to 49064 computations (28.6% saved)

simplify1.3s (1.7%)

Algorithm

1×	egg-herbie

Rules

852×	`associate-/l*_binary64`
378×	`associate-/r/_binary64`
244×	`*-commutative_binary64`
196×	`associate-/l/_binary64`
148×	`distribute-frac-neg_binary64`

Counts

253 → 236

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	894	102107
1	2483	95846
2	5688	95846

prune1.9s (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	224	12	236
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	225	12	237

Error

47.1b

Counts

237 → 12

Alt Table

Status	Error	Program
	63.2b	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 a b) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 y-scale x-scale) 2))))) (/.f64 4 (.f64 x-scale x-scale))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (+.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))) (sqrt.f64 (+.f64 (pow.f64 (-.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))) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 y-scale x-scale)) 2)))))) (/.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 y-scale y-scale))))
▶	57.9b	(.f64 1/4 (.f64 (.f64 y-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
	58.1b	(.f64 1/4 (.f64 (.f64 x-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (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 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
	61.5b	(.f64 -1/4 (.f64 (.f64 a (.f64 (sqrt.f64 8) (.f64 y-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (+.f64 (/.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 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))
	61.0b	(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (+.f64 (sqrt.f64 (+.f64 (.f64 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (+.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 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))))) (.f64 (sqrt.f64 8) (.f64 (.f64 y-scale x-scale) b))) -1/4)
	62.3b	(.f64 1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (+.f64 (/.f64 (.f64 b b) (.f64 x-scale x-scale)) (sqrt.f64 (-.f64 (+.f64 (/.f64 (pow.f64 b 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4))) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 (*.f64 y-scale x-scale) 2))))))))))
	62.2b	(.f64 -1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 b 4)) (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 y-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 y-scale 4)))))))))))
	61.5b	(.f64 1/4 (.f64 (.f64 a (.f64 (sqrt.f64 8) (.f64 y-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (+.f64 (/.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 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))
	61.3b	(.f64 1/4 (.f64 (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (+.f64 (sqrt.f64 (+.f64 (.f64 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (+.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 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))))) (.f64 (sqrt.f64 8) (.f64 (.f64 y-scale x-scale) b))))
	63.1b	(.f64 -1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (.f64 b b)) (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (+.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (pow.f64 b 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 x-scale 4)))))))))))
	62.8b	(.f64 1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 b 4)) (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 y-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 y-scale 4)))))))))))
	62.9b	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 a b) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 y-scale x-scale) 2))))) (/.f64 4 (.f64 y-scale x-scale))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (+.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))) (sqrt.f64 (+.f64 (pow.f64 (-.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))) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 y-scale x-scale)) 2)))))) (/.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 y-scale x-scale))))

Compiler

Compiled 61864 to 36990 computations (40.2% saved)

localize49.0ms (0.1%)

Local error

Found 4 expressions with local error:

25.4b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.5b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.5b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.5b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite225.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

47.1b

Rules

4×	`pow1_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 28

Calls

4 calls:

3.0ms	(cos.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)))
2.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 2665 to 1685 computations (36.8% saved)

series88.0ms (0.1%)

Error

47.1b

Counts

4 → 12

Calls

4 calls:

18.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
16.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
16.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
16.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 2693 to 1837 computations (31.8% saved)

simplify207.0ms (0.3%)

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

prune95.0ms (0.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	3	13	16

Error

47.1b

Counts

16 → 13

Alt Table

Status	Error	Program
	63.2b	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 a b) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 y-scale x-scale) 2))))) (/.f64 4 (.f64 x-scale x-scale))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (+.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))) (sqrt.f64 (+.f64 (pow.f64 (-.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))) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 y-scale x-scale)) 2)))))) (/.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 y-scale y-scale))))
✓	57.9b	(.f64 1/4 (.f64 (.f64 y-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
	58.1b	(.f64 1/4 (.f64 (.f64 x-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (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 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
	61.5b	(.f64 -1/4 (.f64 (.f64 a (.f64 (sqrt.f64 8) (.f64 y-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (+.f64 (/.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 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))
	61.0b	(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (+.f64 (sqrt.f64 (+.f64 (.f64 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (+.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 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))))) (.f64 (sqrt.f64 8) (.f64 (.f64 y-scale x-scale) b))) -1/4)
	62.3b	(.f64 1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (+.f64 (/.f64 (.f64 b b) (.f64 x-scale x-scale)) (sqrt.f64 (-.f64 (+.f64 (/.f64 (pow.f64 b 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4))) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 (*.f64 y-scale x-scale) 2))))))))))
	62.2b	(.f64 -1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 b 4)) (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 y-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 y-scale 4)))))))))))
	61.5b	(.f64 1/4 (.f64 (.f64 a (.f64 (sqrt.f64 8) (.f64 y-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (+.f64 (/.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 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))
	61.3b	(.f64 1/4 (.f64 (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (+.f64 (sqrt.f64 (+.f64 (.f64 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (+.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 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))))) (.f64 (sqrt.f64 8) (.f64 (.f64 y-scale x-scale) b))))
▶	57.9b	(.f64 1/4 (.f64 (.f64 y-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 3)) 2)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
	63.1b	(.f64 -1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (.f64 b b)) (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (+.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (pow.f64 b 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 x-scale 4)))))))))))
	62.8b	(.f64 1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 b 4)) (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 y-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 y-scale 4)))))))))))
	62.9b	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 a b) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 y-scale x-scale) 2))))) (/.f64 4 (.f64 y-scale x-scale))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (+.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))) (sqrt.f64 (+.f64 (pow.f64 (-.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))) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 y-scale x-scale)) 2)))))) (/.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 y-scale x-scale))))

