Details

Time bar (total: 12.9s)

analyze2.7s (21.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%49.9%50.1%0
0%49.9%50.1%1
0%49.9%50.1%2
0%49.9%50.1%3
0%49.9%50.1%4
0%49.9%50.1%5
0%49.9%50.1%6
0%49.9%50.1%7
0%49.9%50.1%8
0.4%49.5%50.1%9
0.4%49.3%50.3%10
0.6%48.9%50.5%11
1.1%48.1%50.9%12
1.5%47.3%51.2%13
1.7%46.9%51.5%14
Compiler

Compiled 34 to 24 computations (29.4% saved)

sample8.4s (65.3%)

Symmetry

(sort a b)

Results
4.9s4124×body2048valid
1.9s2569×body1024valid
402.0ms613×body1024invalid
373.0ms747×body512valid
350.0ms408×body2048invalid
132.0ms312×body512invalid
107.0ms577×body128valid
85.0ms311×body128invalid
70.0ms226×body256valid
41.0ms145×body256invalid
20.0ms13×body4096valid
Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify25.0ms (0.2%)

Algorithm
egg-herbie
Rules
986×times-frac_binary64
580×associate-/l*_binary64
372×fma-def_binary64
126×distribute-rgt-in_binary64
122×distribute-lft-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01828
14728
210828
325428
489728
5529228

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
43.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
43.2b
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
Compiler

Compiled 87 to 54 computations (37.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(expm1.f64 (*.f64 eps (+.f64 a b)))
0.1b
(*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b)))
0.1b
(*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))
41.3b
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series345.0ms (2.7%)

Counts
4 → 144
Calls

4 calls:

273.0ms
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
29.0ms
(*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b)))
27.0ms
(*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))
15.0ms
(expm1.f64 (*.f64 eps (+.f64 a b)))

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube_binary64
20×add-exp-log_binary64
12×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
4 → 74
Calls

4 calls:

4.0ms
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
3.0ms
(*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b)))
3.0ms
(*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))
0.0ms
(expm1.f64 (*.f64 eps (+.f64 a b)))

simplify135.0ms (1%)

Algorithm
egg-herbie
Rules
828×fma-def_binary64
622×times-frac_binary64
470×associate-/l*_binary64
249×*-commutative_binary64
191×+-commutative_binary64
Counts
218 → 229
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
06468872
121668105
253258105

prune161.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2254229
Fresh000
Picked101
Done000
Total2264230
Error
0.0b
Counts
230 → 4
Alt Table
StatusErrorProgram
30.5b
(*.f64 (/.f64 eps (expm1.f64 (*.f64 eps a))) (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps b))))
5.5b
(fma.f64 1/12 (*.f64 a (*.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a))))
43.1b
(/.f64 1 (/.f64 (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))) (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
43.5b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))) (cbrt.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))))) (cbrt.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
Compiler

Compiled 11514 to 3875 computations (66.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (/.f64 1 b) (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)))
0.0b
(fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a))
4.6b
(*.f64 b (*.f64 eps eps))
7.4b
(*.f64 a (*.f64 eps eps))

series59.0ms (0.5%)

Counts
4 → 120
Calls

4 calls:

21.0ms
(+.f64 (/.f64 1 b) (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)))
21.0ms
(fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a))
8.0ms
(*.f64 b (*.f64 eps eps))
8.0ms
(*.f64 a (*.f64 eps eps))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
14×add-cbrt-cube_binary64
14×add-exp-log_binary64
14×pow1_binary64
Counts
4 → 81
Calls

4 calls:

6.0ms
(*.f64 b (*.f64 eps eps))
5.0ms
(+.f64 (/.f64 1 b) (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)))
5.0ms
(*.f64 a (*.f64 eps eps))
0.0ms
(fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a))

simplify106.0ms (0.8%)

Algorithm
egg-herbie
Rules
562×associate-+l+_binary64
523×associate-*l*_binary64
384×associate-*r*_binary64
262×cancel-sign-sub-inv_binary64
220×unswap-sqr_binary64
Counts
201 → 131
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01052505
12362362
26562362
322572360
445242360
550012360

prune88.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1301131
Fresh123
Picked101
Done000
Total1323135
Error
0.0b
Counts
135 → 3
Alt Table
StatusErrorProgram
43.1b
(/.f64 1 (/.f64 (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))) (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
30.5b
(*.f64 (/.f64 eps (expm1.f64 (*.f64 eps a))) (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps b))))
4.3b
(fma.f64 1/12 (*.f64 a (*.f64 eps eps)) (+.f64 (/.f64 1 b) (/.f64 1 a)))
Compiler

Compiled 3641 to 1725 computations (52.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (/.f64 1 b) (/.f64 1 a))
0.0b
(fma.f64 1/12 (*.f64 a (*.f64 eps eps)) (+.f64 (/.f64 1 b) (/.f64 1 a)))
7.4b
(*.f64 a (*.f64 eps eps))

series34.0ms (0.3%)

Counts
2 → 42
Calls

2 calls:

27.0ms
(fma.f64 1/12 (*.f64 a (*.f64 eps eps)) (+.f64 (/.f64 1 b) (/.f64 1 a)))
7.0ms
(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity_binary64
15×times-frac_binary64
13×fma-def_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
Counts
2 → 44
Calls

2 calls:

10.0ms
(+.f64 (/.f64 1 b) (/.f64 1 a))
0.0ms
(fma.f64 1/12 (*.f64 a (*.f64 eps eps)) (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify71.0ms (0.5%)

Algorithm
egg-herbie
Rules
729×fma-def_binary64
726×distribute-rgt-in_binary64
691×distribute-lft-in_binary64
423×associate-/l*_binary64
382×times-frac_binary64
Counts
86 → 71
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0581210
11431139
23561138
310371138
435231138
549171138

prune61.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1021103
Fresh112
Picked101
Done000
Total1042106
Error
0.0b
Counts
106 → 2
Alt Table
StatusErrorProgram
30.5b
(*.f64 (/.f64 eps (expm1.f64 (*.f64 eps a))) (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps b))))
3.0b
(+.f64 (/.f64 1 b) (/.f64 1 a))
Compiler

Compiled 2054 to 1167 computations (43.2% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (/.f64 1 b) (/.f64 1 a))

prune26.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New42042
Fresh011
Picked011
Done000
Total42244
Error
0.0b
Counts
44 → 2
Alt Table
StatusErrorProgram
30.5b
(*.f64 (/.f64 eps (expm1.f64 (*.f64 eps a))) (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps b))))
3.0b
(+.f64 (/.f64 1 b) (/.f64 1 a))
Compiler

Compiled 634 to 474 computations (25.2% saved)

regimes311.0ms (2.4%)

Accuracy

Total 0.1b remaining (71.7%)

Threshold costs 0.1b (71.7%)

Counts
78 → 3
Compiler

Compiled 6638 to 4176 computations (37.1% saved)

bsearch3.0ms (0%)

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
*-lft-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042142
157142
260142
358142

end208.0ms (1.6%)

Compiler

Compiled 415 to 237 computations (42.9% saved)

Profiling

Loading profile data...