Details

Time bar (total: 5.9s)

analyze343.0ms (5.9%)

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)

sample141.0ms (2.4%)

Algorithm
intervals
Results
19.0ms256×body128valid
Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify125.0ms (2.1%)

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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.1b
(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
0.1b
(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
Compiler

Compiled 84 to 53 computations (36.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series332.0ms (5.7%)

Counts
4 → 96
Calls

4 calls:

153.0ms
(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
90.0ms
(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
79.0ms
(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
10.0ms
(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite163.0ms (2.8%)

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity_binary64
27×add-sqr-sqrt_binary64
23×add-cube-cbrt_binary64
20×add-log-exp_binary64
18×prod-diff_binary64
Counts
4 → 119
Calls

4 calls:

142.0ms
(*.f64 (+.f64 y 1/2) (log.f64 y))
7.0ms
(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
5.0ms
(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
3.0ms
(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify198.0ms (3.4%)

Algorithm
egg-herbie
Rules
374×fma-neg_binary64
307×associate--l+_binary64
299×cancel-sign-sub-inv_binary64
275×exp-sum_binary64
242×exp-diff_binary64
Counts
215 → 219
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02423418
16093074
220222997
343502997
448732997

prune301.0ms (5.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2118219
Fresh101
Picked101
Done000
Total2138221
Error
0.0b
Counts
221 → 8
Alt Table
StatusErrorProgram
0.1b
(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
24.4b
(-.f64 (/.f64 (-.f64 (*.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))) (*.f64 y y)) (-.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)) z)
13.9b
(-.f64 (+.f64 (-.f64 x (/.f64 (*.f64 (log.f64 y) (fma.f64 y y -1/4)) (-.f64 y 1/2))) y) z)
35.8b
(-.f64 (+.f64 (-.f64 x (*.f64 (sqrt.f64 (*.f64 (+.f64 y 1/2) (log.f64 y))) (sqrt.f64 (*.f64 (+.f64 y 1/2) (log.f64 y))))) y) z)
30.2b
(-.f64 (/.f64 (+.f64 (pow.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) 3) (pow.f64 y 3)) (+.f64 (*.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))) (-.f64 (*.f64 y y) (*.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)))) z)
0.9b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)) (cbrt.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x))) (cbrt.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x))) z)
32.9b
(-.f64 (+.f64 (expm1.f64 (log1p.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))))) y) z)
0.2b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
Compiler

Compiled 4815 to 2597 computations (46.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
0.0b
(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
0.2b
(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

series155.0ms (2.6%)

Counts
3 → 72
Calls

3 calls:

95.0ms
(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
51.0ms
(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
9.0ms
(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
12×prod-diff_binary64
10×add-log-exp_binary64
Counts
3 → 65
Calls

3 calls:

7.0ms
(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
2.0ms
(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
0.0ms
(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

simplify103.0ms (1.8%)

Algorithm
egg-herbie
Rules
605×fma-neg_binary64
603×fma-def_binary64
350×distribute-rgt-in_binary64
341×associate-*l*_binary64
318×distribute-lft-in_binary64
Counts
137 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01482390
13632232
211082071
345622071
450372071

prune110.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1092111
Fresh257
Picked011
Done000
Total1118119
Error
0.0b
Counts
119 → 8
Alt Table
StatusErrorProgram
0.1b
(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
24.4b
(-.f64 (/.f64 (-.f64 (*.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))) (*.f64 y y)) (-.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)) z)
28.6b
(-.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y))) x) z)
0.2b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
13.9b
(-.f64 (+.f64 (-.f64 x (/.f64 (*.f64 (log.f64 y) (fma.f64 y y -1/4)) (-.f64 y 1/2))) y) z)
35.8b
(-.f64 (+.f64 (-.f64 x (*.f64 (sqrt.f64 (*.f64 (+.f64 y 1/2) (log.f64 y))) (sqrt.f64 (*.f64 (+.f64 y 1/2) (log.f64 y))))) y) z)
30.2b
(-.f64 (/.f64 (+.f64 (pow.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) 3) (pow.f64 y 3)) (+.f64 (*.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))) (-.f64 (*.f64 y y) (*.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)))) z)
0.6b
(-.f64 (fma.f64 (*.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y))) (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) x) z)
Compiler

Compiled 2637 to 1387 computations (47.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y)))
0.1b
(*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y))))
0.2b
(+.f64 (*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
0.6b
(cbrt.f64 y)

series639.0ms (10.9%)

Counts
4 → 48
Calls

4 calls:

