Details

Time bar (total: 1.4s)

analyze123.0ms (8.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%62.4%12.6%6
25%46.8%28.2%7
31.2%35.9%32.9%8
39%25%36%9
42.9%18.7%38.3%10
47.2%12.9%39.9%11
49.4%9.6%41.1%12
51.6%6.5%41.9%13
52.7%4.8%42.4%14
Compiler

Compiled 16 to 10 computations (37.5% saved)

sample38.0ms (2.7%)

Algorithm
intervals
Symmetry

(sort x y)

Results
9.0ms256×body128valid
0.0msbody128invalid
Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify7.0ms (0.5%)

Algorithm
egg-herbie
Rules
33×fma-def_binary64
*-commutative_binary64
+-commutative_binary64
associate-+r+_binary64
associate-+l+_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01017
11914
24512
36812
47012
57012

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.0b
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
0.0b
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x 2) y)) (*.f64 y y))
Compiler

Compiled 76 to 42 computations (44.7% saved)

localize5.0ms (0.4%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

series6.0ms (0.4%)

Counts
1 → 24
Calls

1 calls:

6.0ms
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

0.0ms
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

simplify40.0ms (2.7%)

Algorithm
egg-herbie
Rules
824×associate-+l+_binary64
820×associate-+r+_binary64
311×distribute-lft-in_binary64
310×distribute-rgt-in_binary64
296×distribute-rgt-out_binary64
Counts
34 → 28
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
025473
148376
292373
3310367
41673367
55874367

prune18.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New26228
Fresh101
Picked101
Done000
Total28230
Error
0.0b
Counts
30 → 2
Alt Table
StatusErrorProgram
0.0b
(+.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))
0.0b
(fma.f64 y (fma.f64 2 x y) (*.f64 x x))
Compiler

Compiled 390 to 184 computations (52.8% saved)

localize9.0ms (0.6%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))
0.0b
(*.f64 x (fma.f64 2 y x))

series12.0ms (0.8%)

Counts
2 → 48
Calls

2 calls:

6.0ms
(+.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))
5.0ms
(*.f64 x (fma.f64 2 y x))

rewrite7.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
fma-udef_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 38
Calls

2 calls:

3.0ms
(+.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))
3.0ms
(*.f64 x (fma.f64 2 y x))

simplify55.0ms (3.8%)

Algorithm
egg-herbie
Rules
677×associate-+r+_binary64
627×associate-+l+_binary64
307×associate-*l*_binary64
255×associate-*r*_binary64
251×fma-def_binary64
Counts
86 → 65
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0701041
1183901
2533887
31981887
45570887

prune42.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New64165
Fresh011
Picked011
Done000
Total64367
Error
0.0b
Counts
67 → 3
Alt Table
StatusErrorProgram
11.6b
(+.f64 (*.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (sqrt.f64 (*.f64 x (fma.f64 2 y x)))) (*.f64 y y))
0.0b
(+.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))
0.0b
(fma.f64 y (fma.f64 2 x y) (*.f64 x x))
Compiler

Compiled 1080 to 524 computations (51.5% saved)

localize8.0ms (0.5%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

series6.0ms (0.4%)

Counts
1 → 24
Calls

1 calls:

6.0ms
(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

0.0ms
(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

simplify39.0ms (2.7%)

Algorithm
egg-herbie
Rules
824×associate-+l+_binary64
820×associate-+r+_binary64
313×distribute-lft-in_binary64
313×distribute-rgt-in_binary64
298×distribute-rgt-out_binary64
Counts
34 → 28
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
025473
149373
298367
3316367
41706367
55952367

prune15.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New28028
Fresh011
Picked011
Done011
Total28331
Error
0.0b
Counts
31 → 3
Alt Table
StatusErrorProgram
11.6b
(+.f64 (*.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (sqrt.f64 (*.f64 x (fma.f64 2 y x)))) (*.f64 y y))
0.0b
(+.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))
0.0b
(fma.f64 y (fma.f64 2 x y) (*.f64 x x))
Compiler

Compiled 409 to 197 computations (51.8% saved)

localize11.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (sqrt.f64 (*.f64 x (fma.f64 2 y x)))) (*.f64 y y))
0.0b
(*.f64 x (fma.f64 2 y x))
0.1b
(*.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (sqrt.f64 (*.f64 x (fma.f64 2 y x))))
6.6b
(sqrt.f64 (*.f64 x (fma.f64 2 y x)))

series53.0ms (3.7%)

Counts
3 → 60
Calls

3 calls:

22.0ms
(*.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (sqrt.f64 (*.f64 x (fma.f64 2 y x))))
21.0ms
(sqrt.f64 (*.f64 x (fma.f64 2 y x)))
10.0ms
(+.f64 (*.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (sqrt.f64 (*.f64 x (fma.f64 2 y x)))) (*.f64 y y))

rewrite25.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
55×pow1_binary64
30×sqrt-pow1_binary64
21×pow-prod-down_binary64
11×pow1/2_binary64
10×pow-prod-up_binary64
Counts
3 → 78
Calls

3 calls:

6.0ms
(+.f64 (*.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (sqrt.f64 (*.f64 x (fma.f64 2 y x)))) (*.f64 y y))
6.0ms
(*.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (sqrt.f64 (*.f64 x (fma.f64 2 y x))))
2.0ms
(sqrt.f64 (*.f64 x (fma.f64 2 y x)))

simplify94.0ms (6.5%)

Algorithm
egg-herbie
Rules
967×fma-neg_binary64
703×unswap-sqr_binary64
513×times-frac_binary64
354×fma-def_binary64
217×distribute-rgt-in_binary64
Counts
138 → 127
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0951715
12501445
28371364
327771350
449211350
554971350

prune151.0ms (10.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2260226
Fresh000
Picked011
Done022
Total2263229
Error
0.0b
Counts
229 → 3
Alt Table
StatusErrorProgram
11.6b
(+.f64 (*.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (sqrt.f64 (*.f64 x (fma.f64 2 y x)))) (*.f64 y y))
0.0b
(+.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))
0.0b
(fma.f64 y (fma.f64 2 x y) (*.f64 x x))
Compiler

Compiled 5203 to 2846 computations (45.3% saved)

regimes77.0ms (5.4%)

Accuracy

Total 0.0b remaining (40.8%)

Threshold costs 0.0b (40.8%)

Counts
26 → 1
Compiler

Compiled 906 to 575 computations (36.5% saved)

simplify2.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
1812
2812

end6.0ms (0.4%)

Remove

(sort x y)

Compiler

Compiled 33 to 18 computations (45.5% saved)

sample585.0ms (40.6%)

Algorithm
intervals
Results
339.0ms8000×body128valid
7.0ms200×body128invalid
Compiler

Compiled 73 to 44 computations (39.7% saved)

Profiling

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