Details

Time bar (total: 5.0s)

analyze430.0ms (8.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%50%50%0
0%50%50%1
25%25%50%2
25%25%50%3
31.2%18.7%50%4
31.2%18.7%50%5
34.3%15.6%50%6
34.3%15.6%50%7
35.9%14%50%8
35.9%14%50%9
36.7%13.3%50%10
36.7%13.3%50%11
37.1%12.9%50%12
37.1%12.9%50%13
37.3%12.7%50%14
Compiler

Compiled 20 to 14 computations (30% saved)

sample1.9s (37.2%)

Results
861.0ms6300×body128valid
346.0ms527×body4096valid
326.0ms653×body2048valid
179.0ms426×body1024valid
71.0ms227×body512valid
25.0ms123×body256valid
Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify28.0ms (0.6%)

Algorithm
egg-herbie
Rules
203×fma-def_binary64
142×fma-neg_binary64
51×distribute-rgt-in_binary64
42×cancel-sign-sub-inv_binary64
28×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01315
12015
23315
35015
46915
59815
615115
721115
826315
930515
1034315
1137915
1239615
1341515
1442815
1546515
1647715
1748615
1844915

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
12.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
12.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 2 (-.f64 (hypot.f64 re im) re))
0.1b
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
0.7b
(-.f64 (hypot.f64 re im) re)

series80.0ms (1.6%)

Counts
3 → 56
Calls

3 calls:

47.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
18.0ms
(*.f64 2 (-.f64 (hypot.f64 re im) re))
14.0ms
(-.f64 (hypot.f64 re im) re)

rewrite26.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64
31×*-un-lft-identity_binary64
27×prod-diff_binary64
27×add-cube-cbrt_binary64
13×distribute-lft-in_binary64
Counts
3 → 95
Calls

3 calls:

7.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
5.0ms
(*.f64 2 (-.f64 (hypot.f64 re im) re))
3.0ms
(-.f64 (hypot.f64 re im) re)

simplify142.0ms (2.8%)

Algorithm
egg-herbie
Rules
852×times-frac_binary64
478×cancel-sign-sub-inv_binary64
362×fma-neg_binary64
184×sub-neg_binary64
180×fma-def_binary64
Counts
151 → 183
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03012977
17262646
224322548
348222548
448562548
550002548
648922548

prune131.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1776183
Fresh000
Picked011
Done000
Total1777184
Error
0.2b
Counts
184 → 7
Alt Table
StatusErrorProgram
53.4b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) -1/16)))
12.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
14.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
13.2b
(*.f64 1/2 (sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re)))))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
56.7b
(*.f64 1/2 (sqrt.f64 (-.f64 (+.f64 (*.f64 1/8 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (/.f64 (pow.f64 im 2) re)) (*.f64 1/4 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
56.5b
(*.f64 1/2 (sqrt.f64 (fma.f64 im (/.f64 im re) (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/4))))
Compiler

Compiled 4415 to 2602 computations (41.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re))))
0.3b
(*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re))
0.3b
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re)))
0.7b
(-.f64 (hypot.f64 re im) re)

series100.0ms (2%)

Counts
3 → 56
Calls

3 calls:

44.0ms
(sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re))))
29.0ms
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re)))
26.0ms
(*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re))

rewrite44.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
65×distribute-lft-in_binary64
65×distribute-rgt-in_binary64
56×add-sqr-sqrt_binary64
54×prod-diff_binary64
52×*-un-lft-identity_binary64
Counts
3 → 147
Calls

3 calls:

13.0ms
(sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re))))
9.0ms
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re)))
8.0ms
(*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re))

simplify140.0ms (2.8%)

Algorithm
egg-herbie
Rules
617×fma-neg_binary64
515×cancel-sign-sub-inv_binary64
338×associate-*r*_binary64
324×associate-*l*_binary64
226×*-commutative_binary64
Counts
203 → 247
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04034466
18874068
232543751
348913751
449463751

prune218.0ms (4.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3102312
Fresh055
Picked011
Done011
Total3109319
Error
0.2b
Counts
319 → 9
Alt Table
StatusErrorProgram
53.4b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) -1/16)))
12.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
14.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
13.2b
(*.f64 1/2 (sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re)))))
56.8b
(*.f64 1/2 (sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 1/2 (/.f64 (*.f64 im im) re) (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8)))))))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
53.4b
(*.f64 1/2 (fma.f64 (*.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) -1/16)))
56.7b
(*.f64 1/2 (sqrt.f64 (-.f64 (+.f64 (*.f64 1/8 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (/.f64 (pow.f64 im 2) re)) (*.f64 1/4 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
56.5b
(*.f64 1/2 (sqrt.f64 (fma.f64 im (/.f64 im re) (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/4))))
Compiler

