Details

Time bar (total: 7.9s)

analyze771.0ms (9.7%)

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)

sample1.2s (15%)

Results
1.1s8256×body128valid
64.0ms490×body128invalid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify10.0ms (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
0.0b
(fma.f64 y.re y.re (*.f64 y.im y.im))
27.5b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series105.0ms (1.3%)

Counts
2 → 72
Calls

2 calls:

95.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
10.0ms
(fma.f64 y.re y.re (*.f64 y.im y.im))

rewrite5.0ms (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 y.re y.re (*.f64 y.im y.im))

simplify69.0ms (0.9%)

Algorithm
egg-herbie
Rules
679×fma-def_binary64
413×associate-/l/_binary64
366×fma-neg_binary64
246×distribute-rgt-neg-in_binary64
245×distribute-lft-neg-in_binary64
Counts
111 → 96
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0982376
12002231
25912147
321692099
450912099

prune71.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New88896
Fresh000
Picked101
Done000
Total89897
Error
1.0b
Counts
97 → 8
Alt Table
StatusErrorProgram
28.0b
(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)) (sqrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
36.8b
(/.f64 x.im y.im)
27.3b
(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))))
28.1b
(/.f64 1 (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) (fma.f64 x.re y.re (*.f64 x.im y.im))))
17.2b
(*.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)))
36.7b
(/.f64 x.re y.re)
36.1b
(fma.f64 y.re (/.f64 x.re (*.f64 y.im y.im)) (/.f64 x.im y.im))
41.5b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))) (sqrt.f64 (/.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 2278 to 506 computations (77.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
0.2b
(fma.f64 y.im x.im (*.f64 y.re x.re))
0.3b
(*.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)))
16.1b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series247.0ms (3.1%)

Counts
4 → 168
Calls

4 calls:

119.0ms
(*.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)))
104.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
14.0ms
(hypot.f64 y.im y.re)
9.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))

rewrite22.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt_binary64
34×times-frac_binary64
28×*-un-lft-identity_binary64
28×add-exp-log_binary64
26×add-cube-cbrt_binary64
Counts
4 → 107
Calls

4 calls:

9.0ms
(*.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)))
2.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
0.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))
0.0ms
(hypot.f64 y.im y.re)

simplify152.0ms (1.9%)

Algorithm
egg-herbie
Rules
868×times-frac_binary64
516×fma-neg_binary64
377×fma-def_binary64
306×cancel-sign-sub-inv_binary64
282×distribute-rgt-in_binary64
Counts
275 → 263
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02295947
16195325
220945152
348405152
451435152

prune209.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2996305
Fresh527
Picked011
Done000
Total3049313
Error
0.2b
Counts
313 → 9
Alt Table
StatusErrorProgram
33.2b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
17.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))))
46.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
28.1b
(/.f64 1 (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) (fma.f64 x.re y.re (*.f64 x.im y.im))))
17.2b
(*.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)))
45.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
17.9b
(*.f64 (/.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im))) (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (cbrt.f64 (hypot.f64 y.im y.re))))
31.7b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
28.0b
(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)) (sqrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
Compiler

Compiled 7987 to 2483 computations (68.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))))
0.5b
(*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))))
0.6b
(cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
16.1b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series415.0ms (5.2%)

Counts
3 → 144
Calls

3 calls:

157.0ms
(*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))))
140.0ms
(cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
118.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))))

rewrite50.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
92×cbrt-prod_binary64
78×add-sqr-sqrt_binary64
61×times-frac_binary64
50×*-un-lft-identity_binary64
50×add-cube-cbrt_binary64
Counts
3 → 160
Calls

3 calls:

12.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))))
11.0ms
(*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))))
2.0ms
(cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))

simplify224.0ms (2.8%)

Algorithm
egg-herbie
Rules
559×times-frac_binary64
418×associate-/r*_binary64
373×associate-/l*_binary64
355×fma-def_binary64
248×*-commutative_binary64
Counts
304 → 433
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
067715486
1211314445
2537514445

prune743.0ms (9.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New9411942
Fresh167
Picked011
Done011
Total9429951
Error
0.2b
Counts
951 → 9
Alt Table
StatusErrorProgram
39.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 x.re (*.f64 y.re (sqrt.f64 (/.f64 1 (fma.f64 y.im y.im (*.f64 y.re y.re)))))))
17.2b
(*.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)))
33.2b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
17.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))))
46.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
45.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
17.9b
(*.f64 (/.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im))) (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (cbrt.f64 (hypot.f64 y.im y.re))))
31.7b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
28.0b
(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)) (sqrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
Compiler

Compiled 58500 to 17572 computations (70% saved)

localize102.0ms (1.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(cbrt.f64 (hypot.f64 y.im y.re))
5.5b
(/.f64 (*.f64 (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im))) (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re))))
16.6b
(cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))
16.6b
(cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))

series413.0ms (5.2%)

Counts
4 → 168
Calls

4 calls:

166.0ms
(/.f64 (*.f64 (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im))) (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re))))
130.0ms
(cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))
76.0ms
(cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))
41.0ms
(cbrt.f64 (hypot.f64 y.im y.re))

rewrite12.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
16×add-exp-log_binary64
cbrt-prod_binary64
add-cbrt-cube_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
4 → 62
Calls

4 calls:

7.0ms
(/.f64 (*.f64 (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im))) (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re))))
1.0ms
(cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))
1.0ms
(cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))
1.0ms
(cbrt.f64 (hypot.f64 y.im y.re))

simplify181.0ms (2.3%)

Algorithm
egg-herbie
Rules
799×times-frac_binary64
515×associate-/l*_binary64
331×fma-def_binary64
209×*-commutative_binary64
205×cancel-sign-sub-inv_binary64
Counts
230 → 251
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
063312742
1210511863
2507011863

prune380.0ms (4.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New4330433
Fresh066
Picked011
Done022
Total4339442
Error
0.2b
Counts
442 → 9
Alt Table
StatusErrorProgram
39.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 x.re (*.f64 y.re (sqrt.f64 (/.f64 1 (fma.f64 y.im y.im (*.f64 y.re y.re)))))))
17.2b
(*.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)))
33.2b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
17.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))) (cbrt.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))))
46.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
45.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
17.9b
(*.f64 (/.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im))) (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (cbrt.f64 (hypot.f64 y.im y.re))))
31.7b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
28.0b
(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)) (sqrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
Compiler

Compiled 29260 to 9828 computations (66.4% saved)

regimes2.3s (28.4%)

Accuracy

Total 9.4b remaining (98.3%)

Threshold costs 0b (0%)

Counts
137 → 5
Compiler

Compiled 17293 to 8844 computations (48.9% saved)

bsearch134.0ms (1.7%)

Steps
ItersRangePoint
8
4.600059175016691e+122
3.0699538592237883e+125
1.65314188416292e+124
9
1.9939569543929294e-215
1.3129904177370859e-207
8.257594576029714e-210
10
-2.441238558004582e-136
-1.8691431763602715e-146
-3.2778058876870277e-146
10
-7.246277711792929e+140
-1.0831246780352106e+130
-2.9753592065970103e+133
Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
035109
139109
238109

end140.0ms (1.8%)

Compiler

Compiled 372 to 171 computations (54% saved)

Profiling

Loading profile data...