286.0ms
(+.f64 (*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
166.0ms
(*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y))))
153.0ms
(*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y)))
32.0ms
(cbrt.f64 y)

rewrite37.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
72×log-prod_binary64
60×distribute-lft-in_binary64
60×distribute-rgt-in_binary64
39×cbrt-prod_binary64
36×*-un-lft-identity_binary64
Counts
4 → 152
Calls

4 calls:

12.0ms
(+.f64 (*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
6.0ms
(*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y))))
6.0ms
(*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y)))
1.0ms
(cbrt.f64 y)

simplify137.0ms (2.3%)

Algorithm
egg-herbie
Rules
707×fma-neg_binary64
346×associate-*l*_binary64
337×associate-*r*_binary64
279×distribute-rgt-out_binary64
242×fma-def_binary64
Counts
200 → 275
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02503870
16483338
226063114
345193114
448993114

prune391.0ms (6.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2912293
Fresh246
Picked101
Done011
Total2947301
Error
0b
Counts
301 → 7
Alt Table
StatusErrorProgram
0.2b
(-.f64 (+.f64 (-.f64 x (*.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y) z)
28.6b
(-.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y))) x) z)
13.9b
(-.f64 (+.f64 (-.f64 x (/.f64 (*.f64 (log.f64 y) (fma.f64 y y -1/4)) (-.f64 y 1/2))) y) z)
35.8b
(-.f64 (+.f64 (-.f64 x (*.f64 (sqrt.f64 (*.f64 (+.f64 y 1/2) (log.f64 y))) (sqrt.f64 (*.f64 (+.f64 y 1/2) (log.f64 y))))) y) z)
0.1b
(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
0.2b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (pow.f64 y 1/3))))) y) z)
30.2b
(-.f64 (/.f64 (+.f64 (pow.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) 3) (pow.f64 y 3)) (+.f64 (*.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))) (-.f64 (*.f64 y y) (*.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)))) z)
Compiler

Compiled 9172 to 5119 computations (44.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y))))
0.2b
(+.f64 (*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (pow.f64 y 1/3))))
0.6b
(cbrt.f64 y)
4.9b
(pow.f64 y 1/3)

series350.0ms (6%)

Counts
2 → 16
Calls

2 calls:

326.0ms
(+.f64 (*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (pow.f64 y 1/3))))
23.0ms
(pow.f64 y 1/3)

rewrite20.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
38×log-prod_binary64
31×distribute-lft-in_binary64
31×distribute-rgt-in_binary64
24×associate-+l+_binary64
16×*-un-lft-identity_binary64
Counts
2 → 77
Calls

2 calls:

12.0ms
(+.f64 (*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (pow.f64 y 1/3))))
1.0ms
(pow.f64 y 1/3)

simplify131.0ms (2.2%)

Algorithm
egg-herbie
Rules
400×associate-+l+_binary64
243×fma-def_binary64
242×log-prod_binary64
240×distribute-rgt-out_binary64
233×cancel-sign-sub-inv_binary64
Counts
93 → 148
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02212183
15871860
222291337
346241323
449331323
549991323
649771323

prune313.0ms (5.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2400240
Fresh055
Picked011
Done011
Total2407247
Error
0b
Counts
247 → 7
Alt Table
StatusErrorProgram
0.2b
(-.f64 (+.f64 (-.f64 x (*.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y) z)
28.6b
(-.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y))) x) z)
13.9b
(-.f64 (+.f64 (-.f64 x (/.f64 (*.f64 (log.f64 y) (fma.f64 y y -1/4)) (-.f64 y 1/2))) y) z)
35.8b
(-.f64 (+.f64 (-.f64 x (*.f64 (sqrt.f64 (*.f64 (+.f64 y 1/2) (log.f64 y))) (sqrt.f64 (*.f64 (+.f64 y 1/2) (log.f64 y))))) y) z)
0.1b
(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
0.2b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 1/2 y) (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 1/2 y) (log.f64 (pow.f64 y 1/3))))) y) z)
30.2b
(-.f64 (/.f64 (+.f64 (pow.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) 3) (pow.f64 y 3)) (+.f64 (*.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))) (-.f64 (*.f64 y y) (*.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)))) z)
Compiler

Compiled 7614 to 4833 computations (36.5% saved)

regimes920.0ms (15.7%)

Accuracy

Total 0.1b remaining (80.9%)

Threshold costs 0.1b (80.9%)

Counts
167 → 1
Compiler

Compiled 16562 to 11107 computations (32.9% saved)

simplify3.0ms (0%)

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
01216
11816
22516
32916
43116
53116

end0.0ms (0%)

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample876.0ms (15%)

Algorithm
intervals
Results
501.0ms8000×body128valid
2.0ms34×body128invalid
Compiler

Compiled 208 to 141 computations (32.2% saved)

Profiling

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