Details

Time bar (total: 35.6s)

analyze782.0ms (2.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
25%74.9%0.1%4
50%50%0.1%5
50%50%0.1%6
50%50%0.1%7
50%50%0.1%8
50%50%0.1%9
50%50%0.1%10
50%50%0.1%11
50%50%0.1%12
50%50%0.1%13
50%50%0.1%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample12.8s (35.9%)

Symmetry

(sort a b)

Results
10.0s7892×body8192exit
1.4s1972×body1024valid
603.0ms4561×body128valid
422.0ms997×body512valid
180.0ms200×body2048valid
140.0ms526×body256valid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify9.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
1810
2810

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
31.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
31.9b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (exp.f64 a) (exp.f64 b))
3.3b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series433.0ms (1.2%)

Counts
2 → 48
Calls

2 calls:

427.0ms
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms
(+.f64 (exp.f64 a) (exp.f64 b))

rewrite7.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-log-exp_binary64
add-sqr-sqrt_binary64
log-prod_binary64
add-cube-cbrt_binary64
Counts
2 → 34
Calls

2 calls:

3.0ms
(+.f64 (exp.f64 a) (exp.f64 b))
3.0ms
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

simplify96.0ms (0.3%)

Algorithm
egg-herbie
Rules
618×fma-neg_binary64
418×associate-+l+_binary64
392×fma-def_binary64
238×times-frac_binary64
229×associate-+r+_binary64
Counts
82 → 83
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01231238
13341183
210341155
340621151
448281151
549731151

prune49.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New81283
Fresh000
Picked011
Done000
Total81384
Error
0.4b
Counts
84 → 3
Alt Table
StatusErrorProgram
0.6b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
31.9b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
31.9b
(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
Compiler

Compiled 1349 to 614 computations (54.5% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1 (exp.f64 a))
0.0b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

series242.0ms (0.7%)

Counts
2 → 28
Calls

2 calls:

240.0ms
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
2.0ms
(+.f64 1 (exp.f64 a))

rewrite12.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-log-exp_binary64
fma-def_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 35
Calls

2 calls:

8.0ms
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
2.0ms
(+.f64 1 (exp.f64 a))

simplify67.0ms (0.2%)

Algorithm
egg-herbie
Rules
786×fma-neg_binary64
496×associate-+r+_binary64
405×times-frac_binary64
356×associate-*l*_binary64
317×fma-def_binary64
Counts
63 → 59
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
088955
1256894
2626884
31780874
43990873
55038873

prune44.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New57259
Fresh011
Picked011
Done011
Total57562
Error
0.4b
Counts
62 → 5
Alt Table
StatusErrorProgram
0.6b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
17.9b
(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
0.9b
(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
31.9b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
31.9b
(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
Compiler

Compiled 1054 to 574 computations (45.5% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1 (exp.f64 a))
0.0b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
0.0b
(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
0.1b
(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

series889.0ms (2.5%)

Counts
2 → 48
Calls

2 calls:

646.0ms
(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
242.0ms
(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
expm1-log1p-u_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 22
Calls

2 calls:

0.0ms
(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
0.0ms
(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

simplify104.0ms (0.3%)

Algorithm
egg-herbie
Rules
427×associate-+r+_binary64
269×associate-+l+_binary64
268×+-commutative_binary64
226×cancel-sign-sub-inv_binary64
216×times-frac_binary64
Counts
70 → 76
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02813342
18793194
237483133
349633133
449763133

prune134.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1332135
Fresh112
Picked101
Done022
Total1355140
Error
0.4b
Counts
140 → 5
Alt Table
StatusErrorProgram
31.9b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
63.4b
(expm1.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (-.f64 (+.f64 (/.f64 1 b) (+.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (*.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (exp.f64 a)))) (log1p.f64 (exp.f64 a))) (log.f64 b))))
0.6b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
1.7b
(expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))
31.9b
(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
Compiler

Compiled 5156 to 3150 computations (38.9% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))
0.2b
(*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
0.3b
(*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
0.3b
(cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

series16.9s (47.5%)

Counts
4 → 96
Calls

4 calls:

13.8s
(*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
2.2s
(cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
659.0ms
(*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
239.0ms
(expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))

rewrite25.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
30×pow1_binary64
25×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
16×pow1/3_binary64
15×*-un-lft-identity_binary64
Counts
4 → 104
Calls

4 calls:

8.0ms
(*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
6.0ms
(*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
1.0ms
(cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
0.0ms
(expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))

simplify515.0ms (1.4%)

Algorithm
egg-herbie
Rules
944×fma-def_binary64
404×associate-/l*_binary64
79×sqr-pow_binary64
36×sub-neg_binary64
34×unpow1/3_binary64
Counts
200 → 226
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0351255888
1533455888

prune2.0s (5.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New3191320
Fresh022
Picked101
Done022
Total3205325
Error
0.4b
Counts
325 → 5
Alt Table
StatusErrorProgram
31.9b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
63.4b
(expm1.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (-.f64 (+.f64 (/.f64 1 b) (+.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (*.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (exp.f64 a)))) (log1p.f64 (exp.f64 a))) (log.f64 b))))
0.6b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
1.9b
(expm1.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))))
31.9b
(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
Compiler

Compiled 110531 to 77923 computations (29.5% saved)

regimes208.0ms (0.6%)

Accuracy

Total 0.6b remaining (53.7%)

Threshold costs 0.6b (53.7%)

Counts
38 → 1
Compiler

Compiled 4893 to 3380 computations (30.9% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
11316
21216

end259.0ms (0.7%)

Compiler

Compiled 233 to 140 computations (39.9% saved)

Profiling

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