Details

Time bar (total: 1.2min)

analyze11.4s (16.1%)

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
7.8%92%0.2%9
11.7%88.1%0.2%10
23.8%76%0.2%11
23.8%76%0.2%12
26.9%72.9%0.2%13
26.9%72.9%0.2%14
Compiler

Compiled 115 to 84 computations (27% saved)

sample47.5s (67.5%)

Results
12.5s1483×body4096valid
9.1s1791×body2048valid
7.3s875×body4096invalid
6.1s1215×body2048invalid
2.9s857×body1024valid
2.7s3537×body128valid
2.5s745×body1024invalid
1.3s70×body8192valid
783.0ms357×body512valid
765.0ms1088×body128invalid
617.0ms35×body8192invalid
612.0ms288×body512invalid
229.0ms161×body256valid
139.0ms107×body256invalid
Compiler

Compiled 230 to 168 computations (27% saved)

preprocess56.0ms (0.1%)

Algorithm
egg-herbie
Rules
432×fma-def_binary64
225×distribute-neg-frac_binary64
202×distribute-lft-in_binary64
202×distribute-rgt-in_binary64
193×associate-*r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02491925
17351903
227371903
055
Stop Event
saturated
node limit
Compiler

Compiled 114 to 83 computations (27.2% saved)

simplify20.0ms (0%)

Algorithm
egg-herbie
Rules
545×associate-/l/_binary64
526×associate-/r/_binary64
263×distribute-rgt-in_binary64
260×distribute-lft-in_binary64
157×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
040175
1104173
2339173
31688170
Stop Event
node limit
Counts
1 → 2

prune11.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
41.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
46.3b
(fma.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)) (*.f64 y-scale 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)) (*.f64 x-scale x-scale)) -4) (*.f64 (/.f64 (/.f64 (*.f64 4 (*.f64 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) x-scale) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale)))
41.8b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
Compiler

Compiled 670 to 462 computations (31% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
9.5b
(/.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)
28.7b
(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
29.2b
(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
30.2b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

series2.0s (2.9%)

Counts
4 → 132
Calls

33 calls:

186.0ms
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
angle
-inf
185.0ms
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
angle
inf
173.0ms
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
y-scale
-inf
168.0ms
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
x-scale
0
162.0ms
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
y-scale
inf

rewrite94.0ms (0.1%)

Algorithm
batch-egg-rewrite
Rules
429×log1p-expm1-u_binary64
429×expm1-log1p-u_binary64
413×add-log-exp_binary64
398×pow1_binary64
152×log-prod_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
040190
1918181
Stop Event
node limit
Counts
4 → 91

simplify259.0ms (0.4%)

Algorithm
egg-herbie
Rules
532×unswap-sqr_binary64
356×fma-neg_binary64
278×times-frac_binary64
269×associate-*r*_binary64
265×associate-/l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
025612980
1102912263
2422612135
Stop Event
node limit
Counts
223 → 150

