Details

Time bar (total: 2.5min)

analyze25.8s (17.2%)

Algorithm
search
Search
TrueOtherFalseIter
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)

sample2.8s (1.9%)

Algorithm
intervals
Results
1.4s119×body4096valid
837.0ms39×body8192valid
433.0ms64×body2048valid
76.0ms20×body1024valid
33.0ms11×body512valid
13.0msbody512invalid
8.0msbody1024invalid
5.0msbody256valid
Compiler

Compiled 382 to 254 computations (33.5% saved)

simplify30.0ms (0%)

Algorithm
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)

IterNodesCost
057292
1154279
2569279
35117279

prune11.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
63.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
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 (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)) (hypot.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)) (/.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))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
Compiler

Compiled 540 to 339 computations (37.2% saved)

localize77.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.4b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
26.4b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
26.4b
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
35.0b
(-.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)) (hypot.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)) (/.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))))

rewrite979.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
63.7b
Rules
31×add-cube-cbrt_binary64
18×add-sqr-sqrt_binary64
16×pow1_binary64
14×add-log-exp_binary64
12×add-cbrt-cube_binary64
Counts
4 → 133
Calls

4 calls:

22.0ms
(-.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)) (hypot.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)) (/.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))))
15.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
15.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
14.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
Compiler

Compiled 29662 to 17931 computations (39.5% saved)

series8.6s (5.8%)

Error
63.1b
Counts
4 → 33
Calls

4 calls:

8.3s
(-.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)) (hypot.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)) (/.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))))
19.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
17.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
16.0ms
(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
Compiler

Compiled 67999 to 47441 computations (30.2% saved)

simplify657.0ms (0.4%)

Algorithm
egg-herbie
Rules
440×times-frac_binary64
381×associate-/l*_binary64
278×associate-*r*_binary64
274×fma-def_binary64
273×associate-/r*_binary64
Counts
166 → 99
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
048828658
1136126809
2499726809
3503326809

prune1.0s (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New93699
Fresh000
Picked101
Done000
Total946100
Error
63.1b
Counts
100 → 6
Alt Table
StatusErrorProgram
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 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 a a)) (*.f64 y-scale y-scale))) (sqrt.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 a 4)) (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 y-scale 4)) (/.f64 (*.f64 (pow.f64 b 4) (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 (+.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))) (+.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)))) (pow.f64 (cbrt.f64 (hypot.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))) (/.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 x-scale y-scale)))) 6)) (+.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))) (hypot.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))) (/.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 x-scale y-scale)))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
63.4b
(*.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 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 4)) (+.f64 (/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 b 4)) (pow.f64 x-scale 4)) (/.f64 (*.f64 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-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 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 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (fma.f64 3 (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.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))) 4) (pow.f64 y-scale 4)))) (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale)))))))))) (*.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 a a) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale))) (sqrt.f64 (-.f64 (fma.f64 3 (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.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))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)))) (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale)))))))))) (*.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 (*.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 PI.f64 (/.f64 angle 180)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))) 2)) (*.f64 y-scale y-scale)) (hypot.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))) (/.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 x-scale y-scale)))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
Compiler

Compiled 24724 to 14160 computations (42.7% saved)

localize83.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.4b
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
26.4b
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
26.4b
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
32.3b
(-.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 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 4)) (+.f64 (/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 b 4)) (pow.f64 x-scale 4)) (/.f64 (*.f64 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 4)))))))

rewrite1.6s (1.1%)

Algorithm
rewrite-expression-head
Error
63.1b
Rules
31×add-cube-cbrt_binary64
24×frac-add_binary64
18×add-sqr-sqrt_binary64
16×pow1_binary64
14×add-log-exp_binary64
Counts
4 → 135
Calls

4 calls:

25.0ms
(-.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 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 4)) (+.f64 (/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 b 4)) (pow.f64 x-scale 4)) (/.f64 (*.f64 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 4)))))))
16.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
16.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
15.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
Compiler

Compiled 28809 to 15942 computations (44.7% saved)

series882.0ms (0.6%)

Error
61.3b
Counts
4 → 22
Calls

4 calls:

765.0ms
(-.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 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 4)) (+.f64 (/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 b 4)) (pow.f64 x-scale 4)) (/.f64 (*.f64 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 4)))))))
22.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
18.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
17.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
Compiler

Compiled 6832 to 3955 computations (42.1% saved)

simplify308.0ms (0.2%)

