Details

Time bar (total: 4.3s)

analyze54.0ms (1.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
50%50%0.1%2
50%50%0.1%3
74.9%25%0.1%4
74.9%25%0.1%5
87.4%12.5%0.1%6
87.4%12.5%0.1%7
93.7%6.2%0.1%8
93.7%6.2%0.1%9
96.8%3.1%0.1%10
96.8%3.1%0.1%11
98.3%1.6%0.1%12
98.3%1.6%0.1%13
99.1%0.8%0.1%14
Compiler

Compiled 11 to 8 computations (27.3% saved)

sample16.0ms (0.4%)

Algorithm
intervals
Results
8.0ms252×body128valid
0.0msbody1024valid
0.0msbody512valid
0.0msbody256valid
Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify17.0ms (0.4%)

Algorithm
egg-herbie
Rules
97×fma-neg_binary64
32×cancel-sign-sub-inv_binary64
30×fma-def_binary64
29×sub-neg_binary64
17×distribute-rgt-neg-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 8 (0.0ms)

IterNodesCost
0812
11312
22012
32912
44512
57912
69712
712312
817410
918810
1022910
1126310
1228310
1329110
1429610
1525610

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.0b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
Compiler

Compiled 35 to 21 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

series6.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

5.0ms
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 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 (fabs.f64 (-.f64 y x)) 1/2 x)

simplify71.0ms (1.7%)

Algorithm
egg-herbie
Rules
557×distribute-rgt-neg-out_binary64
515×neg-mul-1_binary64
507×neg-sub0_binary64
481×distribute-rgt-out_binary64
469×*-commutative_binary64
Counts
34 → 21
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
019374
126353
255353
3125353
4320353
5990353
61892353
72461353
83898353
95066353

prune14.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New18321
Fresh000
Picked011
Done000
Total18422
Error
0.0b
Counts
22 → 4
Alt Table
StatusErrorProgram
19.4b
(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
1.4b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
42.5b
(cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 3))
0.0b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
Compiler

Compiled 369 to 180 computations (51.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
0.3b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
0.5b
(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
0.6b
(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

series945.0ms (22.2%)

Counts
3 → 72
Calls

3 calls:

517.0ms
(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
419.0ms
(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
6.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

rewrite18.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
24×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
16×pow1/3_binary64
14×*-un-lft-identity_binary64
Counts
3 → 93
Calls

3 calls:

7.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
4.0ms
(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
1.0ms
(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

simplify113.0ms (2.7%)

Algorithm
egg-herbie
Rules
408×fma-def_binary64
393×*-commutative_binary64
356×cancel-sign-sub-inv_binary64
338×unswap-sqr_binary64
309×fma-neg_binary64
Counts
165 → 178
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01943620
14833205
214653016
339852880
450332880

prune233.0ms (5.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3332335
Fresh022
Picked101
Done011
Total3345339
Error
0.0b
Counts
339 → 5
Alt Table
StatusErrorProgram
31.2b
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 2)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
1.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
19.4b
(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
42.5b
(cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 3))
0.0b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
Compiler

Compiled 11825 to 5843 computations (50.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
0.5b
(cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
0.6b
(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
0.6b
(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))

series924.0ms (21.7%)

Counts
2 → 48
Calls

2 calls:

518.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))
406.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 27
Calls

2 calls:

2.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))
1.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

simplify83.0ms (1.9%)

Algorithm
egg-herbie
Rules
603×associate-*r*_binary64
572×associate-*l*_binary64
446×fma-def_binary64
334×fma-neg_binary64
218×times-frac_binary64
Counts
75 → 88
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01722193
14302169
212241985
348501983
450531983

prune470.0ms (11%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New4830483
Fresh033
Picked011
Done011
Total4835488
Error
0.0b
Counts
488 → 5
Alt Table
StatusErrorProgram
31.2b
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 2)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
1.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
19.4b
(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
42.5b
(cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 3))
0.0b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
Compiler

Compiled 28199 to 14303 computations (49.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
0.0b
(sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
0.3b
(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

series27.0ms (0.6%)

Counts
2 → 40
Calls

2 calls:

19.0ms
(sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
7.0ms
(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

rewrite11.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
21×sqrt-prod_binary64
18×pow1_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
Counts
2 → 68
Calls

2 calls:

5.0ms
(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
1.0ms
(sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

simplify138.0ms (3.2%)

Algorithm
egg-herbie
Rules
682×times-frac_binary64
581×fma-def_binary64
306×distribute-lft-in_binary64
304×distribute-rgt-in_binary64
283×fma-neg_binary64
Counts
108 → 99
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0891747
11801580
24991518
318041478
449261478
550561478

prune103.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1721173
Fresh112
Picked011
Done022
Total1735178
Error
0b
Counts
178 → 5
Alt Table
StatusErrorProgram
33.8b
(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)) 3)))
19.4b
(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
42.5b
(cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 3))
1.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
0.0b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
Compiler

Compiled 4194 to 2066 computations (50.7% saved)

regimes404.0ms (9.5%)

Accuracy

Total 0.0b remaining (48.3%)

Threshold costs 0.0b (48.3%)

Counts
94 → 1
Compiler

Compiled 9062 to 5104 computations (43.7% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
11312
22012
32512
42812
52912
62912

end0.0ms (0%)

Compiler

Compiled 10 to 7 computations (30% saved)

sample563.0ms (13.2%)

Algorithm
intervals
Results
239.0ms7682×body128valid
14.0ms105×body1024valid
13.0ms89×body2048valid
7.0ms79×body512valid
3.0ms45×body256valid
0.0msbody128invalid
Compiler

Compiled 133 to 82 computations (38.3% saved)

Profiling

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