Details

Time bar (total: 5.2s)

analyze48.0ms (0.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
25%74.9%0.1%3
25%74.9%0.1%4
56.2%43.7%0.1%5
65.6%34.3%0.1%6
79.6%20.3%0.1%7
83.5%16.4%0.1%8
90.1%9.8%0.1%9
91.9%8%0.1%10
95.1%4.8%0.1%11
96%4%0.1%12
97.5%2.4%0.1%13
97.9%2%0.1%14
Compiler

Compiled 12 to 8 computations (33.3% saved)

sample312.0ms (6%)

Algorithm
intervals
Results
11.0ms255×body128valid
0.0msbody1024valid
Compiler

Compiled 25 to 17 computations (32% saved)

simplify268.0ms (5.2%)

Algorithm
egg-herbie
Rules
1222×fma-neg_binary64
983×fma-def_binary64
688×div-sub_binary64
423×sub-neg_binary64
412×distribute-rgt-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11813
23513
37413
415113
524513
664113
7112513
8215813
9272913
10303713
11299513
12304913
13306313
14356913
15355913
16355913
17355913
18355913
19355913
20365513
21370313
22378513
23359313

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.0b
(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series17.0ms (0.3%)

Counts
1 → 24
Calls

1 calls:

17.0ms
(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

rewrite16.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity_binary64
40×add-sqr-sqrt_binary64
30×times-frac_binary64
19×distribute-lft-out--_binary64
14×add-cube-cbrt_binary64
Counts
1 → 60
Calls

1 calls:

8.0ms
(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

simplify90.0ms (1.7%)

Algorithm
egg-herbie
Rules
702×fma-def_binary64
518×times-frac_binary64
339×fma-neg_binary64
291×distribute-rgt-in_binary64
228×cancel-sign-sub-inv_binary64
Counts
84 → 109
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02242433
16352369
221152256
348532256
450452256

prune98.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1054109
Fresh000
Picked101
Done000
Total1064110
Error
0.0b
Counts
110 → 4
Alt Table
StatusErrorProgram
5.9b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))
0.2b
(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
0.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (*.f64 (cbrt.f64 (-.f64 2 (+.f64 x y))) (cbrt.f64 (-.f64 2 (+.f64 x y))))) (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 2 (+.f64 x y)))))
31.0b
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2)) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 (*.f64 y x) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 y (-.f64 2 y)) (/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3)))))
Compiler

Compiled 2803 to 1456 computations (48.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (-.f64 2 (+.f64 x y)))
0.2b
(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))

series31.0ms (0.6%)

Counts
2 → 48
Calls

2 calls:

17.0ms
(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
14.0ms
(/.f64 1 (-.f64 2 (+.f64 x y)))

rewrite46.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity_binary64
47×add-sqr-sqrt_binary64
38×times-frac_binary64
24×associate-*r*_binary64
24×add-cube-cbrt_binary64
Counts
2 → 102
Calls

2 calls:

28.0ms
(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
6.0ms
(/.f64 1 (-.f64 2 (+.f64 x y)))

simplify118.0ms (2.3%)

Algorithm
egg-herbie
Rules
654×times-frac_binary64
403×fma-neg_binary64
325×sub-neg_binary64
288×cancel-sign-sub-inv_binary64
188×+-commutative_binary64
Counts
150 → 192
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03063603
18513445
230683427
349423427
451453427

prune173.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1911192
Fresh033
Picked011
Done000
Total1915196
Error
0b
Counts
196 → 5
Alt Table
StatusErrorProgram
5.9b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))
24.0b
(*.f64 (*.f64 (-.f64 x y) (sqrt.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))) (sqrt.f64 (/.f64 1 (-.f64 2 (+.f64 x y)))))
0.2b
(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
0.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (*.f64 (cbrt.f64 (-.f64 2 (+.f64 x y))) (cbrt.f64 (-.f64 2 (+.f64 x y))))) (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 2 (+.f64 x y)))))
31.0b
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2)) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 (*.f64 y x) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 y (-.f64 2 y)) (/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3)))))
Compiler

Compiled 4891 to 2836 computations (42% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 (cbrt.f64 (-.f64 2 (+.f64 x y))) (cbrt.f64 (-.f64 2 (+.f64 x y))))
0.5b
(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
0.6b
(cbrt.f64 (-.f64 x y))
0.6b
(cbrt.f64 (-.f64 2 (+.f64 x y)))

series172.0ms (3.3%)

