Details

Time bar (total: 4.4s)

analyze95.0ms (2.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%62.4%12.6%6
37.5%43.7%18.8%7
50%31.2%18.8%8
56.2%20.3%23.5%9
61.7%14.8%23.5%10
64.4%9.8%25.9%11
66.9%7.2%25.9%12
68.2%4.8%27%13
69.4%3.6%27%14
Compiler

Compiled 11 to 7 computations (36.4% saved)

sample842.0ms (19%)

Symmetry

(sort a b)

Results
789.0ms8256×body128valid
11.0ms123×body128invalid
Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify13.0ms (0.3%)

Algorithm
egg-herbie
Rules
284×fma-def_binary64
35×associate-*l*_binary64
24×distribute-rgt-in_binary64
24×sub-neg_binary64
19×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
12112
25512
39712
414412
518512
623012
726412
827312
926712
1023312

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
16.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
16.1b
(neg.f64 (*.f64 (*.f64 (*.f64 a a) b) b))
Compiler

Compiled 38 to 20 computations (47.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
5.0b
(*.f64 (*.f64 (*.f64 a a) b) b)
10.3b
(*.f64 (*.f64 a a) b)

series21.0ms (0.5%)

Counts
2 → 48
Calls

2 calls:

11.0ms
(*.f64 (*.f64 (*.f64 a a) b) b)
10.0ms
(*.f64 (*.f64 a a) b)

rewrite12.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
16×pow1_binary64
cbrt-unprod_binary64
prod-exp_binary64
Counts
2 → 44
Calls

2 calls:

6.0ms
(*.f64 (*.f64 (*.f64 a a) b) b)
4.0ms
(*.f64 (*.f64 a a) b)

simplify79.0ms (1.8%)

Algorithm
egg-herbie
Rules
599×fma-def_binary64
359×unswap-sqr_binary64
354×associate-/l/_binary64
272×sqr-pow_binary64
262×associate-/r/_binary64
Counts
92 → 56
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
061983
1142854
2480830
3782812
41506801
52460801
64674801
74916801

prune44.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New48856
Fresh000
Picked011
Done000
Total48957
Error
0.0b
Counts
57 → 9
Alt Table
StatusErrorProgram
16.5b
(neg.f64 (*.f64 (*.f64 (*.f64 (*.f64 a a) b) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
16.1b
(neg.f64 (*.f64 (*.f64 (*.f64 a a) b) b))
24.0b
(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
16.5b
(neg.f64 (*.f64 (*.f64 (*.f64 (*.f64 a a) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) b))
5.2b
(neg.f64 (*.f64 (*.f64 a (*.f64 a b)) b))
19.7b
(neg.f64 (*.f64 (*.f64 (*.f64 a (sqrt.f64 b)) (*.f64 a (sqrt.f64 b))) b))
24.8b
(neg.f64 (*.f64 (*.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
0.3b
(neg.f64 (*.f64 (*.f64 a b) (*.f64 a b)))
34.2b
(neg.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 a a) b) (*.f64 (*.f64 a a) b)) (*.f64 (*.f64 a a) b)) (*.f64 (*.f64 b b) b))))
Compiler

Compiled 974 to 350 computations (64.1% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 a b) (*.f64 a b))

series12.0ms (0.3%)

Counts
1 → 24
Calls

1 calls:

12.0ms
(*.f64 (*.f64 a b) (*.f64 a b))

rewrite7.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
40×pow1_binary64
17×pow-prod-down_binary64
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
cbrt-unprod_binary64
Counts
1 → 36
Calls

1 calls:

5.0ms
(*.f64 (*.f64 a b) (*.f64 a b))

simplify77.0ms (1.7%)

Algorithm
egg-herbie
Rules
654×associate-*l*_binary64
551×fma-def_binary64
352×associate-*r*_binary64
341×associate-/l*_binary64
311×associate-/l/_binary64
Counts
60 → 34
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
041613
192508
2315474
31009474
41436372
52353372
64908372
74999372
84954372

prune32.0ms (0.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New31334
Fresh347
Picked011
Done011
Total34943
Error
0.0b
Counts
43 → 9
Alt Table
StatusErrorProgram
0.9b
(neg.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
24.8b
(neg.f64 (*.f64 (*.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
24.0b
(neg.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (*.f64 a b) (*.f64 a b))) (*.f64 (*.f64 a b) (*.f64 a b)))))
0.3b
(neg.f64 (*.f64 (*.f64 a b) (*.f64 a b)))
24.0b
(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
5.2b
(neg.f64 (*.f64 (*.f64 a (*.f64 a b)) b))
19.7b
(neg.f64 (*.f64 (*.f64 (*.f64 a (sqrt.f64 b)) (*.f64 a (sqrt.f64 b))) b))
6.9b
(neg.f64 (*.f64 a (*.f64 b (*.f64 a b))))
16.1b
(neg.f64 (*.f64 (*.f64 (*.f64 a a) b) b))
Compiler

