Details

Time bar (total: 18.3s)

analyze1.8s (9.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
50%50%0.1%4
74.9%25%0.1%5
74.9%25%0.1%6
74.9%25%0.1%7
74.9%25%0.1%8
74.9%25%0.1%9
74.9%25%0.1%10
74.9%25%0.1%11
74.9%25%0.1%12
74.9%25%0.1%13
74.9%25%0.1%14
Compiler

Compiled 53 to 41 computations (22.6% saved)

sample9.4s (51.4%)

Results
6.3s3564×body1024valid
1.5s1443×body512valid
1.1s2625×body128valid
407.0ms604×body256valid
58.0ms20×body2048valid
Compiler

Compiled 158 to 122 computations (22.8% saved)

simplify48.0ms (0.3%)

Algorithm
egg-herbie
Rules
770×neg-mul-1_binary64
444×distribute-rgt-neg-out_binary64
438×distribute-lft-neg-out_binary64
418×distribute-rgt-in_binary64
417×distribute-lft-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03380
18074
220174
362673
4226171
5446071
6542271

prune7.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.5b
(/.f64 (+.f64 2 (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (*.f64 3 (+.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
Compiler

Compiled 295 to 218 computations (26.1% saved)

localize65.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.0b
(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
1.0b
(-.f64 3 (sqrt.f64 5))
2.8b
(-.f64 (cos.f64 x) (cos.f64 y))

series23.0ms (0.1%)

Counts
4 → 32
Calls

4 calls:

16.0ms
(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
7.0ms
(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms
(-.f64 3 (sqrt.f64 5))
0.0ms
(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)

rewrite54.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
179×add-sqr-sqrt_binary64
154×*-un-lft-identity_binary64
128×add-cube-cbrt_binary64
106×times-frac_binary64
105×prod-diff_binary64
Counts
4 → 273
Calls

4 calls:

12.0ms
(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
8.0ms
(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
4.0ms
(-.f64 3 (sqrt.f64 5))
4.0ms
(-.f64 (cos.f64 x) (cos.f64 y))

simplify254.0ms (1.4%)

Algorithm
egg-herbie
Rules
387×cancel-sign-sub-inv_binary64
375×fma-neg_binary64
336×associate-*l*_binary64
316×associate-*r*_binary64
280×*-commutative_binary64
Counts
305 → 333
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05948679
111996233
232235425
346335425
449815425
546965425

prune1.0s (5.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New32211333
Fresh011
Picked101
Done000
Total32312335
Error
0.1b
Counts
335 → 12
Alt Table
StatusErrorProgram
0.6b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (neg.f64 (sqrt.f64 5)))) 3)))
0.5b
(/.f64 (+.f64 2 (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (*.f64 3 (+.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
1.0b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
1.3b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 (-.f64 (sqrt.f64 5) 1))) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.8b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (+.f64 3 (*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5))))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (fma.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (fma.f64 1 (cos.f64 x) (neg.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.8b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (*.f64 (cbrt.f64 (+.f64 -1 (sqrt.f64 5))) (cbrt.f64 (+.f64 -1 (sqrt.f64 5)))) (/.f64 (cbrt.f64 (+.f64 -1 (sqrt.f64 5))) 2/3)) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
Compiler

Compiled 22314 to 14455 computations (35.2% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.0b
(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
1.0b
(-.f64 3 (sqrt.f64 5))
1.0b
(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
2.8b
(-.f64 (cos.f64 x) (cos.f64 y))

series0.0ms (0%)

Counts
2 → 0
Calls

2 calls:

0.0ms
(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
0.0ms
(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))

rewrite63.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
238×add-sqr-sqrt_binary64
172×times-frac_binary64
146×*-un-lft-identity_binary64
141×sqrt-prod_binary64
75×add-cube-cbrt_binary64
Counts
2 → 233
Calls

2 calls:

32.0ms
(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
8.0ms
(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))

simplify196.0ms (1.1%)