Counts
4 → 96
Calls

4 calls:

71.0ms
(*.f64 (cbrt.f64 (-.f64 2 (+.f64 x y))) (cbrt.f64 (-.f64 2 (+.f64 x y))))
35.0ms
(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
33.0ms
(cbrt.f64 (-.f64 2 (+.f64 x y)))
32.0ms
(cbrt.f64 (-.f64 x y))

rewrite43.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity_binary64
79×cbrt-prod_binary64
58×add-sqr-sqrt_binary64
28×cbrt-div_binary64
25×swap-sqr_binary64
Counts
4 → 158
Calls

4 calls:

16.0ms
(*.f64 (cbrt.f64 (-.f64 2 (+.f64 x y))) (cbrt.f64 (-.f64 2 (+.f64 x y))))
8.0ms
(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
4.0ms
(cbrt.f64 (-.f64 2 (+.f64 x y)))
2.0ms
(cbrt.f64 (-.f64 x y))

simplify160.0ms (3.1%)

Algorithm
egg-herbie
Rules
676×fma-def_binary64
656×associate-*r*_binary64
480×associate-*l*_binary64
210×*-commutative_binary64
158×cancel-sign-sub-inv_binary64
Counts
254 → 318
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
06608674
119718330
257308330

prune600.0ms (11.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New5660566
Fresh033
Picked011
Done011
Total5665571
Error
0b
Counts
571 → 5
Alt Table
StatusErrorProgram
5.9b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))
24.0b
(*.f64 (*.f64 (-.f64 x y) (sqrt.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))) (sqrt.f64 (/.f64 1 (-.f64 2 (+.f64 x y)))))
0.2b
(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
0.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (*.f64 (cbrt.f64 (-.f64 2 (+.f64 x y))) (cbrt.f64 (-.f64 2 (+.f64 x y))))) (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 2 (+.f64 x y)))))
31.0b
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2)) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 (*.f64 y x) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 y (-.f64 2 y)) (/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3)))))
Compiler

Compiled 33209 to 18009 computations (45.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
0.0b
(*.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
0.1b
(*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
5.9b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

series190.0ms (3.7%)

Counts
3 → 72
Calls

3 calls:

100.0ms
(*.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
52.0ms
(*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
38.0ms
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

rewrite169.0ms (3.3%)

Algorithm
rewrite-expression-head
Rules
548×*-un-lft-identity_binary64
263×times-frac_binary64
236×add-sqr-sqrt_binary64
180×distribute-lft-out--_binary64
90×swap-sqr_binary64
Counts
3 → 300
Calls

3 calls:

42.0ms
(*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
32.0ms
(*.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
23.0ms
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

simplify259.0ms (5%)

Algorithm
egg-herbie
Rules
794×fma-def_binary64
547×times-frac_binary64
256×*-commutative_binary64
248×+-commutative_binary64
248×associate-*r/_binary64
Counts
372 → 385
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
090818440
1304915668
2496715668

prune789.0ms (15.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New7111712
Fresh112
Picked101
Done022
Total7134717
Error
0b
Counts
717 → 4
Alt Table
StatusErrorProgram
24.0b
(*.f64 (*.f64 (-.f64 x y) (sqrt.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))) (sqrt.f64 (/.f64 1 (-.f64 2 (+.f64 x y)))))
0.2b
(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
6.1b
(/.f64 (cbrt.f64 (*.f64 (*.f64 (-.f64 x y) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))) (cbrt.f64 (-.f64 2 (+.f64 x y))))
0.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (*.f64 (cbrt.f64 (-.f64 2 (+.f64 x y))) (cbrt.f64 (-.f64 2 (+.f64 x y))))) (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 2 (+.f64 x y)))))
Compiler

Compiled 34756 to 17358 computations (50.1% saved)

regimes1.0s (19.5%)

Accuracy

Total 0.0b remaining (18.3%)

Threshold costs 0.0b (18.3%)

Counts
244 → 1
Compiler

Compiled 18385 to 11722 computations (36.2% 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
01013
11713
22713
33513
43913
54013
63913

end0.0ms (0%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample535.0ms (10.3%)

Algorithm
intervals
Results
260.0ms7998×body128valid
0.0msbody1024valid
Compiler

Compiled 131 to 78 computations (40.5% saved)

Profiling

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