Details

Time bar (total: 5.9s)

analyze754.0ms (12.8%)

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
6.2%93.6%0.2%8
25%74.9%0.2%9
28.1%71.7%0.2%10
29.6%70.2%0.2%11
53%46.8%0.2%12
71.3%28.5%0.2%13
71.7%28.1%0.2%14
Compiler

Compiled 20 to 12 computations (40% saved)

sample26.0ms (0.4%)

Algorithm
intervals
Results
14.0ms256×body128valid
1.0ms17×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify14.0ms (0.2%)

Algorithm
egg-herbie
Rules
fma-def_binary64
+-commutative_binary64
*-commutative_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
12026
22426
32426

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
27.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
27.3b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
Compiler

Compiled 55 to 31 computations (43.6% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
26.8b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

rewrite127.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
27.2b
Rules
20×add-cube-cbrt_binary64
10×add-cbrt-cube_binary64
flip3-+_binary64
add-log-exp_binary64
add-exp-log_binary64
Counts
2 → 89
Calls

2 calls:

23.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
15.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
Compiler

Compiled 2068 to 286 computations (86.2% saved)

series107.0ms (1.8%)

Error
4.6b
Counts
2 → 48
Calls

2 calls:

65.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
32.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
Compiler

Compiled 1446 to 906 computations (37.3% saved)

simplify156.0ms (2.6%)

Algorithm
egg-herbie
Rules
893×times-frac_binary64
488×fma-def_binary64
325×fma-neg_binary64
227×distribute-rgt-in_binary64
202×distribute-lft-in_binary64
Counts
137 → 93
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01232869
13552693
214592601
347972599
449972599
549532599

prune46.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New86793
Fresh000
Picked101
Done000
Total87794
Error
6.5b
Counts
94 → 7
Alt Table
StatusErrorProgram
50.3b
(/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 y.re x.re) 3) (pow.f64 (*.f64 y.im x.im) 3)) (fma.f64 y.im (*.f64 x.im (-.f64 (*.f64 y.im x.im) (*.f64 y.re x.re))) (*.f64 (pow.f64 y.re 2) (*.f64 x.re x.re)))) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
38.6b
(fma.f64 (/.f64 x.re (pow.f64 y.im 2)) y.re (/.f64 x.im y.im))
27.3b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))
31.1b
(fma.f64 (/.f64 y.im (pow.f64 y.re 2)) x.im (/.f64 x.re y.re))
26.4b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
27.8b
(/.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))) (/.f64 (fma.f64 y.im y.im (pow.f64 y.re 2)) (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))))
27.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2))))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))))
Compiler

Compiled 1594 to 604 computations (62.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

1.7b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
17.5b
(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))
20.6b
(/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2)))

rewrite140.0ms (2.4%)

Algorithm
rewrite-expression-head
Error
6.5b
Rules
32×add-cube-cbrt_binary64
17×add-cbrt-cube_binary64
16×add-exp-log_binary64
12×pow1_binary64
12×add-sqr-sqrt_binary64
Counts
3 → 125
Calls

3 calls:

18.0ms
(/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2)))
11.0ms
(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))
9.0ms
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
Compiler

Compiled 3096 to 1571 computations (49.3% saved)

series153.0ms (2.6%)

Error
6.3b
Counts
3 → 45
Calls

3 calls:

81.0ms
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
36.0ms
(/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2)))
19.0ms
(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))
Compiler

Compiled 1915 to 1240 computations (35.2% saved)

simplify153.0ms (2.6%)

Algorithm
egg-herbie
Rules
872×associate-/l*_binary64
590×associate-/r*_binary64
221×associate-/l/_binary64
220×associate-/r/_binary64
207×fma-neg_binary64
Counts
170 → 101
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01453663
13253445
211623421
349633421
451023421

prune79.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1001101
Fresh066
Picked011
Done000
Total1008108
Error
6.5b
Counts
108 → 8
Alt Table
StatusErrorProgram
50.3b
(/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 y.re x.re) 3) (pow.f64 (*.f64 y.im x.im) 3)) (fma.f64 y.im (*.f64 x.im (-.f64 (*.f64 y.im x.im) (*.f64 y.re x.re))) (*.f64 (pow.f64 y.re 2) (*.f64 x.re x.re)))) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
38.6b
(fma.f64 (/.f64 x.re (pow.f64 y.im 2)) y.re (/.f64 x.im y.im))
27.3b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))
31.1b
(fma.f64 (/.f64 y.im (pow.f64 y.re 2)) x.im (/.f64 x.re y.re))
26.4b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
26.0b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 y.re (/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re)))
27.8b
(/.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))) (/.f64 (fma.f64 y.im y.im (pow.f64 y.re 2)) (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))))
27.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2))))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))))
Compiler

Compiled 2334 to 1212 computations (48.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 y.re (/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re)))
10.3b
(/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re)
11.5b
(/.f64 y.re (/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re))
17.5b
(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))

rewrite204.0ms (3.5%)

Algorithm
rewrite-expression-head
Error
6.5b
Rules
53×add-cube-cbrt_binary64
24×add-cbrt-cube_binary64
22×add-exp-log_binary64
16×pow1_binary64
16×add-sqr-sqrt_binary64
Counts
4 → 171
Calls

4 calls:

20.0ms
(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))
12.0ms
(/.f64 y.re (/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re))
12.0ms
(/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re)
9.0ms
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 y.re (/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re)))
Compiler