Compiler

Compiled 3180 to 2121 computations (33.3% saved)

localize56.0ms (0.1%)

Local error

Found 4 expressions with local error:

25.4b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.5b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.5b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.5b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite242.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

47.1b

Rules

4×	`pow1_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_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	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 2749 to 1769 computations (35.6% saved)

series94.0ms (0.1%)

Error

47.1b

Counts

4 → 12

Calls

4 calls:

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

Compiler

Compiled 2780 to 1924 computations (30.8% saved)

simplify209.0ms (0.3%)

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

prune101.0ms (0.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	4	13	17

Error

47.1b

Counts

17 → 13

Alt Table

Status	Error	Program
	63.2b	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 a b) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 y-scale x-scale) 2))))) (/.f64 4 (.f64 x-scale x-scale))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (+.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))) (sqrt.f64 (+.f64 (pow.f64 (-.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))) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 y-scale x-scale)) 2)))))) (/.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 y-scale y-scale))))
✓	57.9b	(.f64 1/4 (.f64 (.f64 y-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
▶	58.1b	(.f64 1/4 (.f64 (.f64 x-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (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 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
	61.5b	(.f64 -1/4 (.f64 (.f64 a (.f64 (sqrt.f64 8) (.f64 y-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (+.f64 (/.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 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))
	61.0b	(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (+.f64 (sqrt.f64 (+.f64 (.f64 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (+.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 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))))) (.f64 (sqrt.f64 8) (.f64 (.f64 y-scale x-scale) b))) -1/4)
	62.3b	(.f64 1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (+.f64 (/.f64 (.f64 b b) (.f64 x-scale x-scale)) (sqrt.f64 (-.f64 (+.f64 (/.f64 (pow.f64 b 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4))) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 (*.f64 y-scale x-scale) 2))))))))))
	62.2b	(.f64 -1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 b 4)) (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 y-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 y-scale 4)))))))))))
	61.5b	(.f64 1/4 (.f64 (.f64 a (.f64 (sqrt.f64 8) (.f64 y-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (+.f64 (/.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 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))
	61.3b	(.f64 1/4 (.f64 (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (+.f64 (sqrt.f64 (+.f64 (.f64 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (+.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 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))))) (.f64 (sqrt.f64 8) (.f64 (.f64 y-scale x-scale) b))))
✓	57.9b	(.f64 1/4 (.f64 (.f64 y-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 3)) 2)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
	63.1b	(.f64 -1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (.f64 b b)) (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (+.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (pow.f64 b 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 x-scale 4)))))))))))
	62.8b	(.f64 1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 b 4)) (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 y-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 y-scale 4)))))))))))
	62.9b	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 a b) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 y-scale x-scale) 2))))) (/.f64 4 (.f64 y-scale x-scale))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (+.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))) (sqrt.f64 (+.f64 (pow.f64 (-.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))) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 y-scale x-scale)) 2)))))) (/.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 y-scale x-scale))))

Compiler

Compiled 3096 to 2066 computations (33.3% saved)

localize51.0ms (0.1%)

Local error

Found 4 expressions with local error:

25.4b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.5b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.5b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.5b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite238.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

47.1b

Rules

4×	`pow1_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 28

Calls

4 calls:

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

Compiler

Compiled 2665 to 1685 computations (36.8% saved)

series85.0ms (0.1%)

Error

47.1b

Counts

4 → 12

Calls

4 calls:

18.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
18.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
16.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
16.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 2693 to 1837 computations (31.8% saved)

simplify210.0ms (0.3%)

