Details

Time bar (total: 5.1s)

analyze468.0ms (9.2%)

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 (38.4%)

Results
852.0ms6176×body128valid
379.0ms725×body2048valid
358.0ms557×body4096valid
181.0ms424×body1024valid
93.0ms250×body512valid
27.0ms124×body256valid
Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify29.0ms (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
12.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
12.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 51 to 37 computations (27.5% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
0.8b
(-.f64 (hypot.f64 re im) re)

series73.0ms (1.4%)

Counts
2 → 32
Calls

2 calls:

60.0ms
(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:

6.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
3.0ms
(-.f64 (hypot.f64 re im) re)

simplify93.0ms (1.8%)

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

prune83.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New89897
Fresh000
Picked101
Done000
Total90898
Error
0.2b
Counts
98 → 8
Alt Table
StatusErrorProgram
12.7b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
14.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
55.1b
(*.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)))))
48.8b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
55.1b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
47.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (/.f64 (-.f64 (*.f64 (hypot.f64 re im) (hypot.f64 re im)) (*.f64 re re)) (+.f64 (hypot.f64 re im) re)))))
12.6b
(*.f64 1/2 (*.f64 1 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))
14.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
Compiler

Compiled 2833 to 1876 computations (33.8% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
0.8b
(-.f64 (hypot.f64 re im) re)

prune84.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New97097
Fresh077
Picked011
Done000
Total978105
Error
0.2b
Counts
105 → 8
Alt Table
StatusErrorProgram
12.7b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
14.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
55.1b
(*.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)))))
48.8b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
55.1b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
47.0b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (/.f64 (-.f64 (*.f64 (hypot.f64 re im) (hypot.f64 re im)) (*.f64 re re)) (+.f64 (hypot.f64 re im) re)))))
12.6b
(*.f64 1/2 (*.f64 1 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))
14.9b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
Compiler

Compiled 3013 to 2059 computations (31.7% saved)

localize9.0ms (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)))
0.8b
(-.f64 (hypot.f64 re im) re)

series78.0ms (1.5%)

Counts
2 → 16
Calls

2 calls:

47.0ms
(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
31.0ms
(sqrt.f64 (-.f64 (hypot.f64 re im) re))

rewrite15.0ms (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)))
4.0ms
(sqrt.f64 (-.f64 (hypot.f64 re im) re))

simplify121.0ms (2.4%)

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

prune122.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1455150
Fresh336
Picked101
Done011
Total1499158
Error
0.1b
Counts
158 → 9
Alt Table
StatusErrorProgram
47.2b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (-.f64 (*.f64 (hypot.f64 re im) (hypot.f64 re im)) (*.f64 re re)) (+.f64 re (hypot.f64 re im))))))
12.7b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))))
48.8b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
55.1b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 1/2 (/.f64 (*.f64 im im) re)))))
55.1b
(*.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))))))))))
48.8b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))
55.1b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
12.6b
(*.f64 1/2 (*.f64 1 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))
14.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
Compiler

Compiled 4177 to 2726 computations (34.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (-.f64 (hypot.f64 re im) re))
0.2b
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
0.8b
(-.f64 (hypot.f64 re im) re)

series96.0ms (1.9%)

Counts
2 → 16
Calls

2 calls:

49.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
46.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))

rewrite29.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64
37×sqrt-prod_binary64
18×associate-*l*_binary64
16×rem-sqrt-square_binary64
14×pow1_binary64
Counts
2 → 78
Calls

2 calls:

13.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
10.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))

simplify74.0ms (1.5%)

Algorithm
egg-herbie
Rules
779×fma-def_binary64
494×associate-/l*_binary64
378×times-frac_binary64
273×cancel-sign-sub-inv_binary64
204×associate-*l*_binary64
Counts
94 → 117
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02312547
15982428
220352366
353212366

prune174.0ms (3.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2153218
Fresh257
Picked011
Done011
Total21710227
Error
0.1b
Counts
227 → 10
Alt Table
StatusErrorProgram
47.2b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (-.f64 (*.f64 (hypot.f64 re im) (hypot.f64 re im)) (*.f64 re re)) (+.f64 re (hypot.f64 re im))))))
12.7b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))))
48.8b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 (sqrt.f64 2) re)))))
55.1b
(*.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))))))))))
48.8b
(*.f64 1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))
48.7b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 1/2))))))
55.1b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
55.1b
(*.f64 1/2 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.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)))))))))))
12.6b
(*.f64 1/2 (*.f64 1 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))
14.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
Compiler

Compiled 6597 to 4648 computations (29.5% saved)

regimes1.1s (21.5%)

Accuracy

Total 8.2b remaining (98.8%)

Threshold costs 0b (0%)

Counts
109 → 4
Compiler

Compiled 16643 to 13303 computations (20.1% saved)

bsearch163.0ms (3.2%)

Steps
ItersRangePoint
9
1.273531924543199e+63
6.439999587174156e+69
6.98244041967603e+68
7
9.049355701429076e+20
5.382823496901155e+22
1.8652271911593446e+22
8
1.0769721982353746e-38
2.884234115856925e-34
2.1698433257847657e-35
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
046137
171135
283135
391135
494135
593135

end272.0ms (5.4%)

Compiler

Compiled 527 to 433 computations (17.8% saved)

Profiling

Loading profile data...