Details

Time bar (total: 12.1s)

analyze187.0ms (1.5%)

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%37.5%12.6%6
50%25%25.1%7
50%18.7%31.3%8
50%12.5%37.6%9
50%9.4%40.7%10
50%6.2%43.8%11
50%4.7%45.4%12
50%3.1%46.9%13
50%2.3%47.7%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample212.0ms (1.8%)

Algorithm
intervals
Results
164.0ms73×body1024valid
8.0ms131×body128valid
8.0msbody2048valid
8.0ms25×body512valid
3.0ms18×body256valid
1.0msbody128overflowed
Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify7.0ms (0.1%)

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
31.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
31.7b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
Compiler

Compiled 24 to 18 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (exp.f64 a) (exp.f64 b))
4.1b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series588.0ms (4.9%)

Counts
2 → 48
Calls

2 calls:

583.0ms
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms
(+.f64 (exp.f64 a) (exp.f64 b))

rewrite8.0ms (0.1%)

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)))

simplify84.0ms (0.7%)

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

prune60.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New80383
Fresh000
Picked101
Done000
Total81384
Error
0.8b
Counts
84 → 3
Alt Table
StatusErrorProgram
32.2b
(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
1.6b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
34.4b
(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
Compiler

Compiled 1379 to 624 computations (54.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series844.0ms (7%)

Counts
4 → 44
Calls

4 calls:

427.0ms
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
371.0ms
(log1p.f64 (exp.f64 a))
42.0ms
(/.f64 b (+.f64 1 (exp.f64 a)))
3.0ms
(+.f64 1 (exp.f64 a))

rewrite37.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
15×add-cube-cbrt_binary64
12×times-frac_binary64
add-log-exp_binary64
Counts
4 → 81
Calls

4 calls:

15.0ms
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
8.0ms
(/.f64 b (+.f64 1 (exp.f64 a)))
7.0ms
(+.f64 1 (exp.f64 a))
1.0ms
(log1p.f64 (exp.f64 a))

simplify178.0ms (1.5%)

Algorithm
egg-herbie
Rules
571×fma-neg_binary64
461×cancel-sign-sub-inv_binary64
403×fma-def_binary64
224×distribute-rgt-in_binary64
201×associate-+l+_binary64
Counts
125 → 120
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01521715
13821640
29271622
325711611
447791610
549941610
649231610

prune192.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1155120
Fresh022
Picked101
Done000
Total1167123
Error
0.8b
Counts
123 → 7
Alt Table
StatusErrorProgram
19.5b
(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
34.4b
(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
1.6b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (exp.f64 (log1p.f64 (exp.f64 a)))))
2.4b
(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
27.5b
(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (log.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
27.5b
(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
32.2b
(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
Compiler

Compiled 2209 to 1168 computations (47.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series2.2s (17.9%)

Counts
3 → 60
Calls

3 calls:

1.1s
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (exp.f64 (log1p.f64 (exp.f64 a)))))
723.0ms
(/.f64 b (exp.f64 (log1p.f64 (exp.f64 a))))
344.0ms
(exp.f64 (log1p.f64 (exp.f64 a)))

rewrite23.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity_binary64
13×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
times-frac_binary64
add-log-exp_binary64
Counts
3 → 61
Calls

3 calls:

10.0ms
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (exp.f64 (log1p.f64 (exp.f64 a)))))
6.0ms
(/.f64 b (exp.f64 (log1p.f64 (exp.f64 a))))
2.0ms
(exp.f64 (log1p.f64 (exp.f64 a)))

simplify144.0ms (1.2%)

Algorithm
egg-herbie
Rules
516×fma-neg_binary64
394×associate-/l*_binary64
376×cancel-sign-sub-inv_binary64
324×fma-def_binary64
216×associate-/l/_binary64
Counts
121 → 125
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01311755
13161619
27791601
321411595
445821594
549681594

prune113.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1590159
Fresh066
Picked011
Done000
Total1597166
Error
0.8b
Counts
166 → 7
Alt Table
StatusErrorProgram
19.5b
(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
34.4b
(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
1.6b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (exp.f64 (log1p.f64 (exp.f64 a)))))
2.4b
(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
27.5b
(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (log.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
27.5b
(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
32.2b
(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
Compiler

Compiled 2813 to 1102 computations (60.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
0.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))
0.5b
(*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))
0.6b
(cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))

series2.7s (22.3%)

Counts
4 → 96
Calls

4 calls:

1.6s
(*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))
722.0ms
(cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))
313.0ms
(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
34.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

rewrite87.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
134×cbrt-prod_binary64
116×*-un-lft-identity_binary64
91×times-frac_binary64
90×add-sqr-sqrt_binary64
62×add-cube-cbrt_binary64
Counts
4 → 208
Calls

4 calls:

24.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))
24.0ms
(*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))
4.0ms
(cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))
3.0ms
(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))

simplify253.0ms (2.1%)

Algorithm
egg-herbie
Rules
651×fma-def_binary64
436×fma-neg_binary64
406×cancel-sign-sub-inv_binary64
382×times-frac_binary64
309×associate-*l*_binary64
Counts
304 → 307
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03207416
17026677
223636317
345936317
449476317

prune472.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New3992401
Fresh235
Picked101
Done011
Total4026408
Error
0.8b
Counts
408 → 6
Alt Table
StatusErrorProgram
34.4b
(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
1.6b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (exp.f64 (log1p.f64 (exp.f64 a)))))
19.5b
(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))))
2.6b
(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))))
27.5b
(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
32.2b
(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
Compiler

Compiled 13981 to 8210 computations (41.3% saved)

regimes440.0ms (3.6%)

Accuracy

Total 0.6b remaining (51.3%)

Threshold costs 0.6b (51.3%)

Counts
79 → 1
Compiler

Compiled 7805 to 5644 computations (27.7% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
1917
2917

end9.0ms (0.1%)

Compiler

Compiled 36 to 21 computations (41.7% saved)

sample3.3s (26.9%)

Algorithm
intervals
Results
1.4s1885×body1024valid
366.0ms969×body512valid
335.0ms4449×body128valid
197.0ms203×body2048valid
103.0ms494×body256valid
9.0ms132×body128overflowed
Compiler

Compiled 139 to 89 computations (36% saved)

Profiling

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