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

prune76.0ms (0.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	4	13	17

Error

47.1b

Counts

17 → 13

Alt Table

Status	Error	Program
	63.2b	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 a b) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 y-scale x-scale) 2))))) (/.f64 4 (.f64 x-scale x-scale))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (+.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))) (sqrt.f64 (+.f64 (pow.f64 (-.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))) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 y-scale x-scale)) 2)))))) (/.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 y-scale y-scale))))
	57.9b	(.f64 1/4 (.f64 (.f64 y-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
	58.1b	(.f64 1/4 (.f64 (.f64 x-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (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 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
	61.5b	(.f64 -1/4 (.f64 (.f64 a (.f64 (sqrt.f64 8) (.f64 y-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (+.f64 (/.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 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))
	61.0b	(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (+.f64 (sqrt.f64 (+.f64 (.f64 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (+.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 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))))) (.f64 (sqrt.f64 8) (.f64 (.f64 y-scale x-scale) b))) -1/4)
	62.3b	(.f64 1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 a a) (.f64 y-scale y-scale)) (+.f64 (/.f64 (.f64 b b) (.f64 x-scale x-scale)) (sqrt.f64 (-.f64 (+.f64 (/.f64 (pow.f64 b 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4))) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 (*.f64 y-scale x-scale) 2))))))))))
	62.2b	(.f64 -1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 b 4)) (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 y-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 y-scale 4)))))))))))
	61.5b	(.f64 1/4 (.f64 (.f64 a (.f64 (sqrt.f64 8) (.f64 y-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (+.f64 (/.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 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4))))))))))
	61.3b	(.f64 1/4 (.f64 (sqrt.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (+.f64 (sqrt.f64 (+.f64 (.f64 2 (/.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)) (pow.f64 (.f64 y-scale x-scale) 2))) (+.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 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale))))) (.f64 (sqrt.f64 8) (.f64 (.f64 y-scale x-scale) b))))
	57.9b	(.f64 1/4 (.f64 (.f64 y-scale (sqrt.f64 8)) (sqrt.f64 (+.f64 (.f64 (.f64 a a) (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 3)) 2)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (*.f64 b b)))))))))))))
	63.1b	(.f64 -1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 x-scale x-scale)) (.f64 b b)) (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 x-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (+.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (pow.f64 b 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 x-scale 4)))))))))))
	62.8b	(.f64 1/4 (.f64 (.f64 (sqrt.f64 8) (.f64 y-scale x-scale)) (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 y-scale y-scale)) (.f64 b b)) (sqrt.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 b 4)) (+.f64 (/.f64 (.f64 (pow.f64 a 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 y-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)))) (pow.f64 y-scale 4)))))))))))
	62.9b	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 2 (/.f64 (.f64 4 (.f64 (.f64 a b) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 y-scale x-scale) 2))))) (/.f64 4 (.f64 y-scale x-scale))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (+.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))) (sqrt.f64 (+.f64 (pow.f64 (-.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))) 2) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) (.f64 y-scale x-scale)) 2)))))) (/.f64 (.f64 (.f64 a b) (.f64 b (neg.f64 a))) (.f64 y-scale x-scale))))

Compiler

Compiled 1821 to 1213 computations (33.4% saved)

regimes7.7s (9.8%)

Accuracy

Total 7.4b remaining (13%)

Threshold costs 0b (0%)

Compiler

Compiled 250930 to 166913 computations (33.5% saved)

bsearch647.0ms (0.8%)

Steps

Iters	Range		Point
5	9.262412242672017e-19	3.2650576848078864e-18	1.9372910405772946e-18
9	-3.501740698286326e-58	-3.438660692400615e-67	-7.243317658168165e-65

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

31×	`*-commutative_binary64`
12×	`+-commutative_binary64`
1×	`1-exp_binary64` `*-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	452
1	138	452
2	136	452

end7.0ms (0%)

Compiler: Compiled 285 to 188 computations (34% saved)

sample28.4s (36.2%)

Algorithm

1×

intervals

Results

9.3s	1851×	body	1024	valid
4.9s	923×	body	1024	invalid
3.3s	4538×	body	128	valid
3.2s	958×	body	512	valid
1.6s	481×	body	512	invalid
1.4s	195×	body	2048	valid
1.3s	1799×	body	128	invalid
864.0ms	458×	body	256	valid
487.0ms	235×	body	256	invalid

Compiler

Compiled 1931 to 1290 computations (33.2% saved)

Details

analyze18.5s (23.5%)

sample828.0ms (1.1%)

simplify58.0ms (0.1%)

prune13.0ms (0%)

localize89.0ms (0.1%)

rewrite2.9s (3.6%)

series14.2s (18.1%)

simplify1.3s (1.7%)

prune1.9s (2.4%)

localize49.0ms (0.1%)

rewrite225.0ms (0.3%)

series88.0ms (0.1%)

simplify207.0ms (0.3%)

prune95.0ms (0.1%)

localize56.0ms (0.1%)

rewrite242.0ms (0.3%)

series94.0ms (0.1%)

simplify209.0ms (0.3%)

prune101.0ms (0.1%)

localize51.0ms (0.1%)

rewrite238.0ms (0.3%)

series85.0ms (0.1%)

simplify210.0ms (0.3%)

prune76.0ms (0.1%)

regimes7.7s (9.8%)

bsearch647.0ms (0.8%)

simplify9.0ms (0%)

end7.0ms (0%)

sample28.4s (36.2%)

Profiling