Details

Time bar (total: 11.0s)

analyze2.3s (20.7%)

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)

sample265.0ms (2.4%)

Algorithm
intervals
Symmetry

(sort a b)

Results
117.0ms133×body2048valid
36.0ms66×body1024valid
8.0ms22×body1024overflowed
8.0ms28×body512valid
8.0ms311×pre128true
5.0ms10×body2048overflowed
3.0ms11×body512overflowed
2.0ms21×body128valid
1.0msbody256valid
1.0msbody256overflowed
1.0msbody4096valid
1.0msbody128overflowed
Compiler

Compiled 64 to 46 computations (28.1% saved)

simplify24.0ms (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

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
40.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
40.1b
(/.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
(*.f64 eps (+.f64 a b))
0.1b
(*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))
0.2b
(*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b)))
38.4b
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series365.0ms (3.3%)

Counts
4 → 132
Calls

4 calls:

295.0ms
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
33.0ms
(*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b)))
30.0ms
(*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))
6.0ms
(*.f64 eps (+.f64 a b))

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
22×add-cbrt-cube_binary64
22×add-exp-log_binary64
16×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64
10×associate-*r*_binary64
Counts
4 → 88
Calls

4 calls:

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

simplify122.0ms (1.1%)

Algorithm
egg-herbie
Rules
712×fma-def_binary64
622×times-frac_binary64
470×associate-/l*_binary64
257×*-commutative_binary64
166×+-commutative_binary64
Counts
220 → 226
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
06388331
121077574
253177574

prune246.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2224226
Fresh000
Picked101
Done000
Total2234227
Error
0.0b
Counts
227 → 4
Alt Table
StatusErrorProgram
30.4b
(/.f64 eps (/.f64 (expm1.f64 (*.f64 a eps)) (/.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
15.4b
(/.f64 (+.f64 a b) (*.f64 a b))
8.6b
(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))))
40.3b
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (*.f64 (*.f64 (cbrt.f64 (expm1.f64 (*.f64 eps a))) (cbrt.f64 (expm1.f64 (*.f64 eps a)))) (*.f64 (cbrt.f64 (expm1.f64 (*.f64 eps a))) (expm1.f64 (*.f64 eps b)))))
Compiler

Compiled 10803 to 3550 computations (67.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(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))))
0.0b
(fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a))
6.0b
(*.f64 b (*.f64 eps eps))
6.8b
(*.f64 a (*.f64 eps eps))

series97.0ms (0.9%)

Counts
4 → 120
Calls

4 calls:

48.0ms
(fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a))
30.0ms
(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))))
9.0ms
(*.f64 b (*.f64 eps eps))
8.0ms
(*.f64 a (*.f64 eps eps))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube_binary64
14×add-exp-log_binary64
14×pow1_binary64
add-sqr-sqrt_binary64
associate-*l*_binary64
Counts
4 → 62
Calls

4 calls:

5.0ms
(*.f64 a (*.f64 eps eps))
4.0ms
(*.f64 b (*.f64 eps eps))
0.0ms
(fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a))
0.0ms
(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))))

simplify135.0ms (1.2%)

Algorithm
egg-herbie
Rules
766×unswap-sqr_binary64
610×fma-def_binary64
470×associate-*l*_binary64
333×associate-*r*_binary64
295×associate-+r+_binary64
Counts
182 → 122
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01032698
12022339
25492269
316512269
437882269
550582269

prune82.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1211122
Fresh123
Picked101
Done000
Total1233126
Error
0.0b
Counts
126 → 3
Alt Table
StatusErrorProgram
4.6b
(+.f64 (/.f64 1 b) (/.f64 1 a))
30.4b
(/.f64 eps (/.f64 (expm1.f64 (*.f64 a eps)) (/.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
15.4b
(/.f64 (+.f64 a b) (*.f64 a b))
Compiler

Compiled 3072 to 1488 computations (51.6% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.1%)

Counts
1 → 6
Calls

1 calls:

5.0ms
(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite17.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity_binary64
15×times-frac_binary64
13×fma-def_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
Counts
1 → 34
Calls

1 calls:

15.0ms
(+.f64 (/.f64 1 b) (/.f64 1 a))

simplify115.0ms (1%)

Algorithm
egg-herbie
Rules
450×fma-neg_binary64
421×div-sub_binary64
357×fma-def_binary64
329×sub-neg_binary64
281×distribute-rgt-in_binary64
Counts
40 → 37
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036332
1106302
2241301
3565301
41313301
52794301
64202301
74546301
84845301
94973301
104870301

prune27.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New37037
Fresh022
Picked011
Done000
Total37340
Error
0.0b
Counts
40 → 3
Alt Table
StatusErrorProgram
4.6b
(+.f64 (/.f64 1 b) (/.f64 1 a))
30.4b
(/.f64 eps (/.f64 (expm1.f64 (*.f64 a eps)) (/.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
15.4b
(/.f64 (+.f64 a b) (*.f64 a b))
Compiler

Compiled 589 to 430 computations (27% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

NewErrorProgram
14.8b
(/.f64 (+.f64 a b) (*.f64 a b))

series7.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

7.0ms
(/.f64 (+.f64 a b) (*.f64 a b))

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
associate-/l*_binary64
times-frac_binary64
Counts
1 → 27
Calls

1 calls:

5.0ms
(/.f64 (+.f64 a b) (*.f64 a b))

simplify82.0ms (0.7%)

Algorithm
egg-herbie
Rules
581×associate-/r*_binary64
450×sub-neg_binary64
441×associate-/r/_binary64
370×fma-def_binary64
349×distribute-rgt-in_binary64
Counts
51 → 33
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
057613
1152550
2469550
31544550
43494550
53895550
64902550
75491550

prune17.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New32133
Fresh011
Picked011
Done011
Total32436
Error
0b
Counts
36 → 4
Alt Table
StatusErrorProgram
4.6b
(+.f64 (/.f64 1 b) (/.f64 1 a))
30.4b
(/.f64 eps (/.f64 (expm1.f64 (*.f64 a eps)) (/.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
15.4b
(/.f64 (+.f64 a b) (*.f64 a b))
11.5b
(*.f64 (/.f64 1 a) (/.f64 (+.f64 a b) b))
Compiler

Compiled 479 to 158 computations (67% saved)

regimes260.0ms (2.4%)

Accuracy

Total 0.0b remaining (37.1%)

Threshold costs 0.0b (37.1%)

Counts
45 → 3
Compiler

Compiled 3770 to 2320 computations (38.5% saved)

bsearch2.0ms (0%)

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
1-exp_binary64
if-if-or-not_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037124
153124
256124
354124

end7.0ms (0.1%)

Remove

(sort a b)

Compiler

Compiled 249 to 138 computations (44.6% saved)

sample6.8s (61.6%)

Algorithm
intervals
Results
3.7s4094×body2048valid
1.2s2380×body1024valid
297.0ms589×body1024overflowed
263.0ms9662×pre128true
230.0ms376×body2048overflowed
221.0ms732×body512valid
78.0ms288×body512overflowed
72.0ms534×body128valid
46.0ms245×body256valid
28.0ms275×body128overflowed
24.0ms133×body256overflowed
22.0ms15×body4096valid
1.0msbody2048invalid
Compiler

Compiled 173 to 108 computations (37.6% saved)

Profiling

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