Details

Time bar (total: 8.7s)

analyze304.0ms (3.5%)

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
0%99.9%0.1%5
0%74.9%25.1%6
6.2%68.6%25.1%7
10.1%64.7%25.1%8
17.2%32.8%50.1%9
23%26.9%50.1%10
26.8%23.1%50.1%11
31.6%18.3%50.1%12
35.2%14.7%50.1%13
37.5%12.4%50.1%14
Compiler

Compiled 16 to 11 computations (31.3% saved)

sample142.0ms (1.6%)

Algorithm
intervals
Results
14.0ms256×body128valid
0.0msbody128invalid
Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify128.0ms (1.5%)

Algorithm
egg-herbie
Rules
782×fma-neg_binary64
610×unsub-neg_binary64
567×distribute-rgt-in_binary64
442×sub-neg_binary64
412×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01118
12518
27516
325316
465416
5176716
6216716
7228416
8237516
9237416
10239116
11270116
12341716
13487716
14471316
15496716

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.1b
(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
Compiler

Compiled 54 to 33 computations (38.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)
0.1b
(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
0.1b
(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

series206.0ms (2.4%)

Counts
3 → 96
Calls

3 calls:

84.0ms
(-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)
77.0ms
(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
44.0ms
(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity_binary64
40×add-sqr-sqrt_binary64
33×prod-diff_binary64
28×add-cube-cbrt_binary64
14×associate--r+_binary64
Counts
3 → 96
Calls

3 calls:

6.0ms
(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
3.0ms
(-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)
0.0ms
(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

simplify121.0ms (1.4%)

Algorithm
egg-herbie
Rules
395×associate-+l+_binary64
315×exp-sum_binary64
303×associate-+r+_binary64
250×associate--r+_binary64
246×associate--l+_binary64
Counts
192 → 180
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02023702
14453255
216272853
344632853
449802853

prune134.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1746180
Fresh000
Picked101
Done000
Total1756181
Error
0.0b
Counts
181 → 6
Alt Table
StatusErrorProgram
1.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
46.8b
(*.f64 (+.f64 1 (log.f64 (/.f64 1 y))) y)
0.1b
(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
0.9b
(-.f64 y (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
32.3b
(-.f64 y (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) 3)) x))
29.7b
(-.f64 y (*.f64 (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
Compiler

Compiled 4418 to 2192 computations (50.4% saved)

localize40.0ms (0.5%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
0.1b
(fma.f64 (log.f64 y) (+.f64 1/2 y) z)

series126.0ms (1.5%)

Counts
2 → 60
Calls

2 calls:

86.0ms
(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
40.0ms
(fma.f64 (log.f64 y) (+.f64 1/2 y) z)

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64
13×add-sqr-sqrt_binary64
12×prod-diff_binary64
11×add-cube-cbrt_binary64
add-log-exp_binary64
Counts
2 → 48
Calls

2 calls:

8.0ms
(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
0.0ms
(fma.f64 (log.f64 y) (+.f64 1/2 y) z)

simplify140.0ms (1.6%)

Algorithm
egg-herbie
Rules
554×fma-def_binary64
497×associate-*l*_binary64
423×associate-*r*_binary64
383×associate-+l+_binary64
202×exp-sum_binary64
Counts
108 → 84
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01282050
12911842
211211676
344571676
448441674
549701674
649281674

prune66.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New84084
Fresh055
Picked011
Done000
Total84690
Error
0.0b
Counts
90 → 6
Alt Table
StatusErrorProgram
1.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
46.8b
(*.f64 (+.f64 1 (log.f64 (/.f64 1 y))) y)
0.1b
(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
0.9b
(-.f64 y (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
32.3b
(-.f64 y (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) 3)) x))
29.7b
(-.f64 y (*.f64 (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
Compiler

Compiled 2076 to 1060 computations (48.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 (+.f64 y 1/2) (log.f64 y) z)
0.3b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))
0.5b
(*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))
0.5b
(cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))

series777.0ms (8.9%)

Counts
3 → 72
Calls

3 calls:

629.0ms
(*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))
106.0ms
(cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))
42.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))

rewrite18.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
24×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
16×pow1/3_binary64
14×*-un-lft-identity_binary64
Counts
3 → 93
Calls

3 calls:

6.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))
4.0ms
(*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))
1.0ms
(cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))

simplify306.0ms (3.5%)

Algorithm
egg-herbie
Rules
984×fma-def_binary64
387×*-commutative_binary64
219×+-commutative_binary64
168×associate-+r+_binary64
151×associate-*r*_binary64
Counts
165 → 233
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
094915740
1346614963
2498814963
3500614963

prune921.0ms (10.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4634467
Fresh224
Picked011
Done011
Total4658473
Error
0.0b
Counts
473 → 8
Alt Table
StatusErrorProgram
0.1b
(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
31.3b
(-.f64 y (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) x))
1.1b
(-.f64 y (-.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
1.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
1.1b
(-.f64 y (-.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) x))
31.1b
(-.f64 y (-.f64 (*.f64 (sqrt.f64 (fma.f64 (+.f64 1/2 y) (log.f64 y) z)) (sqrt.f64 (fma.f64 (+.f64 1/2 y) (log.f64 y) z))) x))
0.9b
(-.f64 y (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
32.3b
(-.f64 y (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) 3)) x))
Compiler

Compiled 40937 to 29106 computations (28.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))
0.5b
(*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))
0.5b
(cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))
0.5b
(cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))

series736.0ms (8.5%)

Counts
2 → 48
Calls

2 calls:

630.0ms
(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))
105.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod_binary64
34×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
16×add-cube-cbrt_binary64
associate-*r*_binary64
Counts
2 → 72
Calls

2 calls:

6.0ms
(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))
1.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))

simplify295.0ms (3.4%)

Algorithm
egg-herbie
Rules
893×fma-def_binary64
382×*-commutative_binary64
210×+-commutative_binary64
166×associate-+r+_binary64
146×associate-*r*_binary64
Counts
120 → 197
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
094615941
1340314932
2495114867
3494414867

prune2.2s (25.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New7882790
Fresh055
Picked011
Done022
Total78810798
Error
0.0b
Counts
798 → 10
Alt Table
StatusErrorProgram
0.1b
(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
1.5b
(-.f64 y (-.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (*.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 1/2 y) (log.f64 y) z)))) 4) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 1/2 y) (log.f64 y) z))))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) x))
31.3b
(-.f64 y (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) x))
1.2b
(-.f64 y (-.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))))) x))
31.1b
(-.f64 y (-.f64 (*.f64 (sqrt.f64 (fma.f64 (+.f64 1/2 y) (log.f64 y) z)) (sqrt.f64 (fma.f64 (+.f64 1/2 y) (log.f64 y) z))) x))
1.1b
(-.f64 y (-.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
1.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
1.1b
(-.f64 y (-.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) x))
0.9b
(-.f64 y (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
32.3b
(-.f64 y (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) 3)) x))
Compiler

Compiled 103148 to 73135 computations (29.1% saved)

regimes906.0ms (10.4%)

Accuracy

Total 0.1b remaining (65.4%)

Threshold costs 0.1b (65.4%)

Counts
104 → 1
Compiler

Compiled 19322 to 12118 computations (37.3% saved)

simplify7.0ms (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
01016
11416
21916
32116
42216
52216

end1.0ms (0%)

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample995.0ms (11.4%)

Algorithm
intervals
Results
477.0ms8000×body128valid
2.0ms42×body128invalid
Compiler

Compiled 478 to 298 computations (37.7% saved)

Profiling

Loading profile data...