Algorithm
egg-herbie
Rules
382×distribute-rgt-in_binary64
360×distribute-lft-in_binary64
299×fma-neg_binary64
272×unswap-sqr_binary64
194×associate-*r*_binary64
Counts
157 → 56
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
018912051
151811617
222239434
347839432
449209432

prune591.0ms (0.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New53356
Fresh055
Picked101
Done000
Total54862
Error
63.1b
Counts
62 → 8
Alt Table
StatusErrorProgram
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 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 a a)) (*.f64 y-scale y-scale))) (sqrt.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 a 4)) (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 y-scale 4)) (/.f64 (*.f64 (pow.f64 b 4) (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)))
63.4b
(*.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))) (fma.f64 (*.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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)))) (neg.f64 (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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a 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 (+.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))) (+.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)))) (pow.f64 (cbrt.f64 (hypot.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))) (/.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 x-scale y-scale)))) 6)) (+.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))) (hypot.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))) (/.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 x-scale y-scale)))))))) (*.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 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 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (fma.f64 3 (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.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))) 4) (pow.f64 y-scale 4)))) (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale)))))))))) (*.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 a a) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale))) (sqrt.f64 (-.f64 (fma.f64 3 (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.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))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)))) (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale)))))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
63.4b
(*.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 (cbrt.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))) (cbrt.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale))))))))) (cbrt.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))))))) (*.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 (*.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 PI.f64 (/.f64 angle 180)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))) 2)) (*.f64 y-scale y-scale)) (hypot.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))) (/.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 x-scale y-scale)))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
63.4b
(*.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))) (exp.f64 (log.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
Compiler

Compiled 13020 to 7012 computations (46.1% saved)

localize121.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.4b
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
34.3b
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))
34.3b
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))
34.3b
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))

rewrite3.9s (2.6%)

Algorithm
rewrite-expression-head
Error
63.1b
Rules
53×add-cube-cbrt_binary64
22×add-sqr-sqrt_binary64
20×add-log-exp_binary64
16×pow1_binary64
15×flip3--_binary64
Counts
4 → 175
Calls

4 calls:

20.0ms
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))
18.0ms
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))
17.0ms
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))
17.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
Compiler

Compiled 79947 to 44119 computations (44.8% saved)

series2.7s (1.8%)

Error
63.1b
Counts
4 → 39
Calls

4 calls:

819.0ms
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))
808.0ms
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))
806.0ms
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))
34.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
Compiler

Compiled 28295 to 16681 computations (41% saved)

simplify621.0ms (0.4%)

Algorithm
egg-herbie
Rules
611×associate-/l*_binary64
569×fma-def_binary64
474×associate-/r*_binary64
272×distribute-rgt-in_binary64
236×distribute-lft-in_binary64
Counts
214 → 116
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
016030633
137729886
2131627684
3506427684

prune1.6s (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1160116
Fresh077
Picked011
Done000
Total1168124
Error
63.1b
Counts
124 → 8
Alt Table
StatusErrorProgram
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 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 a a)) (*.f64 y-scale y-scale))) (sqrt.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 a 4)) (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 y-scale 4)) (/.f64 (*.f64 (pow.f64 b 4) (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)))
63.4b
(*.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))) (fma.f64 (*.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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)))) (neg.f64 (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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a 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 (+.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))) (+.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)))) (pow.f64 (cbrt.f64 (hypot.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))) (/.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 x-scale y-scale)))) 6)) (+.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))) (hypot.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))) (/.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 x-scale y-scale)))))))) (*.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 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 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (fma.f64 3 (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.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))) 4) (pow.f64 y-scale 4)))) (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale)))))))))) (*.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 a a) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale))) (sqrt.f64 (-.f64 (fma.f64 3 (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.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))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)))) (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale)))))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
63.4b
(*.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 (cbrt.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))) (cbrt.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale))))))))) (cbrt.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))))))) (*.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 (*.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 PI.f64 (/.f64 angle 180)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))) 2)) (*.f64 y-scale y-scale)) (hypot.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))) (/.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 x-scale y-scale)))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
63.4b
(*.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))) (exp.f64 (log.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
Compiler

Compiled 42921 to 23635 computations (44.9% saved)

localize89.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.4b
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
26.4b
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
26.4b
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
34.3b
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))

rewrite1.5s (1%)

Algorithm
rewrite-expression-head
Error
63.1b
Rules
31×add-cube-cbrt_binary64
18×add-sqr-sqrt_binary64
16×pow1_binary64
12×add-cbrt-cube_binary64
12×add-log-exp_binary64
Counts
4 → 133
Calls

4 calls:

19.0ms
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))
19.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
15.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
15.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
Compiler

Compiled 25138 to 13400 computations (46.7% saved)

series836.0ms (0.6%)

Error
61.3b
Counts
4 → 21
Calls

4 calls:

