Details

Time bar (total: 3.2s)

analyze245.0ms (7.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%18.7%81.3%0
0%18.7%81.3%1
0%18.7%81.3%2
0%18.7%81.3%3
0%18.7%81.3%4
4.7%14%81.3%5
5.3%13.5%81.3%6
18.1%0.6%81.3%7
18.1%0.6%81.3%8
18.6%0.1%81.3%9
18.6%0.1%81.3%10
18.7%0%81.3%11
18.7%0%81.3%12
18.7%0%81.3%13
18.7%0%81.3%14
Compiler

Compiled 25 to 15 computations (40% saved)

sample29.0ms (0.9%)

Algorithm
intervals
Results
13.0ms256×body128valid
5.0ms256×pre128true
Compiler

Compiled 44 to 26 computations (40.9% saved)

simplify170.0ms (5.3%)

Algorithm
egg-herbie
Rules
917×times-frac_binary64
687×unsub-neg_binary64
552×sub-neg_binary64
367×distribute-lft-neg-in_binary64
317×associate-*l/_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01022
12322
25122
310022
421822
549922
689722
7195422
8263122
9433422
10392622
11414022
12422622
13422822
14422822
15497922

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
18.1b
Counts
1 → 1
Alt Table
StatusErrorProgram
18.1b
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))
Compiler

Compiled 34 to 18 computations (47.1% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (*.f64 x x) (*.f64 y y))
17.9b
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))

rewrite49.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
17.7b
Rules
associate-/l/_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
flip-+_binary64
flip3-+_binary64
Counts
2 → 42
Calls

2 calls:

11.0ms
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))
3.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 1156 to 190 computations (83.6% saved)

series59.0ms (1.9%)

Error
0.4b
Counts
2 → 33
Calls

2 calls:

35.0ms
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))
17.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 850 to 636 computations (25.2% saved)

simplify57.0ms (1.8%)

Algorithm
egg-herbie
Rules
949×distribute-rgt-in_binary64
906×times-frac_binary64
134×distribute-lft-in_binary64
127×div-sub_binary64
112×cancel-sign-sub-inv_binary64
Counts
75 → 54
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01161595
13811421
215731410
349921410

prune20.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New51354
Fresh000
Picked011
Done000
Total51455
Error
7.3b
Counts
55 → 4
Alt Table
StatusErrorProgram
24.1b
(+.f64 -1 (*.f64 2 (/.f64 (*.f64 x x) (*.f64 y y))))
18.1b
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))
18.1b
(log.f64 (exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))))
46.7b
(-.f64 1 (*.f64 2 (/.f64 (*.f64 y y) (*.f64 x x))))
Compiler

Compiled 833 to 253 computations (69.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 x x) (*.f64 y y))
0.0b
(exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))))
0.0b
(log.f64 (exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))))
17.9b
(/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))

rewrite83.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
7.1b
Rules
36×exp-prod_binary64
36×times-frac_binary64
30×*-un-lft-identity_binary64
30×add-sqr-sqrt_binary64
30×add-cube-cbrt_binary64
Counts
4 → 105
Calls

4 calls:

8.0ms
(log.f64 (exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))))
7.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))
6.0ms
(exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))))
3.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 3242 to 447 computations (86.2% saved)

series157.0ms (4.9%)

Error
0.4b
Counts
4 → 72
Calls

4 calls:

48.0ms
(log.f64 (exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))))
37.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))
37.0ms
(exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))))
19.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 2032 to 1633 computations (19.6% saved)

simplify145.0ms (4.5%)

Algorithm
egg-herbie
Rules
627×associate-/l*_binary64
463×associate-/r*_binary64
310×associate-*l/_binary64
238×associate-/r/_binary64
192×distribute-rgt-in_binary64
Counts
177 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01944433
14364169
213674149
349344149
449724149

prune39.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1101111
Fresh022
Picked011
Done011
Total1105115
Error
7.1b
Counts
115 → 5
Alt Table
StatusErrorProgram
24.1b
(+.f64 -1 (*.f64 2 (/.f64 (*.f64 x x) (*.f64 y y))))
63.3b
(log.f64 (pow.f64 (exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (-.f64 (pow.f64 x 4) (pow.f64 y 4)))) (-.f64 (*.f64 x x) (*.f64 y y))))
18.1b
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))
18.1b
(log.f64 (exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))))
46.7b
(-.f64 1 (*.f64 2 (/.f64 (*.f64 y y) (*.f64 x x))))
Compiler

Compiled 1793 to 469 computations (73.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 2 (/.f64 (*.f64 x x) (*.f64 y y)))
0.0b
(+.f64 -1 (*.f64 2 (/.f64 (*.f64 x x) (*.f64 y y))))
18.8b
(/.f64 (*.f64 x x) (*.f64 y y))

rewrite54.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
2.7b
Rules
33×add-cbrt-cube_binary64
33×add-exp-log_binary64
13×cbrt-unprod_binary64
13×prod-exp_binary64
add-sqr-sqrt_binary64
Counts
3 → 62
Calls

3 calls:

8.0ms
(*.f64 2 (/.f64 (*.f64 x x) (*.f64 y y)))
5.0ms
(/.f64 (*.f64 x x) (*.f64 y y))
3.0ms
(+.f64 -1 (*.f64 2 (/.f64 (*.f64 x x) (*.f64 y y))))
Compiler

