Details

Time bar (total: 26.1s)

analyze3.0s (11.6%)

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
7.6%92.3%0.2%12
13.3%86.5%0.2%13
15.3%84.5%0.2%14
Compiler

Compiled 42 to 20 computations (52.4% saved)

sample16.1s (61.5%)

Results
11.8s2343×body8192exit
2.1s7839×body128valid
1.2s1286×body1024invalid
305.0ms459×body512invalid
163.0ms176×body1024valid
126.0ms91×body2048invalid
93.0ms140×body512valid
73.0ms169×body256invalid
71.0ms283×body128invalid
39.0ms88×body256valid
19.0ms13×body2048valid
Compiler

Compiled 83 to 39 computations (53% saved)

simplify67.0ms (0.3%)

Algorithm
egg-herbie
Rules
892×unswap-sqr_binary64
461×associate-/l*_binary64
323×associate-/r*_binary64
296×associate-*l/_binary64
286×associate-*r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02040
13938
27038
311838
426338
599638
6304338
7408538
8454138
9486638
10493238

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
9.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
31.9b
(*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
Compiler

Compiled 206 to 96 computations (53.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
2.0b
(*.f64 y.re (atan2.f64 x.im x.re))
2.4b
(*.f64 (atan2.f64 x.im x.re) y.im)
32.9b
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series738.0ms (2.8%)

Counts
4 → 96
Calls

4 calls:

605.0ms
(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
119.0ms
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
7.0ms
(*.f64 y.re (atan2.f64 x.im x.re))
7.0ms
(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite16.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
24×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
21×times-frac_binary64
12×unpow-prod-down_binary64
Counts
4 → 97
Calls

4 calls:

4.0ms
(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
3.0ms
(*.f64 y.re (atan2.f64 x.im x.re))
3.0ms
(*.f64 (atan2.f64 x.im x.re) y.im)
1.0ms
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

simplify249.0ms (1%)

Algorithm
egg-herbie
Rules
731×times-frac_binary64
680×associate-/l*_binary64
644×fma-def_binary64
277×*-commutative_binary64
143×cancel-sign-sub-inv_binary64
Counts
193 → 273
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
06999245
121818424
245208364
349568364
448808364

prune548.0ms (2.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New25716273
Fresh101
Picked101
Done000
Total25916275
Error
3.5b
Counts
275 → 16
Alt Table
StatusErrorProgram
9.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
50.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (fma.f64 1/2 (/.f64 (*.f64 (*.f64 x.re x.re) (*.f64 y.im (cos.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))) (*.f64 x.im x.im)) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im)))))))
43.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (sqrt.f64 y.re) (*.f64 (sqrt.f64 y.re) (atan2.f64 x.im x.re))))))
21.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
9.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (log1p.f64 (expm1.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
41.1b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
9.2b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))) 3)) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
33.3b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (sqrt.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sqrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))
15.1b
(*.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
22.2b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))
39.6b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
9.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
9.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
22.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (fma.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))) (fma.f64 1/2 (*.f64 (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2) (*.f64 (*.f64 y.im y.im) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))) (*.f64 1/6 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (pow.f64 y.im 3) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 3)))))))
9.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (fma.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))
22.9b
(*.f64 (/.f64 1 (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
Compiler

Compiled 16143 to 5230 computations (67.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.0b
(*.f64 y.re (atan2.f64 x.im x.re))
2.4b
(*.f64 y.im (atan2.f64 x.im x.re))
32.9b
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
37.4b
(cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3))

series25.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

16.0ms
(cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3))
8.0ms
(*.f64 y.im (atan2.f64 x.im x.re))

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
cbrt-prod_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 39
Calls

2 calls:

3.0ms
(*.f64 y.im (atan2.f64 x.im x.re))
1.0ms
(cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3))

simplify114.0ms (0.4%)

Algorithm
egg-herbie
Rules
559×unswap-sqr_binary64
408×fabs-mul_binary64
278×*-commutative_binary64
265×sqr-pow_binary64
230×log-div_binary64
Counts
87 → 52
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
066805
1100805
2258797
3484797
4603797
5901797
61427797
72521797
83458797
94543797
104992797
114783797

prune351.0ms (1.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1491150
Fresh01515
Picked101
Done000
Total15016166
Error
3.5b
Counts
166 → 16
Alt Table
StatusErrorProgram
43.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (sqrt.f64 y.re) (*.f64 (sqrt.f64 y.re) (atan2.f64 x.im x.re))))))
21.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
9.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3)))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3)))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
9.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (log1p.f64 (expm1.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
41.1b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
9.2b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))) 3)) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
33.3b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (sqrt.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sqrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))
15.1b
(*.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
22.2b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))
50.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (fma.f64 1/2 (/.f64 (*.f64 (*.f64 x.re x.re) (*.f64 y.im (cos.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))) (*.f64 x.im x.im)) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im)))))))
39.6b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
9.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
9.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
22.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (fma.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))) (fma.f64 1/2 (*.f64 (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2) (*.f64 (*.f64 y.im y.im) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))) (*.f64 1/6 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (pow.f64 y.im 3) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 3)))))))
9.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (fma.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))
22.9b
(*.f64 (/.f64 1 (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
Compiler