Algorithm
egg-herbie
Rules
633×times-frac_binary64
528×cancel-sign-sub-inv_binary64
496×associate-/l*_binary64
318×sub-neg_binary64
318×fma-def_binary64
Counts
233 → 212
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01515163
13754567
212164565
331224503
440954447
552814447

prune1.0s (5.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New3035308
Fresh3811
Picked101
Done000
Total30713320
Error
0.1b
Counts
320 → 13
Alt Table
StatusErrorProgram
0.6b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (neg.f64 (sqrt.f64 5)))) 3)))
0.5b
(/.f64 (+.f64 2 (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (*.f64 3 (+.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
1.0b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 5) 3/2 -3/2))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.8b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 2/3)) 3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
1.3b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.8b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (+.f64 3 (*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5))))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (fma.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (fma.f64 1 (cos.f64 x) (neg.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.3b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
Compiler

Compiled 20296 to 14369 computations (29.2% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.0b
(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
1.0b
(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
2.8b
(-.f64 (cos.f64 x) (cos.f64 y))

prune1.4s (7.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New4222424
Fresh21012
Picked101
Done000
Total42512437
Error
0.1b
Counts
437 → 12
Alt Table
StatusErrorProgram
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (sqrt.f64 2/3)) (*.f64 (-.f64 (sqrt.f64 5) 1) (/.f64 1 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (fma.f64 1 (cos.f64 x) (neg.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.6b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (neg.f64 (sqrt.f64 5)))) 3)))
0.5b
(/.f64 (+.f64 2 (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (*.f64 3 (+.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
1.0b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 5) 3/2 -3/2))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.3b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
1.3b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.8b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (+.f64 3 (*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5))))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (fma.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
Compiler

Compiled 30595 to 21165 computations (30.8% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)
1.0b
(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
1.0b
(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
2.8b
(-.f64 (cos.f64 x) (cos.f64 y))

series24.0ms (0.1%)

Counts
1 → 8
Calls

1 calls:

24.0ms
(pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)

rewrite5.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
cube-prod_binary64
unpow-prod-down_binary64
add-cube-cbrt_binary64
Counts
1 → 33
Calls

1 calls:

4.0ms
(pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)

simplify80.0ms (0.4%)

Algorithm
egg-herbie
Rules
343×distribute-rgt-in_binary64
317×distribute-lft-in_binary64
268×unswap-sqr_binary64
209×fma-neg_binary64
205×fma-def_binary64
Counts
41 → 47
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01701158
15391071
219631048
346501048
449761048
549851048

prune1.1s (6.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New3091310
Fresh11011
Picked011
Done000
Total31012322
Error
0.1b
Counts
322 → 12
Alt Table
StatusErrorProgram
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (sqrt.f64 2/3)) (*.f64 (-.f64 (sqrt.f64 5) 1) (/.f64 1 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
0.3b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (cbrt.f64 (pow.f64 (+.f64 (cos.f64 x) (*.f64 (neg.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))) 3)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (fma.f64 1 (cos.f64 x) (neg.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.6b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (neg.f64 (sqrt.f64 5)))) 3)))
0.5b
(/.f64 (+.f64 2 (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (*.f64 3 (+.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
1.0b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
0.4b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.5b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 5) 3/2 -3/2))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.3b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)) 2) (fma.f64 (cos.f64 x) (*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
1.3b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
0.8b
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (+.f64 3 (*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5))))) 3)))
Compiler

Compiled 21516 to 15436 computations (28.3% saved)

regimes1.1s (6.2%)

Accuracy

Total 0.3b remaining (73.6%)

Threshold costs 0.3b (73.6%)

Counts
190 → 1
Compiler

Compiled 31823 to 24445 computations (23.2% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
040104
160104
276104
388104
496104
598104
696104

end546.0ms (3%)

Compiler

Compiled 845 to 616 computations (27.1% saved)

Profiling

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