Metrics for b from scale-rotated-ellipse

analyze12.9s (8.6%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
0%	0%	99.8%	0.2%	0%	0%	0%	1
0%	0%	99.8%	0.2%	0%	0%	0%	2
0%	0%	99.8%	0.2%	0%	0%	0%	3
0%	0%	99.8%	0.2%	0%	0%	0%	4
0%	0%	99.8%	0.2%	0%	0%	0%	5
0%	0%	99.8%	0.2%	0%	0%	0%	6
0%	0%	99.8%	0.2%	0%	0%	0%	7
0%	0%	99.8%	0.2%	0%	0%	0%	8
0%	0%	99.8%	0.2%	0%	0%	0%	9
0%	0%	99.8%	0.2%	0%	0%	0%	10
0%	0%	99.8%	0.2%	0%	0%	0%	11
0%	0%	99.8%	0.2%	0%	0%	0%	12

Compiler

Compiled 189 to 125 computations (33.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.2s

Operation ival-pow, time spent: 4.9s, 53.0% of total-time

Operation ival-mult, time spent: 1.7s, 19.0% of total-time

Operation ival-div, time spent: 845.0ms, 9.0% of total-time

Operation ival-cos, time spent: 514.0ms, 6.0% of total-time

Operation ival-sin, time spent: 481.0ms, 5.0% of total-time

Operation ival-add, time spent: 269.0ms, 3.0% of total-time

Operation const, time spent: 165.0ms, 2.0% of total-time

Operation ival-sqrt, time spent: 129.0ms, 1.0% of total-time

Operation ival-neg, time spent: 103.0ms, 1.0% of total-time

Operation ival-sub, time spent: 99.0ms, 1.0% of total-time

Operation ival-pi, time spent: 37.0ms, 0.0% of total-time

sample2.0min (80.6%)

Results

58.3s	3626×	body	4096	valid
29.6s	1113×	body	8192	valid
23.3s	2094×	body	2048	valid
7.1s	822×	body	1024	valid
1.7s	342×	body	512	valid
318.0ms	163×	body	256	valid
278.0ms	35×	body	1024	infinite
168.0ms	18×	body	2048	infinite
98.0ms	21×	body	512	infinite
41.0ms	22×	body	256	infinite

Precisions

Click to see histograms. Total time spent on operations: 1.5min

Operation ival-sin, time spent: 20.2s, 23.0% of total-time

Operation ival-pow, time spent: 18.0s, 20.0% of total-time

Operation ival-cos, time spent: 17.3s, 19.0% of total-time

Operation ival-mult, time spent: 15.3s, 17.0% of total-time

Operation ival-div, time spent: 12.2s, 14.0% of total-time

Operation ival-add, time spent: 2.1s, 2.0% of total-time

Operation const, time spent: 1.5s, 2.0% of total-time

Operation ival-sqrt, time spent: 1.4s, 2.0% of total-time

Operation ival-sub, time spent: 1.0s, 1.0% of total-time

Operation ival-neg, time spent: 611.0ms, 1.0% of total-time

Operation ival-pi, time spent: 250.0ms, 0.0% of total-time

Bogosity

preprocess16.2s (10.8%)

Algorithm

1×	egg-herbie

Rules

1420×	`fma-def`
1270×	`associate-r`
1184×	`associate-l`
730×	`*-commutative`
524×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	565	15874
1	1692	14816
2	7436	14744

Stop Event

1×	node limit

Calls

Call 1

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

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

Symmetry

(abs a)

(abs b)

Results

Compiler

Compiled 1619 to 1053 computations (35% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.5s

Operation ival-cos, time spent: 3.3s, 27.0% of total-time

Operation ival-sin, time spent: 3.2s, 26.0% of total-time

Operation ival-pow, time spent: 2.1s, 17.0% of total-time

Operation ival-mult, time spent: 1.7s, 14.0% of total-time

Operation ival-div, time spent: 1.4s, 11.0% of total-time

Operation ival-add, time spent: 222.0ms, 2.0% of total-time

Operation const, time spent: 196.0ms, 2.0% of total-time

Operation ival-sub, time spent: 141.0ms, 1.0% of total-time

Operation ival-sqrt, time spent: 128.0ms, 1.0% of total-time

Operation ival-neg, time spent: 15.0ms, 0.0% of total-time

Operation ival-pi, time spent: 11.0ms, 0.0% of total-time

analyze12.9s (8.6%)

sample2.0min (80.6%)

preprocess16.2s (10.8%)

Profiling