Details

Time bar (total: 3.0s)

analyze48.0ms (1.6%)

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)

sample21.0ms (0.7%)

Algorithm
intervals
Results
11.0ms244×body128valid
1.0msbody1024valid
0.0msbody2048valid
0.0msbody512valid
0.0msbody256valid
Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify18.0ms (0.6%)

Algorithm
egg-herbie
Rules
32×sub-neg_binary64 cancel-sign-sub-inv_binary64
17×distribute-rgt-neg-in_binary64
14×neg-mul-1_binary64 associate--r+_binary64
11×distribute-rgt-in_binary64
10×fabs-sub_binary64 distribute-lft-neg-in_binary64 associate--r-_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
11312
22012
32812
44212
57312
68812
710312
812912
913812
1016612
1118012
1219512
1319912
1420012
1516012

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.1b
Counts
1 → 1
Alt Table
StatusErrorProgram
0.1b
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
Compiler

Compiled 20 to 14 computations (30% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

rewrite25.0ms (0.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
add-log-exp_binary64 *-un-lft-identity_binary64
sum-log_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 flip3-+_binary64 flip-+_binary64 distribute-lft-out_binary64 +-commutative_binary64
Counts
1 → 12
Calls

1 calls:

14.0ms
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
Compiler

Compiled 201 to 97 computations (51.7% saved)

series22.0ms (0.7%)

Error
0.1b
Counts
1 → 9
Calls

1 calls:

20.0ms
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
Compiler

Compiled 151 to 103 computations (31.8% saved)

simplify79.0ms (2.6%)

Algorithm
egg-herbie
Rules
563×times-frac_binary64
403×div-sub_binary64
382×distribute-rgt-in_binary64
336×cancel-sign-sub-inv_binary64
320×neg-mul-1_binary64
Counts
21 → 9
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032334
193309
2191302
3411302
41006302
52771302
64297302
74923302

prune15.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New549
Fresh000
Picked011
Done000
Total5510
Error
0.0b
Counts
10 → 5
Alt Table
StatusErrorProgram
44.3b
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) 3)) (+.f64 (*.f64 x x) (*.f64 (fabs.f64 (-.f64 y x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) 4) (/.f64 x 2)))))
0.1b
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
14.3b
(*.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
1.3b
(*.f64 (*.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
44.1b
(cbrt.f64 (pow.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))) 3))
Compiler

Compiled 353 to 202 computations (42.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
0.5b
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.5b
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.5b
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))

rewrite126.0ms (4.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
25×cbrt-prod_binary64
23×add-sqr-sqrt_binary64
18×cbrt-div_binary64
15×add-cube-cbrt_binary64 *-un-lft-identity_binary64
11×pow1_binary64
Counts
4 → 87
Calls

4 calls:

12.0ms
(*.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
2.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
2.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
2.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
Compiler

Compiled 3569 to 1814 computations (49.2% saved)

series268.0ms (8.9%)

Error
0.0b
Counts
4 → 51
Calls

4 calls:

66.0ms
(*.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
53.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
52.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
52.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
Compiler

Compiled 4414 to 2792 computations (36.7% saved)

simplify145.0ms (4.8%)

Algorithm
egg-herbie
Rules
417×*-commutative_binary64
411×distribute-rgt-in_binary64
392×distribute-lft-in_binary64
309×cancel-sign-sub-inv_binary64
271×unswap-sqr_binary64
Counts
138 → 105
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01834395
14534101
212983967
325513941
450143941

prune85.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1032105
Fresh033
Picked011
Done011
Total1037110
Error
0.0b
Counts
110 → 7
Alt Table
StatusErrorProgram
2.1b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 5) (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
14.5b
(*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
44.3b
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) 3)) (+.f64 (*.f64 x x) (*.f64 (fabs.f64 (-.f64 y x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) 4) (/.f64 x 2)))))
0.1b
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
14.3b
(*.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
1.3b
(*.f64 (*.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
44.1b
(cbrt.f64 (pow.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))) 3))
Compiler

