Details

Time bar (total: 2.9s)

analyze57.0ms (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)

sample2.0s (70.3%)

Symmetry

(sort a x)

Results
732.0ms1483×body2048valid
572.0ms1813×body1024valid
285.0ms3193×body128valid
260.0ms1147×body512valid
92.0ms620×body256valid
14.0ms156×body128invalid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify74.0ms (2.6%)

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 (0.2%)

Counts
1 → 24
Calls

1 calls:

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

rewrite77.0ms (2.7%)

Algorithm
batch-egg-rewrite
Rules
736×log1p-udef_binary64
405×log1p-expm1-u_binary64
405×expm1-log1p-u_binary64
342×pow1_binary64
287×unpow-prod-down_binary64
Counts
1 → 36
Calls

1 calls:

77.0ms
(expm1.f64 (*.f64 a x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
1956
210806
346626
458836
000
100

simplify57.0ms (2%)

Algorithm
egg-herbie
Rules
1324×distribute-lft-out_binary64
882×fma-def_binary64
423×associate-/l/_binary64
368×*-commutative_binary64
362×associate-/r/_binary64
Counts
60 → 44
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
030284
186284
2234278
3888262
42148248
52915248
63566248
75038248

prune21.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New43144
Fresh000
Picked011
Done000
Total43245
Error
0b
Counts
45 → 2
Alt Table
StatusErrorProgram
21.6b
(fma.f64 a x (fma.f64 1/24 (pow.f64 (*.f64 a x) 4) (fma.f64 1/2 (pow.f64 (*.f64 a x) 2) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))))
0.0b
(expm1.f64 (*.f64 a x))
Compiler

Compiled 566 to 260 computations (54.1% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (*.f64 a x) 3)
0.2b
(pow.f64 (*.f64 a x) 4)
10.8b
(fma.f64 1/24 (pow.f64 (*.f64 a x) 4) (fma.f64 1/2 (pow.f64 (*.f64 a x) 2) (*.f64 1/6 (pow.f64 (*.f64 a x) 3))))
11.0b
(fma.f64 1/2 (pow.f64 (*.f64 a x) 2) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))

series80.0ms (2.8%)

Counts
4 → 96
Calls

4 calls:

28.0ms
(fma.f64 1/24 (pow.f64 (*.f64 a x) 4) (fma.f64 1/2 (pow.f64 (*.f64 a x) 2) (*.f64 1/6 (pow.f64 (*.f64 a x) 3))))
25.0ms
(fma.f64 1/2 (pow.f64 (*.f64 a x) 2) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))
14.0ms
(pow.f64 (*.f64 a x) 4)
12.0ms
(pow.f64 (*.f64 a x) 3)

rewrite73.0ms (2.6%)

Algorithm
batch-egg-rewrite
Rules
631×log-prod_binary64
251×expm1-udef_binary64
251×log1p-udef_binary64
216×log-pow_binary64
200×prod-diff_binary64
Counts
4 → 118
Calls

4 calls:

71.0ms
(pow.f64 (*.f64 a x) 3)
71.0ms
(pow.f64 (*.f64 a x) 4)
71.0ms
(fma.f64 1/24 (pow.f64 (*.f64 a x) 4) (fma.f64 1/2 (pow.f64 (*.f64 a x) 2) (*.f64 1/6 (pow.f64 (*.f64 a x) 3))))
71.0ms
(fma.f64 1/2 (pow.f64 (*.f64 a x) 2) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01664
134164
2324964
3558764
000
100

simplify176.0ms (6.2%)

Algorithm
egg-herbie
Rules
1219×unswap-sqr_binary64
1139×fma-def_binary64
508×*-commutative_binary64
487×sqr-pow_binary64
318×distribute-lft-out_binary64
Counts
214 → 133
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
0251728
1651728
21881696
37541628
415021404
520841404
623141296
724501296
826121296
927641296
1047671296
1144041296
1246971296
1349321296
1449621296

prune106.0ms (3.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1330133
Fresh000
Picked011
Done011
Total1332135
Error
0b
Counts
135 → 2
Alt Table
StatusErrorProgram
21.6b
(fma.f64 a x (fma.f64 1/24 (pow.f64 (*.f64 a x) 4) (fma.f64 1/2 (pow.f64 (*.f64 a x) 2) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))))
0.0b
(expm1.f64 (*.f64 a x))
Compiler

Compiled 4091 to 2368 computations (42.1% saved)

regimes57.0ms (2%)

Accuracy

Total 0.0b remaining (49.4%)

Threshold costs 0.0b (49.4%)

Counts
10 → 1
Compiler

Compiled 735 to 444 computations (39.6% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
266

end48.0ms (1.7%)

Remove

(sort a x)

Compiler

Compiled 56 to 36 computations (35.7% saved)

Profiling

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