Compiled 658 to 268 computations (59.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
0.3b
(pow.f64 (*.f64 a b) 2)
0.4b
(*.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
19.9b
(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series1.2s (27%)

Counts
4 → 96
Calls

4 calls:

586.0ms
(cbrt.f64 (pow.f64 (*.f64 a b) 2))
585.0ms
(*.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
13.0ms
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
8.0ms
(pow.f64 (*.f64 a b) 2)

rewrite31.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod_binary64
34×add-sqr-sqrt_binary64
33×pow1_binary64
20×unswap-sqr_binary64
18×associate-*r*_binary64
Counts
4 → 142
Calls

4 calls:

10.0ms
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
7.0ms
(*.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
2.0ms
(pow.f64 (*.f64 a b) 2)
1.0ms
(cbrt.f64 (pow.f64 (*.f64 a b) 2))

simplify176.0ms (4%)

Algorithm
egg-herbie
Rules
865×fma-def_binary64
708×unswap-sqr_binary64
612×exp-prod_binary64
576×fma-neg_binary64
540×log-prod_binary64
Counts
238 → 193
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
01843987
13213345
27762770
316502453
438742219
548322215
643912210
752172210

prune321.0ms (7.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New3032305
Fresh066
Picked011
Done022
Total30311314
Error
0.0b
Counts
314 → 11
Alt Table
StatusErrorProgram
0.9b
(neg.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
24.8b
(neg.f64 (*.f64 (*.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
24.0b
(neg.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (*.f64 a b) (*.f64 a b))) (*.f64 (*.f64 a b) (*.f64 a b)))))
0.3b
(neg.f64 (*.f64 (*.f64 a b) (*.f64 a b)))
24.0b
(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
0.9b
(neg.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))) (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
5.2b
(neg.f64 (*.f64 (*.f64 a (*.f64 a b)) b))
19.7b
(neg.f64 (*.f64 (*.f64 (*.f64 a (sqrt.f64 b)) (*.f64 a (sqrt.f64 b))) b))
6.9b
(neg.f64 (*.f64 a (*.f64 b (*.f64 a b))))
16.1b
(neg.f64 (*.f64 (*.f64 (*.f64 a a) b) b))
0.9b
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
Compiler

Compiled 8304 to 4972 computations (40.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
0.3b
(pow.f64 (*.f64 a b) 2)
2.8b
(sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
19.9b
(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series380.0ms (8.6%)

Counts
2 → 48
Calls

2 calls:

376.0ms
(sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
4.0ms
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))

rewrite17.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
48×cbrt-prod_binary64
34×sqrt-prod_binary64
34×add-sqr-sqrt_binary64
20×unswap-sqr_binary64
13×sqr-pow_binary64
Counts
2 → 85
Calls

2 calls:

8.0ms
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
2.0ms
(sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))

simplify150.0ms (3.4%)

Algorithm
egg-herbie
Rules
734×fma-neg_binary64
374×*-commutative_binary64
271×fma-def_binary64
258×exp-prod_binary64
181×distribute-rgt-in_binary64
Counts
133 → 124
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01202514
11962302
24052094
39411532
417211478
537871478
649851478
749941478
848851478

prune519.0ms (11.7%)

Pruning

12 alts after pruning (8 fresh and 4 done)

PrunedKeptTotal
New3881389
Fresh077
Picked011
Done033
Total38812400
Error
0.0b
Counts
400 → 12
Alt Table
StatusErrorProgram
0.9b
(neg.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
24.8b
(neg.f64 (*.f64 (*.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
24.0b
(neg.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (*.f64 a b) (*.f64 a b))) (*.f64 (*.f64 a b) (*.f64 a b)))))
0.3b
(neg.f64 (*.f64 (*.f64 a b) (*.f64 a b)))
24.0b
(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
0.9b
(neg.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))) (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
5.2b
(neg.f64 (*.f64 (*.f64 a (*.f64 a b)) b))
19.7b
(neg.f64 (*.f64 (*.f64 (*.f64 a (sqrt.f64 b)) (*.f64 a (sqrt.f64 b))) b))
1.1b
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))) (*.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
6.9b
(neg.f64 (*.f64 a (*.f64 b (*.f64 a b))))
16.1b
(neg.f64 (*.f64 (*.f64 (*.f64 a a) b) b))
0.9b
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
Compiler

Compiled 13833 to 8399 computations (39.3% saved)

regimes210.0ms (4.7%)

Accuracy

Total 0.3b remaining (85.7%)

Threshold costs 0.3b (85.7%)

Counts
45 → 1
Compiler

Compiled 4716 to 2863 computations (39.3% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0612
11412
22412
33112
43612
53812
63812

end164.0ms (3.7%)

Remove

(sort a b)

Compiler

Compiled 290 to 171 computations (41% saved)

Profiling

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