Details

Time bar (total: 6.9s)

analyze737.0ms (10.7%)

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)

sample1.1s (16.2%)

Results
1.0s8256×body128valid
61.0ms463×body128invalid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
fma-def_binary64
+-commutative_binary64
*-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01218
11818
22218
32218

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
28.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
28.0b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
Compiler

Compiled 66 to 32 computations (51.5% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
1.0b
(fma.f64 x.re y.re (*.f64 x.im y.im))
27.4b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series90.0ms (1.3%)

Counts
2 → 96
Calls

2 calls:

77.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
13.0ms
(fma.f64 x.re y.re (*.f64 x.im y.im))

rewrite4.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
2 → 39
Calls

2 calls:

2.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
0.0ms
(fma.f64 x.re y.re (*.f64 x.im y.im))

simplify73.0ms (1.1%)

Algorithm
egg-herbie
Rules
687×fma-def_binary64
413×associate-/l/_binary64
364×fma-neg_binary64
246×distribute-rgt-neg-in_binary64
245×distribute-lft-neg-in_binary64
Counts
135 → 95
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0972544
12022411
26062327
321922279
451012279

prune79.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New831295
Fresh000
Picked011
Done000
Total831396
Error
2.4b
Counts
96 → 13
Alt Table
StatusErrorProgram
39.1b
(/.f64 x.re y.re)
40.4b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)) (/.f64 (sqrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)))
32.7b
(+.f64 (/.f64 x.im y.im) (*.f64 (/.f64 y.re (*.f64 y.im y.im)) (-.f64 x.re (/.f64 (*.f64 x.im y.re) y.im))))
45.7b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im))) (*.f64 (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))) (/.f64 (sqrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im))) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)))))
35.1b
(/.f64 x.im y.im)
20.0b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)))
25.5b
(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re))) (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
27.9b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (sqrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)))) (sqrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
35.8b
(-.f64 (fma.f64 y.re (/.f64 x.re (*.f64 y.im y.im)) (/.f64 x.im y.im)) (*.f64 (/.f64 (*.f64 y.re y.re) (pow.f64 y.im 3)) (+.f64 x.im (/.f64 x.re (/.f64 y.im y.re)))))
28.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im))) (cbrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)))) (*.f64 (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))) (/.f64 (cbrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im))) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)))))
28.0b
(*.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
28.0b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
19.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
Compiler

Compiled 2621 to 621 computations (76.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
0.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
0.3b
(fma.f64 y.im x.im (*.f64 y.re x.re))
18.3b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series223.0ms (3.2%)

Counts
4 → 168
Calls

4 calls:

103.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
92.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
17.0ms
(/.f64 1 (hypot.f64 y.im y.re))
10.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))

rewrite24.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt_binary64
43×times-frac_binary64
36×*-un-lft-identity_binary64
34×add-cube-cbrt_binary64
32×add-exp-log_binary64
Counts
4 → 130
Calls

4 calls:

8.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
5.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
2.0ms
(/.f64 1 (hypot.f64 y.im y.re))
0.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))

simplify234.0ms (3.4%)

Algorithm
egg-herbie
Rules
872×times-frac_binary64
508×fma-neg_binary64
381×fma-def_binary64
335×cancel-sign-sub-inv_binary64
274×distribute-rgt-in_binary64
Counts
298 → 285
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02356511
16295720
221355547
348795539
451835539

prune207.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2778285
Fresh8311
Picked101
Done101
Total28711298
Error
0.1b
Counts
298 → 11
Alt Table
StatusErrorProgram
44.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
19.4b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
25.5b
(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re))) (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
47.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
40.4b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)) (/.f64 (sqrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)))
41.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
32.7b
(+.f64 (/.f64 x.im y.im) (*.f64 (/.f64 y.re (*.f64 y.im y.im)) (-.f64 x.re (/.f64 (*.f64 x.im y.re) y.im))))
29.0b
(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (*.f64 y.re y.re))) y.re (/.f64 (*.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
29.5b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
34.9b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
45.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
Compiler

Compiled 7462 to 2255 computations (69.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
0.1b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
1.0b
(fma.f64 x.re y.re (*.f64 y.im x.im))
18.3b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

series225.0ms (3.3%)

Counts
4 → 168
Calls

4 calls:

109.0ms
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
97.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))
11.0ms
(hypot.f64 y.im y.re)
8.0ms
(fma.f64 x.re y.re (*.f64 y.im x.im))

rewrite19.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
84×times-frac_binary64
54×*-un-lft-identity_binary64
54×add-sqr-sqrt_binary64
54×add-cube-cbrt_binary64
16×associate-/l*_binary64
Counts
4 → 121
Calls

