Details

Time bar (total: 2.5min)

analyze303.0ms (0.2%)

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
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)

sample266.0ms (0.2%)

Algorithm
intervals
Results
15.0ms256×body128valid
0.0msbody128invalid
Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify126.0ms (0.1%)

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)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
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)

series137.0ms (0.1%)

Counts
2 → 60
Calls

2 calls:

84.0ms
(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
52.0ms
(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

rewrite12.0ms (0%)

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity_binary64
29×add-sqr-sqrt_binary64
24×prod-diff_binary64
19×add-cube-cbrt_binary64
14×associate--r+_binary64
Counts
2 → 65
Calls

2 calls:

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

simplify130.0ms (0.1%)

Algorithm
egg-herbie
Rules
667×fma-def_binary64
547×distribute-rgt-in_binary64
508×distribute-lft-in_binary64
456×fma-neg_binary64
232×exp-sum_binary64
Counts
125 → 125
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01712510
13732200
212561943
344721943
451111943

prune151.0ms (0.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1187125
Fresh000
Picked101
Done000
Total1197126
Error
0.0b
Counts
126 → 7
Alt Table
StatusErrorProgram
47.2b
(-.f64 y (-.f64 (log.f64 (*.f64 (exp.f64 z) (pow.f64 y (+.f64 1/2 y)))) x))
62.5b
(-.f64 y (-.f64 (log1p.f64 (expm1.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
0.1b
(+.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) x)
25.2b
(*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (-.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
46.1b
(/.f64 (-.f64 (pow.f64 y 3) (pow.f64 (-.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) x) 3)) (fma.f64 y y (*.f64 (-.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) x) (+.f64 y (-.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) x)))))
1.4b
(*.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))))
44.7b
(*.f64 (+.f64 1 (log.f64 (/.f64 1 y))) y)
Compiler

Compiled 3297 to 1680 computations (49% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

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

series53.0ms (0%)

Counts
1 → 24
Calls

1 calls:

52.0ms
(-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))

rewrite5.0ms (0%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
prod-diff_binary64
add-cube-cbrt_binary64
cancel-sign-sub-inv_binary64
Counts
1 → 31
Calls

1 calls:

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

simplify110.0ms (0.1%)

Algorithm
egg-herbie
Rules
449×distribute-rgt-in_binary64
440×associate-*l*_binary64
433×distribute-lft-in_binary64
408×fma-def_binary64
379×associate-*r*_binary64
Counts
55 → 62
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01041128
1226979
2723852
34560852
44987852
55000852
64863852

prune92.0ms (0.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New90494
Fresh516
Picked011
Done000
Total956101
Error
0.0b
Counts
101 → 6
Alt Table
StatusErrorProgram
0.9b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) x)
47.2b
(-.f64 y (-.f64 (log.f64 (*.f64 (exp.f64 z) (pow.f64 y (+.f64 1/2 y)))) x))
18.9b
(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
0.1b
(+.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) x)
28.1b
(+.f64 (*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (-.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) x)
36.5b
(+.f64 (/.f64 (-.f64 (pow.f64 y 3) (pow.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) 3)) (fma.f64 y y (*.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) (+.f64 z (fma.f64 (log.f64 y) (+.f64 1/2 y) y))))) x)
Compiler

Compiled 2246 to 1234 computations (45.1% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 (+.f64 y 1/2) (log.f64 y) z)
0.4b
(*.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))
0.5b
(*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))
0.5b
(cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))

series7.0s (4.7%)

Counts
3 → 72
Calls

3 calls:

6.7s
(*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))
287.0ms
(cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))
57.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))

rewrite55.0ms (0%)

Algorithm
rewrite-expression-head
Rules
68×cbrt-div_binary64
39×cbrt-prod_binary64
36×add-sqr-sqrt_binary64
34×flip--_binary64
34×flip3--_binary64
Counts
3 → 141
Calls

3 calls:

13.0ms
(*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))
12.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))
2.0ms
(cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))

simplify369.0ms (0.2%)

Algorithm
egg-herbie
Rules
458×fma-def_binary64
413×associate-*r*_binary64
245×associate-/l*_binary64
243×associate-*r/_binary64
226×associate-/r*_binary64
Counts
213 → 274
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0188636086
1505436086

prune1.5s (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4973500
Fresh134
Picked011
Done011
Total4988506
Error
0.0b
Counts
506 → 8
Alt Table
StatusErrorProgram
0.9b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) x)
1.1b
(+.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) x)
18.9b
(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
0.1b
(+.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) x)
1.5b
(+.f64 (*.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) x)
29.7b
(+.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y y) (*.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) (cbrt.f64 (-.f64 (*.f64 y y) (*.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (*.f64 (cbrt.f64 (+.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (+.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) x)
28.1b
(+.f64 (*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (-.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))) x)
36.5b
(+.f64 (/.f64 (-.f64 (pow.f64 y 3) (pow.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) 3)) (fma.f64 y y (*.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) (+.f64 z (fma.f64 (log.f64 y) (+.f64 1/2 y) y))))) x)
Compiler

Compiled 73091 to 53224 computations (27.2% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))))
0.5b
(*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))
0.5b
(cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))
0.6b
(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))))

series2.2min (87.4%)

Counts
2 → 48
Calls

2 calls:

2.1min
(*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))))
5.2s
(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))))

rewrite102.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
380×cbrt-div_binary64
140×frac-times_binary64
114×flip--_binary64
114×flip3--_binary64
46×associate-*r/_binary64
Counts
2 → 135
Calls

2 calls:

8.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z)))))
8.0ms
(*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (+.f64 y 1/2) (log.f64 y) z))))))

simplify882.0ms (0.6%)

Algorithm
egg-herbie
Counts
183 → 171
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06100141349

prune7.4s (5%)

Compiler

Compiled 338360 to 257325 computations (23.9% saved)

Profiling

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