prune1.1s (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New27612288
Fresh101
Picked101
Done000
Total27812290
Error
20.3b
Counts
290 → 12
Alt Table
StatusErrorProgram
41.6b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 b (/.f64 x-scale b)) 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)))
42.0b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (log.f64 (exp.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
39.3b
(*.f64 (fma.f64 4 (*.f64 (*.f64 (/.f64 b y-scale) (/.f64 b y-scale)) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (*.f64 x-scale x-scale))) (fma.f64 4 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (/.f64 (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale)) (*.f64 b b))) (*.f64 (/.f64 8 (*.f64 y-scale y-scale)) (/.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (*.f64 b b))) (*.f64 x-scale x-scale))))) (*.f64 (neg.f64 a) a))
32.1b
0
30.8b
(neg.f64 (/.f64 (*.f64 (*.f64 4 (*.f64 a a)) (*.f64 b b)) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale))))
37.4b
(/.f64 (neg.f64 (fma.f64 4 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (*.f64 (/.f64 y-scale (*.f64 a a)) (/.f64 y-scale (*.f64 b b)))) (fma.f64 4 (*.f64 (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (*.f64 b (*.f64 b (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4)))) (*.f64 (/.f64 8 y-scale) (/.f64 (*.f64 (*.f64 a a) (*.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (*.f64 b b)))) y-scale))))) (*.f64 x-scale x-scale))
30.5b
(*.f64 -4 (*.f64 (/.f64 (*.f64 a a) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale))) (*.f64 b b)))
44.1b
(fma.f64 4 (-.f64 (*.f64 (/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (pow.f64 a 4)) (*.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (*.f64 x-scale x-scale))) (*.f64 (*.f64 (/.f64 b (/.f64 x-scale b)) (/.f64 (*.f64 a a) x-scale)) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (*.f64 y-scale y-scale)))) (neg.f64 (fma.f64 4 (fma.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (*.f64 y-scale y-scale)) (/.f64 (pow.f64 a 4) (/.f64 (*.f64 x-scale x-scale) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))) (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (*.f64 (/.f64 (*.f64 x-scale x-scale) (*.f64 a a)) (/.f64 (*.f64 y-scale y-scale) (*.f64 b b))))) (*.f64 8 (*.f64 (/.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (*.f64 a a)) (*.f64 x-scale x-scale)) (/.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (/.f64 (*.f64 y-scale y-scale) (*.f64 b b))))))))
42.2b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (*.f64 (pow.f64 (hypot.f64 (*.f64 a (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))) (*.f64 b (cos.f64 (*.f64 (*.f64 angle 1/180) (PI.f64))))) 2) (/.f64 1 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)))
37.2b
(/.f64 (neg.f64 (fma.f64 4 (*.f64 (/.f64 (/.f64 (*.f64 a a) x-scale) x-scale) (*.f64 b (*.f64 b (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4)))) (fma.f64 8 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (/.f64 (*.f64 (/.f64 x-scale (*.f64 b b)) (/.f64 x-scale (*.f64 a a))) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))) (*.f64 4 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (*.f64 (/.f64 x-scale (*.f64 b b)) (/.f64 x-scale (*.f64 a a)))))))) (*.f64 y-scale y-scale))
38.8b
(*.f64 -4 (/.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)) (*.f64 (pow.f64 y-scale 2) (pow.f64 x-scale 2))))
42.0b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (/.f64 x-scale (*.f64 b b))) (*.f64 (/.f64 (*.f64 a a) x-scale) (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2))) 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)))
Compiler

Compiled 36875 to 25264 computations (31.5% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 -4 (*.f64 (/.f64 (*.f64 a a) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale))) (*.f64 b b)))
0.3b
(*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale))
16.4b
(/.f64 (*.f64 a a) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale)))
19.9b
(*.f64 (/.f64 (*.f64 a a) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale))) (*.f64 b b))

series415.0ms (0.6%)

Counts
4 → 156
Calls

39 calls:

18.0ms
(*.f64 (/.f64 (*.f64 a a) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale))) (*.f64 b b))
x-scale
-inf
18.0ms
(*.f64 -4 (*.f64 (/.f64 (*.f64 a a) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale))) (*.f64 b b)))
b
0
16.0ms
(*.f64 -4 (*.f64 (/.f64 (*.f64 a a) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale))) (*.f64 b b)))
a
-inf
16.0ms
(*.f64 -4 (*.f64 (/.f64 (*.f64 a a) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale))) (*.f64 b b)))
b
-inf
15.0ms
(*.f64 -4 (*.f64 (/.f64 (*.f64 a a) (*.f64 (*.f64 y-scale x-scale) (*.f64 y-scale x-scale))) (*.f64 b b)))
a
0

rewrite64.0ms (0.1%)

Algorithm
batch-egg-rewrite
Rules
237×expm1-udef_binary64
237×log1p-udef_binary64
219×log-pow_binary64
141×associate-*r*_binary64
136×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01361
127846
2386546
Stop Event
node limit
Counts
4 → 106

simplify73.0ms (0.1%)