Compiled 1201 to 471 computations (60.8% saved)

series55.0ms (1.7%)

Error
7.1b
Counts
3 → 24
Calls

3 calls:

23.0ms
(+.f64 -1 (*.f64 2 (/.f64 (*.f64 x x) (*.f64 y y))))
16.0ms
(*.f64 2 (/.f64 (*.f64 x x) (*.f64 y y)))
14.0ms
(/.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 544 to 460 computations (15.4% saved)

simplify96.0ms (3%)

Algorithm
egg-herbie
Rules
732×times-frac_binary64
587×associate-*l/_binary64
559×associate-*l*_binary64
531×associate-*r/_binary64
425×associate-/l*_binary64
Counts
86 → 57
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01041378
12511190
28801102
344341096
449821096
549821096

prune21.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New54357
Fresh112
Picked101
Done022
Total56662
Error
2.7b
Counts
62 → 6
Alt Table
StatusErrorProgram
18.1b
(log.f64 (exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))))
38.9b
(+.f64 -1 (*.f64 2 (exp.f64 (*.f64 2 (log.f64 (/.f64 x y))))))
18.1b
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))
19.5b
(+.f64 -1 (*.f64 2 (/.f64 x (/.f64 y (/.f64 x y)))))
19.3b
(+.f64 -1 (*.f64 2 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))))
46.7b
(-.f64 1 (*.f64 2 (/.f64 (*.f64 y y) (*.f64 x x))))
Compiler

Compiled 416 to 243 computations (41.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 2 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))))
0.0b
(+.f64 -1 (*.f64 2 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))))
0.3b
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))

rewrite158.0ms (5%)

Algorithm
rewrite-expression-head
Error
2.7b
Rules
119×add-sqr-sqrt_binary64
72×fabs-mul_binary64
60×times-frac_binary64
36×*-un-lft-identity_binary64
36×add-cube-cbrt_binary64
Counts
3 → 132
Calls

3 calls:

12.0ms
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
8.0ms
(*.f64 2 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))))
2.0ms
(+.f64 -1 (*.f64 2 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))))
Compiler

Compiled 2832 to 941 computations (66.8% saved)

series43.0ms (1.3%)

Error
2.7b
Counts
3 → 18
Calls

3 calls:

16.0ms
(+.f64 -1 (*.f64 2 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))))
14.0ms
(*.f64 2 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))))
11.0ms
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
Compiler

Compiled 454 to 376 computations (17.2% saved)

simplify130.0ms (4.1%)

Algorithm
egg-herbie
Rules
444×*-commutative_binary64
330×log-prod_binary64
303×associate-/l*_binary64
219×distribute-rgt-neg-in_binary64
216×unswap-sqr_binary64
Counts
150 → 139
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02012847
13942202
212872088
325102008
446412008
549572008

prune94.0ms (2.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1327139
Fresh123
Picked101
Done022
Total13411145
Error
2.7b
Counts
145 → 11
Alt Table
StatusErrorProgram
19.3b
(+.f64 -1 (*.f64 2 (*.f64 (pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) 4) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 y) (cbrt.f64 y))))))
18.1b
(log.f64 (exp.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y)))))
38.9b
(+.f64 -1 (*.f64 2 (exp.f64 (*.f64 2 (log.f64 (/.f64 x y))))))
19.3b
(+.f64 -1 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 (/.f64 x y) 2))) (sqrt.f64 (*.f64 2 (pow.f64 (/.f64 x y) 2)))))
19.3b
(+.f64 -1 (*.f64 (*.f64 (cbrt.f64 (*.f64 2 (pow.f64 (/.f64 x y) 2))) (cbrt.f64 (*.f64 2 (pow.f64 (/.f64 x y) 2)))) (cbrt.f64 (*.f64 2 (pow.f64 (/.f64 x y) 2)))))
20.3b
(+.f64 -1 (log.f64 (pow.f64 (exp.f64 (pow.f64 (/.f64 x y) 2)) 2)))
19.3b
(+.f64 -1 (exp.f64 (log.f64 (*.f64 2 (pow.f64 (/.f64 x y) 2)))))
20.6b
(+.f64 -1 (*.f64 2 (*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) (/.f64 x (cbrt.f64 y))))))
18.1b
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))
19.3b
(+.f64 -1 (*.f64 2 (*.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) y)) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) y))))
46.7b
(-.f64 1 (*.f64 2 (/.f64 (*.f64 y y) (*.f64 x x))))
Compiler

Compiled 1614 to 818 computations (49.3% saved)

regimes379.0ms (11.9%)

Accuracy

Total 0.1b remaining (1.2%)

Threshold costs 0.1b (1.2%)

Compiler

Compiled 5434 to 3040 computations (44.1% saved)

bsearch3.0ms (0.1%)

Compiler

Compiled 17 to 9 computations (47.1% saved)

simplify6.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02577
14577
26377
37377
47977
58077
67777

end1.0ms (0%)

Compiler

Compiled 54 to 26 computations (51.9% saved)

sample1.1s (33.3%)

Algorithm
intervals
Results
382.0ms8000×body128valid
184.0ms8000×pre128true
Compiler

Compiled 301 to 181 computations (39.9% saved)

Profiling

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