Details

Time bar (total: 4.9s)

analyze434.0ms (8.9%)

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)

sample81.0ms (1.7%)

Algorithm
intervals
Results
13.0ms194×body128valid
6.0ms22×body2048valid
6.0ms17×body4096valid
4.0ms256×pre128true
3.0ms12×body1024valid
1.0msbody512valid
0.0msbody256valid
Compiler

Compiled 39 to 28 computations (28.2% 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

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
13.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
13.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 51 to 37 computations (27.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
1.1b
(-.f64 (hypot.f64 re im) re)

series58.0ms (1.2%)

Counts
2 → 32
Calls

2 calls:

45.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
13.0ms
(-.f64 (hypot.f64 re im) re)

rewrite12.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
prod-diff_binary64
pow1_binary64
Counts
2 → 45
Calls

2 calls:

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

simplify100.0ms (2.1%)

Algorithm
egg-herbie
Rules
849×fma-def_binary64
693×times-frac_binary64
644×fma-neg_binary64
347×cancel-sign-sub-inv_binary64
198×neg-mul-1_binary64
Counts
77 → 97
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02151773
15371528
218531480
343611478
449661478
549011478

prune80.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New91697
Fresh000
Picked011
Done000
Total91798
Error
0.2b
Counts
98 → 7
Alt Table
StatusErrorProgram
14.1b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
56.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
54.0b
(*.f64 1/2 (-.f64 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (fma.f64 1/32 (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 7)) (sqrt.f64 1/2))) 1/256))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (fma.f64 1/8192 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 7)) (pow.f64 (sqrt.f64 1/2) 5)) (*.f64 5/256 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 7)) (sqrt.f64 1/2)))) (fma.f64 1/16 (*.f64 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (*.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9)))) 1/256)))))
46.8b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
14.1b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))))
13.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
17.3b
(*.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))))
Compiler

Compiled 2761 to 1843 computations (33.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
0.1b
(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))
1.1b
(-.f64 (hypot.f64 re im) re)

series102.0ms (2.1%)

Counts
2 → 32
Calls

2 calls:

52.0ms
(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
49.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))

rewrite32.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
80×sqrt-pow1_binary64
63×pow1_binary64
31×sqrt-prod_binary64
28×sqrt-div_binary64
28×add-sqr-sqrt_binary64
Counts
2 → 104
Calls

2 calls:

15.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))
4.0ms
(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))

simplify126.0ms (2.6%)

Algorithm
egg-herbie
Rules
787×times-frac_binary64
385×cancel-sign-sub-inv_binary64
284×fma-neg_binary64
236×associate-*r*_binary64
232×associate-*l*_binary64
Counts
136 → 159
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03154120
18193789
225593619
349753619
449643619

prune351.0ms (7.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4093412
Fresh235
Picked101
Done011
Total4127419
Error
0.2b
Counts
419 → 7
Alt Table
StatusErrorProgram
14.1b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
56.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
15.5b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (*.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))) (fma.f64 (neg.f64 (cbrt.f64 re)) (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (*.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))))))))
15.2b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))))
13.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
52.5b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 2) im) (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)))
46.8b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
Compiler

Compiled 15581 to 9927 computations (36.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (-.f64 (hypot.f64 re im) re))
0.4b
(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
1.1b
(-.f64 (hypot.f64 re im) re)

series74.0ms (1.5%)

Counts
2 → 16
Calls

2 calls:

45.0ms
(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
29.0ms
(sqrt.f64 (-.f64 (hypot.f64 re im) re))

rewrite14.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64
17×sqrt-prod_binary64
11×*-un-lft-identity_binary64
associate-*r*_binary64
add-cube-cbrt_binary64
Counts
2 → 56
Calls

2 calls:

8.0ms
(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
3.0ms
(sqrt.f64 (-.f64 (hypot.f64 re im) re))

simplify79.0ms (1.6%)

Algorithm
egg-herbie
Rules
778×fma-def_binary64
344×associate-/l*_binary64
291×times-frac_binary64
285×fma-neg_binary64
275×associate-*l/_binary64
Counts
72 → 85
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02021877
15341832
217571756
349351754
450051754

prune121.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1473150
Fresh145
Picked011
Done011
Total1489157
Error
0.2b
Counts
157 → 9
Alt Table
StatusErrorProgram
46.8b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
46.8b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))
14.1b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
56.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
15.5b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (*.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))) (fma.f64 (neg.f64 (cbrt.f64 re)) (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (*.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))))))))
15.2b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))))
13.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
54.0b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (-.f64 (fma.f64 1/32 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (fma.f64 im (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))) 1/256))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (pow.f64 im 3) (sqrt.f64 1/2))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (*.f64 1/256 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (+.f64 (*.f64 1/8192 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5))) (*.f64 5/256 (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))))))))))
56.0b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
Compiler

Compiled 4224 to 2738 computations (35.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))))
1.1b
(-.f64 (hypot.f64 re im) re)
15.8b
(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

series527.0ms (10.8%)

Counts
3 → 30
Calls

3 calls:

355.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))))
132.0ms
(sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
39.0ms
(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

rewrite19.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
26×sqrt-pow1_binary64
23×pow1_binary64
19×sqrt-prod_binary64
19×add-sqr-sqrt_binary64
13×pow-prod-down_binary64
Counts
3 → 71
Calls

3 calls:

11.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))))
2.0ms
(sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
0.0ms
(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

simplify75.0ms (1.5%)

Algorithm
egg-herbie
Rules
521×fma-def_binary64
506×associate-/l*_binary64
446×associate-/r*_binary64
282×cancel-sign-sub-inv_binary64
163×associate-*r*_binary64
Counts
101 → 159
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02692686
16322483
219212255
351322255

prune173.0ms (3.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2213224
Fresh156
Picked101
Done022
Total22310233
Error
0.1b
Counts
233 → 10
Alt Table
StatusErrorProgram
46.8b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
46.8b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))
14.1b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
56.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
15.9b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))))))
14.9b
(*.f64 1/2 (sqrt.f64 (*.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))) (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))))
54.0b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (-.f64 (fma.f64 1/32 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (fma.f64 im (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))) 1/256))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (pow.f64 im 3) (sqrt.f64 1/2))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (*.f64 1/256 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (+.f64 (*.f64 1/8192 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5))) (*.f64 5/256 (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))))))))))
56.0b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
53.6b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (*.f64 im (pow.f64 (/.f64 1/4 (*.f64 re re)) 1/4))))
13.8b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 8189 to 4379 computations (46.5% saved)

regimes804.0ms (16.5%)

Accuracy

Total 6.3b remaining (97.7%)

Threshold costs 0b (0%)

Counts
84 → 3
Compiler

Compiled 15888 to 11218 computations (29.4% saved)

bsearch4.0ms (0.1%)

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
11×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039108
154108
259108
361108
462108
561108

end1.0ms (0%)

Compiler

Compiled 72 to 48 computations (33.3% saved)

sample1.5s (31.3%)

Algorithm
intervals
Results
365.0ms6034×body128valid
201.0ms663×body2048valid
190.0ms525×body4096valid
129.0ms8000×pre128true
101.0ms444×body1024valid
38.0ms214×body512valid
14.0ms120×body256valid
Compiler

Compiled 379 to 286 computations (24.5% saved)

Profiling

Loading profile data...