Algorithm
egg-herbie
Rules
780×associate-*r*_binary64
759×associate-*l*_binary64
615×associate-/l/_binary64
451×associate-/r/_binary64
292×times-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0203072
1563072
22033072
316643072
Stop Event
node limit
Counts
262 → 118

prune204.0ms (0.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New10513118
Fresh8311
Picked101
Done000
Total11416130
Error
3.2b
Counts
130 → 16
Alt Table
StatusErrorProgram
41.6b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 b (/.f64 x-scale b)) 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)))
42.0b
(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (log.f64 (exp.f64 (sin.f64 (*.f64 (*.f64 angle 1/180) (PI.f64)))))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
26.0b
(*.f64 -4 (*.f64 (*.f64 (/.f64 a y-scale) (/.f64 a (*.f64 x-scale (*.f64 y-scale x-scale)))) (*.f64 b b)))
18.4b
(*.f64 -4 (/.f64 (/.f64 (pow.f64 (*.f64 a b) 2) (*.f64 y-scale (*.f64 y-scale x-scale))) x-scale))
37.4b
(/.f64 (neg.f64 (fma.f64 4 (/.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4) (*.f64 (/.f64 y-scale (*.f64 a a)) (/.f64 y-scale (*.f64 b b)))) (fma.f64 4 (*.f64 (*.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (*.f64 b (*.f64 b (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 4)))) (*.f64 (/.f64 8 y-scale) (/.f64 (*.f64 (*.f64 a a) (*.f64 (pow.f64 (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (*.f64 (pow.f64 (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))) 2) (*.f64 b b)))) y-scale))))) (*.f64 x-scale x-scale))
14.3b
(*.f64 -4 (/.f64 (/.f64 (pow.f64 (*.f64 a b) 2) (*.f64 y-scale x-scale)) (*.f64 y-scale x-scale)))
6.0b
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2) -4)) 3)
19.2b
(*.f64 -4 (/.f64 (/.f64 (pow.f64 (*.f64 a b) 2) y-scale) (*.f64 x-scale (*.f64 y-scale x-scale))))
17.5b
(/.f64 (*.f64 (pow.f64 (*.f64 a b) 2) -4) (pow.f64 (*.f64 y-scale x-scale) 2))
23.7b
(*.f64 (*.f64 b (*.f64 (*.f64 b (/.f64 a x-scale)) (/.f64 a x-scale))) (/.f64 -4 (*.f64 y-scale y-scale)))
20.3b
(*.f64 -4 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2) 3)))
5.7b
(*.f64 -4 (pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2))
6.0b
(*.f64 -4 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2)) 3))
22.1b
(*.f64 -4 (/.f64 (*.f64 (*.f64 (/.f64 a y-scale) (/.f64 a x-scale)) (*.f64 b b)) (*.f64 y-scale x-scale)))
30.9b
(*.f64 -4 (*.f64 (*.f64 b b) (*.f64 (/.f64 a x-scale) (/.f64 a (*.f64 (*.f64 y-scale y-scale) x-scale)))))
22.6b
(*.f64 -4 (*.f64 (*.f64 (*.f64 (/.f64 a y-scale) (/.f64 a x-scale)) (/.f64 1 (*.f64 y-scale x-scale))) (*.f64 b b)))
Compiler

Compiled 3084 to 1731 computations (43.9% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 -4 (pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2))
0.3b
(pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2)
4.1b
(*.f64 b (/.f64 a (*.f64 y-scale x-scale)))
5.7b
(/.f64 a (*.f64 y-scale x-scale))

series279.0ms (0.4%)

Counts
4 → 164
Calls

45 calls:

41.0ms
(*.f64 -4 (pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2))
x-scale
inf
19.0ms
(*.f64 -4 (pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2))
b
0
18.0ms
(*.f64 -4 (pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2))
b
-inf
18.0ms
(*.f64 -4 (pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2))
a
0
16.0ms
(*.f64 -4 (pow.f64 (*.f64 b (/.f64 a (*.f64 y-scale x-scale))) 2))
a
inf

rewrite59.0ms (0.1%)

Algorithm
batch-egg-rewrite
Rules
638×log-prod_binary64
217×expm1-udef_binary64
217×log1p-udef_binary64
193×log-pow_binary64
122×egg-rr
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01246
125346
2317046
Stop Event
node limit
Counts
4 → 122

simplify69.0ms (0.1%)