4 calls:

4.0ms
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
2.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))
0.0ms
(fma.f64 x.re y.re (*.f64 y.im x.im))
0.0ms
(hypot.f64 y.im y.re)

simplify160.0ms (2.3%)

Algorithm
egg-herbie
Rules
834×times-frac_binary64
632×fma-neg_binary64
365×associate-/l/_binary64
347×fma-def_binary64
305×cancel-sign-sub-inv_binary64
Counts
289 → 293
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02646978
16666470
218596153
346416153
450626153

prune204.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3314335
Fresh5510
Picked101
Done000
Total3379346
Error
0.1b
Counts
346 → 9
Alt Table
StatusErrorProgram
25.5b
(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re))) (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
47.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
43.8b
(/.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im) (hypot.f64 y.im y.re))
34.9b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
41.4b
(/.f64 (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)) (hypot.f64 y.im y.re))
19.5b
(/.f64 1 (*.f64 (hypot.f64 y.im y.re) (/.f64 (hypot.f64 y.im y.re) (fma.f64 y.im x.im (*.f64 y.re x.re)))))
19.5b
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))))
29.0b
(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (*.f64 y.re y.re))) y.re (/.f64 (*.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
45.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
Compiler

Compiled 8581 to 1979 computations (76.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (hypot.f64 y.im y.re) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)))
0.2b
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))))
1.0b
(fma.f64 x.re y.re (*.f64 y.im x.im))
18.3b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

series184.0ms (2.7%)

Counts
2 → 96
Calls

2 calls:

114.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))))
70.0ms
(/.f64 (hypot.f64 y.im y.re) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)))

rewrite94.0ms (1.4%)

Algorithm
rewrite-expression-head
Rules
471×times-frac_binary64
229×*-un-lft-identity_binary64
229×add-sqr-sqrt_binary64
229×add-cube-cbrt_binary64
57×associate-/r*_binary64
Counts
2 → 278
Calls

2 calls:

29.0ms
(/.f64 (hypot.f64 y.im y.re) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)))
9.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))))

simplify318.0ms (4.6%)

Algorithm
egg-herbie
Rules
684×fma-def_binary64
413×cancel-sign-sub-inv_binary64
313×associate-/r/_binary64
264×times-frac_binary64
255×associate-/l*_binary64
Counts
374 → 439
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
035416097
186614499
2327513677
3495113677
4514913677

prune336.0ms (4.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New5481549
Fresh178
Picked011
Done000
Total5499558
Error
0.1b
Counts
558 → 9
Alt Table
StatusErrorProgram
25.5b
(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re))) (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
47.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
43.8b
(/.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im) (hypot.f64 y.im y.re))
34.9b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
41.4b
(/.f64 (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)) (hypot.f64 y.im y.re))
43.3b
(/.f64 1 (-.f64 (fma.f64 (/.f64 y.im y.re) (/.f64 y.im x.re) (fma.f64 (/.f64 (*.f64 y.im y.im) (pow.f64 x.re 3)) (/.f64 (*.f64 x.im x.im) y.re) (/.f64 y.re x.re))) (/.f64 (*.f64 y.im x.im) (*.f64 x.re x.re))))
19.5b
(/.f64 1 (*.f64 (hypot.f64 y.im y.re) (/.f64 (hypot.f64 y.im y.re) (fma.f64 y.im x.im (*.f64 y.re x.re)))))
19.5b
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))))
45.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
Compiler

Compiled 17545 to 3945 computations (77.5% saved)

regimes2.3s (33.1%)

Accuracy

Total 11.1b remaining (98.6%)

Threshold costs 0b (0%)

Counts
148 → 7
Compiler

Compiled 13848 to 7839 computations (43.4% saved)

bsearch120.0ms (1.7%)

Steps
ItersRangePoint
10
6.736288909680009e+143
3.7245003593291906e+156
1.8003344749034084e+144
5
19035638361.52358
56947318017.81081
19451542890.138916
8
2.3704126260502583e-26
1.0266492853082982e-23
1.0320858618106521e-25
9
2.5646288356942223e-136
6.064998058725015e-127
4.961282432869017e-134
8
-6.244292495569735e-91
-3.021929989140534e-94
-8.982511531385342e-94
7
-3.42147644238279e+138
-1.5874657500695323e+137
-9.10122331774869e+137
Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

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
046162
154162
258162
361162
462162
561162

end131.0ms (1.9%)

Compiler

Compiled 411 to 183 computations (55.5% saved)

Profiling

Loading profile data...