Details

Time bar (total: 5.9s)

analyze66.0ms (1.1%)

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)

sample251.0ms (4.2%)

Algorithm
intervals
Symmetry

(sort a b)

Results
30.0ms59×body1024valid
9.0ms35×body512valid
8.0ms150×body128valid
5.0msbody2048valid
1.0msbody256valid
1.0ms10×body128overflowed
Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify6.0ms (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
28.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
28.8b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (exp.f64 a) (exp.f64 b))
4.5b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series505.0ms (8.6%)

Counts
2 → 48
Calls

2 calls:

500.0ms
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms
(+.f64 (exp.f64 a) (exp.f64 b))

rewrite7.0ms (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)))

simplify87.0ms (1.5%)

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

prune63.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New80383
Fresh000
Picked101
Done000
Total81384
Error
1.0b
Counts
84 → 3
Alt Table
StatusErrorProgram
29.0b
(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
1.8b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
30.8b
(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
Compiler

Compiled 1365 to 624 computations (54.3% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series519.0ms (8.8%)

Counts
4 → 44
Calls

4 calls:

304.0ms
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
195.0ms
(log1p.f64 (exp.f64 a))
18.0ms
(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms
(+.f64 1 (exp.f64 a))

rewrite17.0ms (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:

7.0ms
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
4.0ms
(/.f64 b (+.f64 1 (exp.f64 a)))
3.0ms
(+.f64 1 (exp.f64 a))
0.0ms
(log1p.f64 (exp.f64 a))

simplify116.0ms (2%)

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

prune99.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1155120
Fresh022
Picked101
Done000
Total1167123
Error
1.0b
Counts
123 → 7
Alt Table
StatusErrorProgram
2.4b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 (*.f64 (cbrt.f64 b) (cbrt.f64 b)) (/.f64 (+.f64 1 (exp.f64 a)) (cbrt.f64 b))))
1.8b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
26.7b
(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (log.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
29.0b
(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
20.0b
(cbrt.f64 (pow.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))) 3))
20.2b
(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
30.8b
(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
Compiler

Compiled 2183 to 1163 computations (46.7% saved)

localize10.0ms (0.2%)

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
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))
0.5b
(log1p.f64 (+.f64 1 (exp.f64 a)))

series287.0ms (4.9%)

Counts
2 → 24
Calls

2 calls:

285.0ms
(log1p.f64 (+.f64 1 (exp.f64 a)))
2.0ms
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

rewrite1.0ms (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 1 (exp.f64 a)))
0.0ms
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

simplify67.0ms (1.1%)

Algorithm
egg-herbie
Rules
1017×fma-def_binary64
626×associate-*l/_binary64
298×*-commutative_binary64
275×distribute-rgt-out_binary64
273×distribute-rgt-in_binary64
Counts
46 → 52
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
050411
199378
2228378
3525367
41112364
52190364
62879364
73136364
85311364

prune87.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New94195
Fresh246
Picked011
Done000
Total966102
Error
1.0b
Counts
102 → 6
Alt Table
StatusErrorProgram
2.9b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))))
20.2b
(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
29.0b
(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
20.0b
(cbrt.f64 (pow.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))) 3))
30.8b
(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
1.8b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
Compiler

Compiled 1711 to 1021 computations (40.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
0.5b
(*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
0.5b
(log1p.f64 (+.f64 1 (exp.f64 a)))
0.8b
(cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

series623.0ms (10.6%)

Counts
3 → 36
Calls

3 calls:

433.0ms
(cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))
188.0ms
(*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
2.0ms
(expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))

rewrite11.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
22×pow1_binary64
10×pow1/3_binary64
pow-prod-up_binary64
add-sqr-sqrt_binary64
add-exp-log_binary64
Counts
3 → 62
Calls

3 calls:

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

simplify123.0ms (2.1%)

Algorithm
egg-herbie
Rules
571×fma-neg_binary64
388×fma-def_binary64
362×associate-*l*_binary64
332×unswap-sqr_binary64
323×associate-*r*_binary64
Counts
98 → 103
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01251409
12871271
27971231
325801223
449621133
549971133
649931133
749241133

prune295.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2271228
Fresh044
Picked101
Done011
Total2286234
Error
1.0b
Counts
234 → 6
Alt Table
StatusErrorProgram
30.8b
(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
3.1b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (*.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (sqrt.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))) (*.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (sqrt.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))))))
29.0b
(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
20.0b
(cbrt.f64 (pow.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))) 3))
20.2b
(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
1.8b
(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
Compiler

Compiled 7435 to 5061 computations (31.9% saved)

regimes353.0ms (6%)

Accuracy

Total 0.5b remaining (55.5%)

Threshold costs 0.5b (55.5%)

Counts
70 → 1
Compiler

Compiled 6684 to 4923 computations (26.3% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01120
11520
21420

end7.0ms (0.1%)

Compiler

Compiled 42 to 30 computations (28.6% saved)

sample2.3s (38.5%)

Algorithm
intervals
Results
1.0s1970×body1024valid
260.0ms987×body512valid
234.0ms4389×body128valid
111.0ms166×body2048valid
71.0ms488×body256valid
6.0ms140×body128overflowed
Compiler

Compiled 128 to 94 computations (26.6% saved)

Profiling

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