Compiled 3267 to 1752 computations (46.4% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.5b
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.5b
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
1.0b
(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 5)

rewrite89.0ms (3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
18×cbrt-prod_binary64
11×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
unpow-prod-down_binary64
cbrt-div_binary64
pow1_binary64 add-exp-log_binary64
Counts
4 → 63
Calls

4 calls:

5.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 5)
3.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
2.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
2.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
Compiler

Compiled 2759 to 1556 computations (43.6% saved)

series313.0ms (10.4%)

Error
0.0b
Counts
4 → 48
Calls

4 calls:

87.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 5)
57.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
57.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
55.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
Compiler

Compiled 4970 to 3244 computations (34.7% saved)

simplify128.0ms (4.3%)

Algorithm
egg-herbie
Rules
691×associate-*r*_binary64
680×associate-*l*_binary64
422×distribute-rgt-neg-in_binary64
285×*-commutative_binary64
225×sqr-pow_binary64
Counts
111 → 97
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01943244
14883106
212333043
341253036
450633036

prune100.0ms (3.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New97097
Fresh044
Picked011
Done022
Total977104
Error
0.0b
Counts
104 → 7
Alt Table
StatusErrorProgram
2.1b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 5) (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
14.5b
(*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
44.3b
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) 3)) (+.f64 (*.f64 x x) (*.f64 (fabs.f64 (-.f64 y x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) 4) (/.f64 x 2)))))
0.1b
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
14.3b
(*.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
1.3b
(*.f64 (*.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
44.1b
(cbrt.f64 (pow.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))) 3))
Compiler

Compiled 3902 to 2251 computations (42.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))
0.0b
(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.0b
(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.5b
(*.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))

rewrite114.0ms (3.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
32×add-sqr-sqrt_binary64
24×sqrt-prod_binary64
21×pow1_binary64
16×sqrt-div_binary64
14×add-cube-cbrt_binary64 *-un-lft-identity_binary64
Counts
4 → 100
Calls

4 calls:

10.0ms
(*.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
3.0ms
(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
3.0ms
(+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))
2.0ms
(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
Compiler

Compiled 2667 to 1362 computations (48.9% saved)

series105.0ms (3.5%)

Error
0.0b
Counts
4 → 36
Calls

4 calls:

27.0ms
(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
26.0ms
(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
21.0ms
(+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))
17.0ms
(*.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
Compiler

Compiled 1658 to 1067 computations (35.6% saved)

simplify197.0ms (6.6%)

Algorithm
egg-herbie
Rules
682×times-frac_binary64
450×associate-*l*_binary64
373×associate-*r*_binary64
268×cancel-sign-sub-inv_binary64
201×unswap-sqr_binary64
Counts
136 → 78
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01152929
12502748
27102683
324562554
447052554
548982554
649952554
749502554

prune57.0ms (1.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New77178
Fresh033
Picked011
Done033
Total77885
Error
0.0b
Counts
85 → 8
Alt Table
StatusErrorProgram
2.1b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 5) (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
14.5b
(*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
15.1b
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 4) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
44.3b
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) 3)) (+.f64 (*.f64 x x) (*.f64 (fabs.f64 (-.f64 y x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) 4) (/.f64 x 2)))))
0.1b
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
14.3b
(*.f64 (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
1.3b
(*.f64 (*.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
44.1b
(cbrt.f64 (pow.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))) 3))
Compiler

Compiled 1582 to 860 computations (45.6% saved)

regimes377.0ms (12.6%)

Accuracy

Total 0.0b remaining (67.7%)

Threshold costs 0.0b (67.7%)

Compiler

Compiled 7688 to 4585 computations (40.4% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
neg-mul-1_binary64 neg-sub0_binary64 *-commutative_binary64
fabs-sub_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
11312
22012
32512
42812
52912
62912

end1.0ms (0%)

Compiler

Compiled 10 to 7 computations (30% saved)

sample628.0ms (20.9%)

Algorithm
intervals
Results
194.0ms7707×body128valid
10.0ms108×body1024valid
9.0ms82×body2048valid
5.0ms70×body512valid
2.0ms33×body256valid
Compiler

Compiled 223 to 142 computations (36.3% saved)

Profiling

Loading profile data...