Details

Time bar (total: 4.1s)

analyze87.0ms (2.1%)

Algorithm
1×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)

sample2.2s (54.1%)

Symmetry

(sort a x)

Results
753.0ms1502×body2048valid
696.0ms1884×body1024valid
357.0ms3112×body128valid
265.0ms1138×body512valid
92.0ms620×body256valid
13.0ms152×body128invalid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify74.0ms (1.8%)

Algorithm
1×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))

rewrite71.0ms (1.7%)

Algorithm
2×batch-egg-rewrite
Rules
36×egg-rr
Counts
1 → 36
Calls

2 calls:

70.0ms
((expm1.f64 (*.f64 a x)))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
1956
210806
346626
458836
000
100

simplify55.0ms (1.3%)

Algorithm
1×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

prune26.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New42244
Fresh000
Picked011
Done000
Total42345
Error
0b
Counts
45 → 3
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (*.f64 a x))
37.7b
(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) 2/3))
▶19.7b
(fma.f64 a x (*.f64 1/2 (pow.f64 (*.f64 a x) 2)))
Compiler

Compiled 566 to 260 computations (54.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 a x (*.f64 1/2 (pow.f64 (*.f64 a x) 2)))
✓0.0b
(*.f64 1/2 (pow.f64 (*.f64 a x) 2))
✓0.2b
(pow.f64 (*.f64 a x) 2)

series37.0ms (0.9%)

Counts
3 → 72
Calls

3 calls:

16.0ms
(*.f64 1/2 (pow.f64 (*.f64 a x) 2))
14.0ms
(fma.f64 a x (*.f64 1/2 (pow.f64 (*.f64 a x) 2)))
7.0ms
(pow.f64 (*.f64 a x) 2)

rewrite47.0ms (1.1%)

Algorithm
2×batch-egg-rewrite
Rules
59×egg-rr
Counts
3 → 59
Calls

2 calls:

46.0ms
((pow.f64 (*.f64 a x) 2) (*.f64 1/2 (pow.f64 (*.f64 a x) 2)) (fma.f64 a x (*.f64 1/2 (pow.f64 (*.f64 a x) 2))))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0931
118531
2190431
3512531
000
100

simplify197.0ms (4.8%)

Algorithm
1×egg-herbie
Rules
743×unswap-sqr_binary64
738×fma-def_binary64
718×sqr-pow_binary64
653×fabs-mul_binary64
584×cube-prod_binary64
Counts
131 → 65
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
011918
126918
255900
3156864
4588864
51035864
61210864
71316864
81450864
91560864
101707864
112799864
122800864
133046864
143266864
153584864
164011864
174303864
184485864
194700864
204950864

prune34.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New65065
Fresh011
Picked011
Done011
Total65368
Error
0b
Counts
68 → 3
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (*.f64 a x))
▶37.7b
(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) 2/3))
✓19.7b
(fma.f64 a x (*.f64 1/2 (pow.f64 (*.f64 a x) 2)))
Compiler

Compiled 961 to 529 computations (45% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
✓0.1b
(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) 2/3))
✓11.3b
(cbrt.f64 (expm1.f64 (*.f64 a x)))
✓11.7b
(pow.f64 (expm1.f64 (*.f64 a x)) 2/3)

series938.0ms (22.7%)

Counts
3 → 72
Calls

3 calls:

476.0ms
(cbrt.f64 (expm1.f64 (*.f64 a x)))
456.0ms
(pow.f64 (expm1.f64 (*.f64 a x)) 2/3)
6.0ms
(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) 2/3))

rewrite48.0ms (1.2%)

Algorithm
2×batch-egg-rewrite
Rules
72×egg-rr
Counts
3 → 72
Calls

2 calls:

46.0ms
((pow.f64 (expm1.f64 (*.f64 a x)) 2/3) (cbrt.f64 (expm1.f64 (*.f64 a x))) (*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) 2/3)))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0923
115923
2162323
3491823
000
100

simplify83.0ms (2%)

Algorithm
1×egg-herbie
Rules
740×associate-*l*_binary64
627×associate-*r*_binary64
556×fma-def_binary64
434×distribute-rgt-out_binary64
362×distribute-lft-out_binary64
Counts
144 → 101
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0831420
12601412
26901142
330961002
44755972
54953972

prune91.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1890189
Fresh000
Picked011
Done022
Total1893192
Error
0b
Counts
192 → 3
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (*.f64 a x))
✓37.7b
(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) 2/3))
✓19.7b
(fma.f64 a x (*.f64 1/2 (pow.f64 (*.f64 a x) 2)))
Compiler

Compiled 3669 to 1519 computations (58.6% saved)

regimes30.0ms (0.7%)

Accuracy

Total 0.0b remaining (40.4%)

Threshold costs 0.0b (40.4%)

Counts
5 → 1
Compiler

Compiled 275 to 179 computations (34.9% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
266

end52.0ms (1.3%)

Remove

(sort a x)

Compiler

Compiled 56 to 36 computations (35.7% saved)

Profiling

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