Details

Time bar (total: 2.9s)

analyze50.0ms (1.7%)

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)

sample17.0ms (0.6%)

Algorithm
intervals
Results
7.0ms243×body128valid
1.0msbody2048valid
0.0msbody512valid
0.0msbody1024valid
Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify19.0ms (0.7%)

Algorithm
egg-herbie
Rules
32×cancel-sign-sub-inv_binary64
32×sub-neg_binary64
17×distribute-rgt-neg-in_binary64
14×associate--r+_binary64
14×neg-mul-1_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

prune1.0ms (0%)

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)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite18.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
*-un-lft-identity_binary64
add-log-exp_binary64
+-commutative_binary64
distribute-lft-out_binary64
flip-+_binary64
Counts
1 → 12
Calls

1 calls:

9.0ms
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
Compiler

Compiled 201 to 97 computations (51.7% saved)

series16.0ms (0.6%)

Error
0.1b
Counts
1 → 9
Calls

1 calls:

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

Compiled 151 to 103 computations (31.8% saved)

simplify72.0ms (2.5%)

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 → 15
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032334
193309
2191302
3411302
41006302
52771302
64297302
74923302

prune11.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New11415
Fresh000
Picked011
Done000
Total11516
Error
0.0b
Counts
16 → 5
Alt Table
StatusErrorProgram
0.1b
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
32.0b
(/.f64 (+.f64 (*.f64 x x) (*.f64 (/.f64 (-.f64 x y) 4) (-.f64 y x))) (-.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
43.1b
(/.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)))))
15.2b
(*.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))))))
Compiler

Compiled 383 to 213 computations (44.4% saved)

localize9.0ms (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)))))

rewrite92.0ms (3.2%)

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

4 calls:

7.0ms
(*.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))))))
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 3569 to 1814 computations (49.2% saved)

series213.0ms (7.3%)

Error
0.0b
Counts
4 → 49
Calls

4 calls:

50.0ms
(*.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))))))
45.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
44.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
43.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
Compiler

Compiled 4228 to 2671 computations (36.8% saved)

simplify128.0ms (4.4%)

Algorithm
egg-herbie
Rules
762×unswap-sqr_binary64
369×distribute-rgt-in_binary64
355×*-commutative_binary64
346×distribute-lft-in_binary64
234×cancel-sign-sub-inv_binary64
Counts
136 → 107
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01674236
14073942
211373844
321743818
452023818

prune63.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1043107
Fresh213
Picked101
Done011
Total1075112
Error
0.0b
Counts
112 → 5
Alt Table
StatusErrorProgram
0.1b
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
15.5b
(*.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))))))
15.2b
(*.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))))))
1.8b
(*.f64 (*.f64 (cbrt.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))))))) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 4)) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
32.5b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (fabs.f64 (-.f64 y x)) 2) 1/4))) (cbrt.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (fabs.f64 (-.f64 y x)) 2) 1/4)))) (*.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))))))
Compiler

Compiled 3257 to 1737 computations (46.7% saved)

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
0.6b
(cbrt.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)))))))
0.6b
(cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
0.9b
(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 4)

rewrite93.0ms (3.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
26×cbrt-div_binary64
22×cbrt-prod_binary64
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
Counts
4 → 70
Calls

4 calls:

7.0ms
(cbrt.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)))))))
4.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 4)
2.0ms
(cbrt.f64 (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 3967 to 2174 computations (45.2% saved)

series240.0ms (8.3%)

Error
0.0b
Counts
4 → 44
Calls

4 calls:

58.0ms
(cbrt.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)))))))
58.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 4)
51.0ms
(cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
41.0ms
(cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
Compiler

Compiled 4922 to 3112 computations (36.8% saved)

simplify183.0ms (6.3%)

Algorithm
egg-herbie
Rules
458×*-commutative_binary64
345×cancel-sign-sub-inv_binary64
285×unswap-sqr_binary64
285×sqr-pow_binary64
274×distribute-rgt-neg-in_binary64
Counts
114 → 98
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02703653
16223478
216073457
333023437
445963375
549003375
648253375

prune68.0ms (2.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New98098
Fresh033
Picked011
Done011
Total985103
Error
0.0b
Counts
103 → 5
Alt Table
StatusErrorProgram
0.1b
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
15.5b
(*.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))))))
15.2b
(*.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))))))
1.8b
(*.f64 (*.f64 (cbrt.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))))))) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 4)) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
32.5b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (fabs.f64 (-.f64 y x)) 2) 1/4))) (cbrt.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (fabs.f64 (-.f64 y x)) 2) 1/4)))) (*.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))))))
Compiler

Compiled 3745 to 2131 computations (43.1% saved)

localize7.0ms (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)))))
0.4b
(*.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))))))

rewrite136.0ms (4.7%)

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×*-un-lft-identity_binary64
Counts
4 → 100
Calls

4 calls:

11.0ms
(*.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))))))
4.0ms
(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
4.0ms
(+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))
4.0ms
(sqrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))
Compiler

Compiled 2667 to 1362 computations (48.9% saved)

series93.0ms (3.2%)

Error
0.0b
Counts
4 → 34
Calls

4 calls:

26.0ms
(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)))))
18.0ms
(+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))
15.0ms
(*.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 1527 to 976 computations (36.1% saved)

simplify179.0ms (6.2%)

Algorithm
egg-herbie
Rules
631×distribute-rgt-in_binary64
421×associate-*l*_binary64
347×associate-*r*_binary64
305×times-frac_binary64
189×unswap-sqr_binary64
Counts
134 → 94
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01052845
12202586
26152514
320712435
448612390
549822390
649982390
749412390

prune48.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New92294
Fresh112
Picked011
Done022
Total93699
Error
0.0b
Counts
99 → 6
Alt Table
StatusErrorProgram
0.1b
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
15.4b
(*.f64 (*.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))) (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))))))
15.2b
(*.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))))))
1.8b
(*.f64 (*.f64 (cbrt.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))))))) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 4)) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
32.5b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (fabs.f64 (-.f64 y x)) 2) 1/4))) (cbrt.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (fabs.f64 (-.f64 y x)) 2) 1/4)))) (*.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))))))
15.9b
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x)))))) 4) (cbrt.f64 (+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))))
Compiler

Compiled 1479 to 786 computations (46.9% saved)

regimes450.0ms (15.5%)

Accuracy

Total 0.0b remaining (53.8%)

Threshold costs 0.0b (53.8%)

Compiler

Compiled 11198 to 6757 computations (39.7% 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)

sample665.0ms (22.9%)

Algorithm
intervals
Results
249.0ms7715×body128valid
12.0ms93×body1024valid
11.0ms81×body2048valid
6.0ms69×body512valid
2.0ms42×body256valid
Compiler

Compiled 214 to 132 computations (38.3% saved)

Profiling

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