740.0ms
(-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))
16.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
15.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
15.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle PI.f64)))
Compiler

Compiled 6005 to 3525 computations (41.3% saved)

simplify273.0ms (0.2%)

Algorithm
egg-herbie
Rules
611×associate-/l*_binary64
569×fma-def_binary64
474×associate-/r*_binary64
272×distribute-rgt-in_binary64
236×distribute-lft-in_binary64
Counts
154 → 52
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
016010995
137710714
213169980
350649980

prune536.0ms (0.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New52052
Fresh066
Picked011
Done011
Total52860
Error
63.1b
Counts
60 → 8
Alt Table
StatusErrorProgram
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 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 a a)) (*.f64 y-scale y-scale))) (sqrt.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)) (pow.f64 a 4)) (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 y-scale 4)) (/.f64 (*.f64 (pow.f64 b 4) (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)))
63.4b
(*.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))) (fma.f64 (*.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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)))) (neg.f64 (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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a 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 (+.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))) (+.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)))) (pow.f64 (cbrt.f64 (hypot.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))) (/.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 x-scale y-scale)))) 6)) (+.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))) (hypot.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))) (/.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 x-scale y-scale)))))))) (*.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 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 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 x-scale 4)) (fma.f64 3 (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.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))) 4) (pow.f64 y-scale 4)))) (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale)))))))))) (*.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 a a) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale))) (sqrt.f64 (-.f64 (fma.f64 3 (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.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))) 4) (pow.f64 x-scale 4)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 4) (pow.f64 y-scale 4)))) (*.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 y-scale y-scale)))))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
63.4b
(*.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 (cbrt.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))) (cbrt.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale))))))))) (cbrt.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))))))) (*.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 (*.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 PI.f64 (/.f64 angle 180)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))) 2)) (*.f64 y-scale y-scale)) (hypot.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))) (/.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 x-scale y-scale)))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
63.4b
(*.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))) (exp.f64 (log.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) x-scale) (/.f64 (*.f64 b b) x-scale) (/.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 b 4)) (pow.f64 x-scale 4)) (*.f64 (/.f64 (*.f64 a (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2) (*.f64 (*.f64 b b) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle PI.f64))) 2)))) (pow.f64 x-scale 3)) (+.f64 (/.f64 a x-scale) (/.f64 a x-scale)))))))))))) (*.f64 (*.f64 b a) (*.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2)))
Compiler

Compiled 10906 to 5875 computations (46.1% saved)

regimes5.1s (3.4%)

Compiler

Compiled 227040 to 135770 computations (40.2% saved)

simplify10.0ms (0%)

Algorithm
egg-herbie
Rules
45×distribute-rgt-neg-in_binary64
31×distribute-lft-neg-in_binary64
24×neg-sub0_binary64
24×neg-mul-1_binary64
21×*-commutative_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
02573
13873
24773
36273
48371
510569
614069
717269
819569
920769
1021169
1120569

end1.0ms (0%)

Compiler

Compiled 50 to 28 computations (44% saved)

sample1.5min (59.5%)

Algorithm
intervals
Results
262.0msbody4096valid
261.0msbody4096valid
240.0msbody4096valid
240.0msbody4096valid
235.0msbody4096valid
71.0msbody8192valid
71.0msbody4096valid
70.0msbody8192valid
68.0msbody4096valid
66.0msbody8192valid
66.0msbody8192valid
66.0msbody4096valid
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64.0msbody8192valid
63.0msbody8192valid
59.0msbody4096valid
58.0msbody4096valid
57.0msbody2048valid
56.0msbody4096valid
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50.0msbody8192valid
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49.0msbody4096valid
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44.0msbody8192valid
44.0msbody8192valid
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40.0msbody4096valid
40.0msbody8192valid
38.0msbody8192valid
38.0msbody2048valid
38.0msbody8192valid
37.0msbody4096valid
36.0msbody8192valid
34.0msbody4096valid
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31.0msbody4096valid
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28.0msbody4096valid
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26.0msbody4096valid
26.0msbody8192exit
26.0msbody8192valid
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26.0msbody4096valid
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24.0msbody4096valid
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2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256invalid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256invalid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody128valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256invalid
2.0msbody256valid
2.0msbody256valid
2.0msbody256invalid
2.0msbody256valid
2.0msbody256valid
2.0msbody256invalid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
2.0msbody256valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128invalid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128invalid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128invalid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128invalid
1.0msbody128valid
1.0msbody128invalid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128invalid
1.0msbody128valid
1.0msbody128invalid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
1.0msbody128valid
Compiler

Compiled 194 to 130 computations (33% saved)

Profiling

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