Details

Time bar (total: 4.3s)

analyze54.0ms (1.2%)

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)

sample92.0ms (2.1%)

Algorithm
intervals
Symmetry

(sort a x)

Results
16.0ms54×body1024valid
11.0ms39×body2048valid
5.0ms46×body512valid
3.0ms96×body128valid
1.0ms21×body256valid
0.0msbody128invalid
Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify74.0ms (1.7%)

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))

series7.0ms (0.2%)

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))

simplify71.0ms (1.6%)

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

prune10.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New18119
Fresh000
Picked011
Done000
Total18220
Error
0.0b
Counts
20 → 2
Alt Table
StatusErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
18.8b
(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))
Compiler

Compiled 261 to 121 computations (53.6% 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)))
0.2b
(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))
18.8b
(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))

series41.0ms (1%)

Counts
3 → 72
Calls

3 calls:

20.0ms
(*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x)))
15.0ms
(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))
6.0ms
(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))

rewrite13.0ms (0.3%)

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:

4.0ms
(*.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)))

simplify108.0ms (2.5%)

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

prune84.0ms (1.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1681169
Fresh000
Picked011
Done011
Total1683171
Error
0.0b
Counts
171 → 3
Alt Table
StatusErrorProgram
46.5b
(pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)
18.8b
(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))
0.0b
(expm1.f64 (*.f64 a x))
Compiler

Compiled 3515 to 1095 computations (68.8% saved)

localize7.0ms (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)))
0.2b
(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))
22.6b
(pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)

series629.0ms (14.5%)

Counts
1 → 24
Calls

1 calls:

628.0ms
(pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)

rewrite7.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
21×pow1_binary64
12×pow-pow_binary64
add-exp-log_binary64
pow-plus_binary64
pow-prod-up_binary64
Counts
1 → 31
Calls

1 calls:

5.0ms
(pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)

simplify62.0ms (1.4%)

Algorithm
egg-herbie
Rules
379×exp-sum_binary64
346×associate-*l*_binary64
309×associate-*r*_binary64
295×fma-def_binary64
240×distribute-rgt-out_binary64
Counts
55 → 49
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01011078
1199842
2500491
31742453
44053453
55058453

prune86.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1901191
Fresh000
Picked101
Done022
Total1913194
Error
0.0b
Counts
194 → 3
Alt Table
StatusErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
18.8b
(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))
46.5b
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)))
Compiler

Compiled 4288 to 1597 computations (62.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)))
0.2b
(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))
5.0b
(cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3))
22.6b
(pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)

series1.0s (23.1%)

Counts
2 → 48
Calls

2 calls:

564.0ms
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)))
437.0ms
(cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3))

rewrite21.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
37×cbrt-prod_binary64
23×add-sqr-sqrt_binary64
11×sqr-pow_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
Counts
2 → 68
Calls

2 calls:

7.0ms
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)))
1.0ms
(cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3))

simplify148.0ms (3.4%)

Algorithm
egg-herbie
Rules
668×unswap-sqr_binary64
594×fma-def_binary64
451×*-commutative_binary64
271×log-prod_binary64
246×fma-neg_binary64
Counts
116 → 120
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01553562
13612822
29251966
320021700
435851428
543561428
649991428
749731428

prune317.0ms (7.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New4681469
Fresh000
Picked101
Done022
Total4693472
Error
0b
Counts
472 → 3
Alt Table
StatusErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
18.8b
(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))
46.5b
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3))) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)) (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)))))
Compiler

Compiled 27802 to 7988 computations (71.3% saved)

regimes116.0ms (2.7%)

Accuracy

Total 0.0b remaining (27.5%)

Threshold costs 0.0b (27.5%)

Counts
25 → 1
Compiler

Compiled 2245 to 1219 computations (45.7% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
266

end6.0ms (0.1%)

Remove

(sort a x)

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.4s (31.3%)

Algorithm
intervals
Results
469.0ms1447×body2048valid
332.0ms1754×body1024valid
120.0ms1114×body512valid
98.0ms3069×body128valid
40.0ms616×body256valid
4.0ms131×body128invalid
Compiler

Compiled 132 to 50 computations (62.1% saved)

Profiling

Loading profile data...