Compiled 4186 to 2267 computations (45.8% saved)

series279.0ms (4.7%)

Error
6.5b
Counts
4 → 60
Calls

4 calls:

125.0ms
(/.f64 y.re (/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re))
79.0ms
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 y.re (/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re)))
38.0ms
(/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re)
22.0ms
(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))
Compiler

Compiled 2614 to 1675 computations (35.9% saved)

simplify169.0ms (2.9%)

Algorithm
egg-herbie
Rules
436×associate-/l/_binary64
394×associate-/r/_binary64
383×fma-neg_binary64
200×fma-def_binary64
162×cancel-sign-sub-inv_binary64
Counts
231 → 118
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02034642
14014332
216664288
348994288
451984288

prune80.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1171118
Fresh066
Picked011
Done011
Total1179126
Error
6.5b
Counts
126 → 9
Alt Table
StatusErrorProgram
26.0b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (*.f64 y.re (/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2)))))
31.1b
(fma.f64 (/.f64 y.im (pow.f64 y.re 2)) x.im (/.f64 x.re y.re))
50.3b
(/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 y.re x.re) 3) (pow.f64 (*.f64 y.im x.im) 3)) (fma.f64 y.im (*.f64 x.im (-.f64 (*.f64 y.im x.im) (*.f64 y.re x.re))) (*.f64 (pow.f64 y.re 2) (*.f64 x.re x.re)))) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
38.6b
(fma.f64 (/.f64 x.re (pow.f64 y.im 2)) y.re (/.f64 x.im y.im))
27.3b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))
26.4b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
26.0b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 y.re (/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re)))
27.8b
(/.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))) (/.f64 (fma.f64 y.im y.im (pow.f64 y.re 2)) (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))))
27.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2))))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))))
Compiler

Compiled 2538 to 1346 computations (47% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (*.f64 y.re (/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2)))))
10.4b
(/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2)))
11.3b
(*.f64 y.re (/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2))))
17.5b
(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))

rewrite197.0ms (3.3%)

Algorithm
rewrite-expression-head
Error
6.5b
Rules
42×add-cube-cbrt_binary64
23×pow1_binary64
22×add-exp-log_binary64
22×add-cbrt-cube_binary64
20×add-sqr-sqrt_binary64
Counts
4 → 169
Calls

4 calls:

19.0ms
(*.f64 y.re (/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2))))
15.0ms
(/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2)))
12.0ms
(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))
9.0ms
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (*.f64 y.re (/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2)))))
Compiler

Compiled 4023 to 2190 computations (45.6% saved)

series244.0ms (4.1%)

Error
6.5b
Counts
4 → 57
Calls

4 calls:

135.0ms
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (*.f64 y.re (/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2)))))
41.0ms
(*.f64 y.re (/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2))))
35.0ms
(/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2)))
20.0ms
(/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2)))
Compiler

Compiled 2582 to 1663 computations (35.6% saved)

simplify135.0ms (2.3%)

Algorithm
egg-herbie
Rules
775×associate-/r*_binary64
226×associate-/r/_binary64
210×fma-def_binary64
205×associate-/l/_binary64
149×distribute-rgt-neg-in_binary64
Counts
226 → 100
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01884508
13884202
216004172
353054172

prune65.0ms (1.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1000100
Fresh066
Picked011
Done022
Total1009109
Error
6.5b
Counts
109 → 9
Alt Table
StatusErrorProgram
26.0b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (*.f64 y.re (/.f64 x.re (fma.f64 y.im y.im (pow.f64 y.re 2)))))
31.1b
(fma.f64 (/.f64 y.im (pow.f64 y.re 2)) x.im (/.f64 x.re y.re))
50.3b
(/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 y.re x.re) 3) (pow.f64 (*.f64 y.im x.im) 3)) (fma.f64 y.im (*.f64 x.im (-.f64 (*.f64 y.im x.im) (*.f64 y.re x.re))) (*.f64 (pow.f64 y.re 2) (*.f64 x.re x.re)))) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
38.6b
(fma.f64 (/.f64 x.re (pow.f64 y.im 2)) y.re (/.f64 x.im y.im))
27.3b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))
26.4b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
26.0b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) x.im (/.f64 y.re (/.f64 (fma.f64 y.re y.re (pow.f64 y.im 2)) x.re)))
27.8b
(/.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))) (/.f64 (fma.f64 y.im y.im (pow.f64 y.re 2)) (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))))
27.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2))))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.im y.im (pow.f64 y.re 2)))))
Compiler

Compiled 1811 to 962 computations (46.9% saved)

regimes1.4s (23.5%)

Accuracy

Total 9.7b remaining (63.2%)

Threshold costs 0b (0%)

Compiler

Compiled 10587 to 5412 computations (48.9% saved)

bsearch109.0ms (1.9%)

Steps
ItersRangePoint
11
2.570911435004365e-48
1.4860990387338942e-28
4.956468580167358e-31
7
-4.682373346087479e-146
-5.658725066767652e-148
-3.398154527463994e-146
8
-1.0319829341514429e+108
-1.8857803363521585e+103
-5.484152777650426e+107
Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031114
136114
235114

end1.0ms (0%)

Compiler

Compiled 65 to 36 computations (44.6% saved)

sample1.2s (20.7%)

Algorithm
intervals
Results
458.0ms8000×body128valid
32.0ms482×body128invalid
Compiler

Compiled 332 to 185 computations (44.3% saved)

Profiling

Loading profile data...