Details

Time bar (total: 4.5s)

analyze60.0ms (1.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
50%50%0.1%3
50%50%0.1%4
62.4%37.5%0.1%5
62.4%31.2%6.3%6
68.7%21.9%9.5%7
68.7%17.2%14.1%8
71.8%11.7%16.5%9
71.8%9%19.2%10
73.4%6%20.6%11
73.4%4.6%22%12
74.1%3.1%22.8%13
74.1%2.3%23.5%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.1s (47%)

Symmetry

(sort a x)

Results
812.0ms1624×body2048valid
559.0ms1789×body1024valid
284.0ms3023×body128valid
262.0ms1174×body512valid
106.0ms646×body256valid
12.0ms138×body128invalid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify70.0ms (1.6%)

Algorithm
egg-herbie
Rules
571×fma-neg_binary64
455×*-commutative_binary64
440×unswap-sqr_binary64
344×associate-*l*_binary64
274×associate-+l+_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
076
1166
2236
3356
4706
51606
64326
715646
834906
949546
1049936
1148746

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
Compiler

Compiled 24 to 15 computations (37.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(expm1.f64 (*.f64 a x))

series6.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

6.0ms
(expm1.f64 (*.f64 a x))

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
log1p-expm1-u_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
1 → 11
Calls

1 calls:

0.0ms
(expm1.f64 (*.f64 a x))

simplify67.0ms (1.5%)

Algorithm
egg-herbie
Rules
910×fma-def_binary64
844×distribute-lft-out_binary64
785×fma-neg_binary64
383×*-commutative_binary64
308×unswap-sqr_binary64
Counts
35 → 19
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
040382
196369
2262363
3966347
42376333
53696333
64842333
75375333

prune12.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New17219
Fresh000
Picked011
Done000
Total17320
Error
0.0b
Counts
20 → 3
Alt Table
StatusErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
19.8b
(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))
21.0b
(fma.f64 x (fma.f64 x (*.f64 1/2 (*.f64 a a)) a) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))
Compiler

Compiled 299 to 145 computations (51.5% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
0.1b
(*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x)))
0.1b
(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))
19.8b
(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))

series45.0ms (1%)

Counts
3 → 72
Calls

3 calls:

22.0ms
(*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x)))
12.0ms
(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))
11.0ms
(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))

rewrite17.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
13×add-cbrt-cube_binary64
11×add-sqr-sqrt_binary64
10×add-exp-log_binary64
*-un-lft-identity_binary64
Counts
3 → 70
Calls

3 calls:

5.0ms
(*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x)))
3.0ms
(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))
3.0ms
(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))

simplify106.0ms (2.4%)

Algorithm
egg-herbie
Rules
627×fma-neg_binary64
445×fma-def_binary64
248×distribute-neg-in_binary64
237×*-commutative_binary64
233×sqr-pow_binary64
Counts
142 → 112
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01071870
12461686
27781664
321261610
429091543
547661543
652511543

prune94.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1672169
Fresh011
Picked101
Done011
Total1684172
Error
0b
Counts
172 → 4
Alt Table
StatusErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
19.8b
(cbrt.f64 (expm1.f64 (log1p.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))))
21.0b
(fma.f64 x (fma.f64 x (*.f64 1/2 (*.f64 a a)) a) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))
13.6b
(*.f64 (cbrt.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
Compiler

Compiled 3574 to 1130 computations (68.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))
0.2b
(*.f64 (cbrt.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
10.5b
(cbrt.f64 (expm1.f64 (*.f64 a x)))
21.9b
(cbrt.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))))

series1.0s (23%)

Counts
3 → 72
Calls

3 calls:

589.0ms
(cbrt.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))))
427.0ms
(cbrt.f64 (expm1.f64 (*.f64 a x)))
6.0ms
(*.f64 (cbrt.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

rewrite11.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod_binary64
13×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
associate-*r*_binary64
Counts
3 → 54
Calls

3 calls:

4.0ms
(*.f64 (cbrt.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
2.0ms
(cbrt.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))))
1.0ms
(cbrt.f64 (expm1.f64 (*.f64 a x)))

simplify112.0ms (2.5%)

Algorithm
egg-herbie
Rules
731×fma-def_binary64
449×*-commutative_binary64
249×log-prod_binary64
241×sqr-pow_binary64
217×unswap-sqr_binary64
Counts
126 → 111
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01532373
13882304
211171982
326051576
438361508
546611500
649521500

prune87.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1550155
Fresh022
Picked011
Done011
Total1554159
Error
0b
Counts
159 → 4
Alt Table
StatusErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
19.8b
(cbrt.f64 (expm1.f64 (log1p.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))))
21.0b
(fma.f64 x (fma.f64 x (*.f64 1/2 (*.f64 a a)) a) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))
13.6b
(*.f64 (cbrt.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
Compiler

Compiled 3784 to 1169 computations (69.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
0.1b
(*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x)))
0.1b
(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))
19.8b
(cbrt.f64 (expm1.f64 (log1p.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))))

series7.0ms (0.2%)

Counts
1 → 24
Calls

1 calls:

7.0ms
(cbrt.f64 (expm1.f64 (log1p.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))))

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
cbrt-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
1 → 13
Calls

1 calls:

1.0ms
(cbrt.f64 (expm1.f64 (log1p.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))))

simplify70.0ms (1.6%)

Algorithm
egg-herbie
Rules
910×fma-def_binary64
844×distribute-lft-out_binary64
785×fma-neg_binary64
386×*-commutative_binary64
308×unswap-sqr_binary64
Counts
37 → 31
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
049657
1106475
2268414
3964398
42374380
53682380
64833380
75364380

prune110.0ms (2.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1730173
Fresh011
Picked011
Done022
Total1734177
Error
0b
Counts
177 → 4
Alt Table
StatusErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
19.8b
(cbrt.f64 (expm1.f64 (log1p.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))))
21.0b
(fma.f64 x (fma.f64 x (*.f64 1/2 (*.f64 a a)) a) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))
13.6b
(*.f64 (cbrt.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
Compiler

Compiled 3944 to 1378 computations (65.1% saved)

regimes370.0ms (8.3%)

Accuracy

Total 0.0b remaining (32.3%)

Threshold costs 0.0b (32.3%)

Counts
70 → 1
Compiler

Compiled 5320 to 3538 computations (33.5% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
266

end63.0ms (1.4%)

Remove

(sort a x)

Compiler

Compiled 86 to 49 computations (43% saved)

Profiling

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