Algorithm
egg-herbie
Rules
835×associate-*r*_binary64
803×associate-*l*_binary64
584×associate-/l/_binary64
438×associate-/r/_binary64
256×times-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0242876
1742876
22262876
315192876
Stop Event
node limit
Counts
286 → 131

prune214.0ms (0.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New11912131
Fresh11415
Picked101
Done000
Total13116147
Error
0.0b
Counts
147 → 16
Alt Table
StatusErrorProgram
4.1b
(*.f64 -4 (pow.f64 (*.f64 b (pow.f64 (cbrt.f64 (/.f64 (/.f64 a y-scale) x-scale)) 3)) 2))
23.7b
(*.f64 (*.f64 b (*.f64 (*.f64 b (/.f64 a x-scale)) (/.f64 a x-scale))) (/.f64 -4 (*.f64 y-scale y-scale)))
15.0b
(*.f64 -4 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b)) 2) (cbrt.f64 (pow.f64 (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b) 4))))
5.6b
(*.f64 -4 (pow.f64 (*.f64 b (*.f64 (/.f64 1 y-scale) (/.f64 a x-scale))) 2))
5.7b
(*.f64 -4 (pow.f64 (/.f64 (/.f64 (*.f64 a b) y-scale) x-scale) 2))
21.6b
(*.f64 (*.f64 b b) (*.f64 (*.f64 (/.f64 a (*.f64 x-scale y-scale)) (/.f64 a (*.f64 x-scale y-scale))) -4))
10.6b
(*.f64 -4 (/.f64 (*.f64 (*.f64 a b) (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b)) (*.f64 y-scale x-scale)))
6.4b
(*.f64 -4 (*.f64 b (*.f64 (/.f64 (/.f64 a y-scale) x-scale) (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b))))
3.3b
(*.f64 -4 (pow.f64 (/.f64 b (/.f64 x-scale (/.f64 a y-scale))) 2))
3.8b
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b) 2) -4)) 3)
6.0b
(*.f64 -4 (*.f64 (/.f64 (/.f64 a y-scale) x-scale) (*.f64 b (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b))))
22.6b
(*.f64 -4 (*.f64 (*.f64 (*.f64 (/.f64 a y-scale) (/.f64 a x-scale)) (/.f64 1 (*.f64 y-scale x-scale))) (*.f64 b b)))
19.5b
(*.f64 -4 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b) 2) 3)))
23.9b
(*.f64 -4 (*.f64 (sqrt.f64 (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b)) (*.f64 (sqrt.f64 (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b)) (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b))))
30.9b
(*.f64 -4 (*.f64 (*.f64 b b) (*.f64 (/.f64 a x-scale) (/.f64 a (*.f64 (*.f64 y-scale y-scale) x-scale)))))
14.3b
(*.f64 -4 (/.f64 (/.f64 (pow.f64 (*.f64 a b) 2) (*.f64 y-scale x-scale)) (*.f64 y-scale x-scale)))
Compiler

Compiled 2817 to 1428 computations (49.3% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 -4 (pow.f64 (/.f64 b (/.f64 x-scale (/.f64 a y-scale))) 2))
0.3b
(pow.f64 (/.f64 b (/.f64 x-scale (/.f64 a y-scale))) 2)
3.9b
(/.f64 x-scale (/.f64 a y-scale))
3.9b
(/.f64 b (/.f64 x-scale (/.f64 a y-scale)))

series261.0ms (0.4%)

Counts
4 → 180
Calls

45 calls:

20.0ms
(*.f64 -4 (pow.f64 (/.f64 b (/.f64 x-scale (/.f64 a y-scale))) 2))
a
inf
19.0ms
(*.f64 -4 (pow.f64 (/.f64 b (/.f64 x-scale (/.f64 a y-scale))) 2))
a
0
16.0ms
(*.f64 -4 (pow.f64 (/.f64 b (/.f64 x-scale (/.f64 a y-scale))) 2))
a
-inf
16.0ms
(*.f64 -4 (pow.f64 (/.f64 b (/.f64 x-scale (/.f64 a y-scale))) 2))
b
inf
15.0ms
(*.f64 -4 (pow.f64 (/.f64 b (/.f64 x-scale (/.f64 a y-scale))) 2))
b
-inf

rewrite65.0ms (0.1%)