Compiled 9061 to 5715 computations (36.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))
0.0b
(sqrt.f64 (hypot.f64 re im))
0.1b
(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))
14.3b
(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

series185.0ms (3.7%)

Counts
4 → 36
Calls

4 calls:

86.0ms
(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))
42.0ms
(*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))
38.0ms
(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))
19.0ms
(sqrt.f64 (hypot.f64 re im))

rewrite8.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt_binary64
10×pow1_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
4 → 60
Calls

4 calls:

3.0ms
(*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))
2.0ms
(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))
1.0ms
(sqrt.f64 (hypot.f64 re im))
0.0ms
(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

simplify80.0ms (1.6%)

Algorithm
egg-herbie
Rules
722×fma-def_binary64
373×associate-/l*_binary64
362×times-frac_binary64
356×cancel-sign-sub-inv_binary64
356×fma-neg_binary64
Counts
96 → 153
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02491957
16381771
219181711
348651706
450041706

prune120.0ms (2.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1812183
Fresh156
Picked011
Done022
Total18210192
Error
0.2b
Counts
192 → 10
Alt Table
StatusErrorProgram
53.4b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) -1/16)))
12.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
14.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
13.2b
(*.f64 1/2 (sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re)))))
56.8b
(*.f64 1/2 (sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 1/2 (/.f64 (*.f64 im im) re) (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8)))))))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
53.4b
(*.f64 1/2 (fma.f64 (*.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) -1/16)))
18.2b
(*.f64 1/2 (sqrt.f64 (exp.f64 (+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))))
55.7b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
56.5b
(*.f64 1/2 (sqrt.f64 (fma.f64 im (/.f64 im re) (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/4))))
Compiler

Compiled 4898 to 2853 computations (41.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (exp.f64 (+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))))
0.2b
(+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))
4.9b
(exp.f64 (+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
14.3b
(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

series281.0ms (5.6%)

Counts
3 → 30
Calls

3 calls:

137.0ms
(sqrt.f64 (exp.f64 (+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))))
75.0ms
(exp.f64 (+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
70.0ms
(+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))

rewrite18.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity_binary64
17×pow1_binary64
14×exp-prod_binary64
13×log-pow_binary64
12×distribute-lft-out_binary64
Counts
3 → 69
Calls

3 calls:

7.0ms
(sqrt.f64 (exp.f64 (+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))))
4.0ms
(exp.f64 (+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
3.0ms
(+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))

simplify101.0ms (2%)

Algorithm
egg-herbie
Rules
645×fma-def_binary64
326×cancel-sign-sub-inv_binary64
286×fma-neg_binary64
172×distribute-rgt-in_binary64
169×sub-neg_binary64
Counts
99 → 153
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02663358
16512236
225432098
345642090
450192090

prune147.0ms (2.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1843187
Fresh246
Picked101
Done033
Total18710197
Error
0.2b
Counts
197 → 10
Alt Table
StatusErrorProgram
53.4b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) -1/16)))
12.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
19.5b
(*.f64 1/2 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 (+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))) (cbrt.f64 (+.f64 (log.f64 2) (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))))) (/.f64 (cbrt.f64 (log.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) 2)))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
14.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
13.2b
(*.f64 1/2 (sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (hypot.f64 re im) re)))))
56.8b
(*.f64 1/2 (sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 1/2 (/.f64 (*.f64 im im) re) (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8)))))))
53.4b
(*.f64 1/2 (fma.f64 (*.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) -1/16)))
53.9b
(*.f64 1/2 (sqrt.f64 (exp.f64 (fma.f64 (log.f64 im) 2 (+.f64 (log.f64 2) (log.f64 (/.f64 1/2 re)))))))
55.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 im im) (/.f64 1/2 re)))))
Compiler

Compiled 5669 to 3348 computations (40.9% saved)

regimes630.0ms (12.6%)

Accuracy

Total 5.9b remaining (96.1%)

Threshold costs 0b (0%)

Counts
59 → 2
Compiler

Compiled 9109 to 6926 computations (24% saved)

bsearch2.0ms (0%)

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify3.0ms (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
02857
13957
24457
34657
44757
54657

end182.0ms (3.6%)

Compiler

Compiled 325 to 247 computations (24% saved)

Profiling

Loading profile data...