Compiled 9223 to 3616 computations (60.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.4b
(*.f64 y.im (atan2.f64 x.im x.re))
6.7b
(cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3)))
32.9b
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
37.4b
(cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3))

series1.2s (4.4%)

Counts
1 → 36
Calls

1 calls:

1.2s
(cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3)))

rewrite8.0ms (0%)

Algorithm
rewrite-expression-head
Rules
19×cbrt-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
sqr-pow_binary64
Counts
1 → 21
Calls

1 calls:

2.0ms
(cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3)))

simplify81.0ms (0.3%)

Algorithm
egg-herbie
Rules
420×fma-neg_binary64
342×distribute-rgt-in_binary64
315×*-commutative_binary64
308×distribute-lft-in_binary64
286×associate-+l+_binary64
Counts
57 → 38
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
070986
1120946
2267832
3833672
41718668
54808668
65068668

prune936.0ms (3.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New3431344
Fresh01515
Picked101
Done000
Total34416360
Error
3.5b
Counts
360 → 16
Alt Table
StatusErrorProgram
43.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (sqrt.f64 y.re) (*.f64 (sqrt.f64 y.re) (atan2.f64 x.im x.re))))))
21.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
9.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (log1p.f64 (expm1.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
41.1b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
9.2b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))) 3)) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
33.3b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (sqrt.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sqrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))
15.1b
(*.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
22.2b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))
50.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (fma.f64 1/2 (/.f64 (*.f64 (*.f64 x.re x.re) (*.f64 y.im (cos.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))) (*.f64 x.im x.im)) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im)))))))
14.1b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3)))) (exp.f64 (log.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3)))))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
39.6b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
9.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
9.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
22.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (fma.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))) (fma.f64 1/2 (*.f64 (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2) (*.f64 (*.f64 y.im y.im) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))) (*.f64 1/6 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (pow.f64 y.im 3) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 3)))))))
9.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (fma.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))
22.9b
(*.f64 (/.f64 1 (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
Compiler

Compiled 23017 to 8789 computations (61.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
2.0b
(*.f64 y.re (atan2.f64 x.im x.re))
2.4b
(*.f64 (atan2.f64 x.im x.re) y.im)
32.9b
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series961.0ms (3.7%)

Counts
1 → 48
Calls

1 calls:

960.0ms
(log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
expm1-log1p-u_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
1 → 11
Calls

1 calls:

0.0ms
(log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

simplify124.0ms (0.5%)

Algorithm
egg-herbie
Rules
868×associate-/l*_binary64
637×associate-/r*_binary64
345×fma-def_binary64
249×*-commutative_binary64
95×+-commutative_binary64
Counts
59 → 77
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05608118
121637529
247447529

prune476.0ms (1.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2033206
Fresh31215
Picked101
Done000
Total20715222
Error
3.4b
Counts
222 → 15
Alt Table
StatusErrorProgram
9.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))))) (cbrt.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))))
39.6b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
21.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.im x.re)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) 3))))
9.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
9.2b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))) 3)) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
33.3b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (sqrt.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sqrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))
15.1b
(*.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
22.2b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))
50.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (fma.f64 1/2 (/.f64 (*.f64 (*.f64 x.re x.re) (*.f64 y.im (cos.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))) (*.f64 x.im x.im)) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im)))))))
14.1b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3)))) (exp.f64 (log.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 y.im (atan2.f64 x.im x.re)) 3)))))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
43.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (sqrt.f64 y.re) (*.f64 (sqrt.f64 y.re) (atan2.f64 x.im x.re))))))
17.3b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (+.f64 (log1p.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))) (/.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (+.f64 1 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))))))
22.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (fma.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))) (fma.f64 1/2 (*.f64 (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2) (*.f64 (*.f64 y.im y.im) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))))) (*.f64 1/6 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (pow.f64 y.im 3) (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 3)))))))
9.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (fma.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))
22.9b
(*.f64 (/.f64 1 (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
Compiler

Compiled 18709 to 7470 computations (60.1% saved)

regimes666.0ms (2.6%)

Accuracy

Total 3.7b remaining (54.5%)

Threshold costs 0b (0%)

Counts
83 → 2
Compiler

Compiled 15317 to 8370 computations (45.4% saved)

bsearch42.0ms (0.2%)

Steps
ItersRangePoint
1
-1.1034745856408464e+81
-9.672901891510776e+70
-1.054865446815132e+76
Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029110
134110
234110

end342.0ms (1.3%)

Compiler

Compiled 775 to 379 computations (51.1% saved)

Profiling

Loading profile data...