Algorithm
batch-egg-rewrite
Rules
229×expm1-udef_binary64
229×log1p-udef_binary64
203×log-pow_binary64
179×log-div_binary64
146×egg-rr
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01246
126246
2360246
Stop Event
node limit
Counts
4 → 146

simplify99.0ms (0.1%)

Algorithm
egg-herbie
Rules
824×associate-*l*_binary64
579×associate-/l/_binary64
440×associate-/r/_binary64
258×times-frac_binary64
219×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0252988
1762988
22292988
315322988
448212988
549842988
Stop Event
node limit
Counts
326 → 156

prune212.0ms (0.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1506156
Fresh9615
Picked101
Done000
Total16012172
Error
0.0b
Counts
172 → 12
Alt Table
StatusErrorProgram
5.7b
(*.f64 -4 (pow.f64 (*.f64 b (/.f64 a (*.f64 x-scale y-scale))) 2))
14.3b
(*.f64 -4 (/.f64 (/.f64 (pow.f64 (*.f64 a b) 2) (*.f64 y-scale x-scale)) (*.f64 y-scale x-scale)))
20.5b
(*.f64 -4 (/.f64 (*.f64 b b) (pow.f64 (*.f64 x-scale (/.f64 y-scale a)) 2)))
4.7b
(*.f64 -4 (/.f64 (*.f64 (/.f64 a y-scale) (/.f64 b x-scale)) (/.f64 x-scale (*.f64 b (/.f64 a y-scale)))))
7.2b
(*.f64 -4 (/.f64 b (*.f64 (/.f64 x-scale (*.f64 b (/.f64 a y-scale))) (*.f64 x-scale (/.f64 y-scale a)))))
19.5b
(*.f64 -4 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b) 2) 3)))
17.7b
(*.f64 -4 (*.f64 (pow.f64 (/.f64 b x-scale) 2) (pow.f64 (/.f64 a y-scale) 2)))
23.7b
(*.f64 (*.f64 b (*.f64 (*.f64 b (/.f64 a x-scale)) (/.f64 a x-scale))) (/.f64 -4 (*.f64 y-scale y-scale)))
6.5b
(*.f64 -4 (pow.f64 (*.f64 (/.f64 1 (/.f64 x-scale a)) (/.f64 b y-scale)) 2))
21.6b
(*.f64 (*.f64 b b) (*.f64 (*.f64 (/.f64 a (*.f64 x-scale y-scale)) (/.f64 a (*.f64 x-scale y-scale))) -4))
30.9b
(*.f64 -4 (*.f64 (*.f64 b b) (*.f64 (/.f64 a x-scale) (/.f64 a (*.f64 (*.f64 y-scale y-scale) x-scale)))))
6.4b
(*.f64 -4 (*.f64 b (*.f64 (/.f64 (/.f64 a y-scale) x-scale) (*.f64 (/.f64 (/.f64 a y-scale) x-scale) b))))
Compiler

Compiled 2737 to 1284 computations (53.1% saved)

regimes2.5s (3.6%)

Accuracy

Total 5.9b remaining (98.7%)

Threshold costs 0b (0%)

Counts
169 → 3
Compiler

Compiled 62480 to 44847 computations (28.2% saved)

bsearch3.2s (4.5%)

Algorithm
binary-search
Calls

2 calls:

2.1s
y-scale
1.1s
y-scale
Steps
ItersPointRange
1.0890629128264413e-154
∈ [
5.9981436181684076e-155
,
1.3992416110807618e-150
]
-1.7936283151776695e-283
∈ [
-1.2205428814730726e-272
,
-2.0027745512547489e-286
]
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03467
15167
25967
36567
46767
Stop Event
saturated

end148.0ms (0.2%)

Stop Event
fuel
Compiler

Compiled 341 to 231 computations (32.3% saved)

Profiling

Loading profile data...