Details

Time bar (total: 7.0s)

analyze145.0ms (2.1%)

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)

sample79.0ms (1.1%)

Algorithm
intervals
Results
39.0ms73×body1024valid
8.0ms11×body2048valid
7.0ms138×body128valid
7.0ms25×body512valid
1.0msbody256valid
0.0msbody128overflowed
Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
1810
2810

prune66.0ms (0.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
29.9b
Counts
1 → 1
Alt Table
StatusErrorProgram
29.9b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (exp.f64 a) (exp.f64 b))
3.5b
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite67.0ms (1%)

Algorithm
rewrite-expression-head
Error
29.9b
Rules
*-un-lft-identity_binary64
add-log-exp_binary64
log-prod_binary64
add-exp-log_binary64
add-sqr-sqrt_binary64
Counts
2 → 27
Calls

2 calls:

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

Compiled 332 to 84 computations (74.7% saved)

series47.0ms (0.7%)

Error
0.2b
Counts
2 → 19
Calls

2 calls:

26.0ms
(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
10.0ms
(+.f64 (exp.f64 a) (exp.f64 b))
Compiler

Compiled 533 to 392 computations (26.5% saved)

simplify79.0ms (1.1%)

Algorithm
egg-herbie
Rules
372×times-frac_binary64
274×associate-+l+_binary64
274×distribute-rgt-in_binary64
226×distribute-rgt-out_binary64
215×distribute-lft-in_binary64
Counts
46 → 26
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
080705
1182658
2392646
3930646
42663641
54832641
64966641

prune19.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New23326
Fresh000
Picked101
Done000
Total24327
Error
0.2b
Counts
27 → 3
Alt Table
StatusErrorProgram
0.6b
(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (*.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 (*.f64 b 1/2) (+.f64 (*.f64 b (/.f64 -1/2 (+.f64 1 (exp.f64 a)))) 1))))
29.9b
(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3)) (+.f64 (pow.f64 (exp.f64 a) 2) (*.f64 (exp.f64 b) (-.f64 (exp.f64 b) (exp.f64 a))))))
30.7b
(log.f64 (+.f64 1 (+.f64 b (+.f64 (exp.f64 a) (*.f64 b (*.f64 b (+.f64 1/2 (*.f64 b 1/6))))))))
Compiler

Compiled 483 to 233 computations (51.8% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (*.f64 b 1/2) (+.f64 (*.f64 b (/.f64 -1/2 (+.f64 1 (exp.f64 a)))) 1))
0.0b
(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (*.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 (*.f64 b 1/2) (+.f64 (*.f64 b (/.f64 -1/2 (+.f64 1 (exp.f64 a)))) 1))))

rewrite57.0ms (0.8%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
add-log-exp_binary64
*-un-lft-identity_binary64
associate-+l+_binary64
log-prod_binary64
sum-log_binary64
Counts
2 → 32
Calls

2 calls:

9.0ms
(+.f64 (*.f64 b 1/2) (+.f64 (*.f64 b (/.f64 -1/2 (+.f64 1 (exp.f64 a)))) 1))
5.0ms
(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (*.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 (*.f64 b 1/2) (+.f64 (*.f64 b (/.f64 -1/2 (+.f64 1 (exp.f64 a)))) 1))))
Compiler

Compiled 1383 to 952 computations (31.2% saved)

series128.0ms (1.8%)

Error
0.2b
Counts
2 → 23
Calls

2 calls:

87.0ms
(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (*.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 (*.f64 b 1/2) (+.f64 (*.f64 b (/.f64 -1/2 (+.f64 1 (exp.f64 a)))) 1))))
29.0ms
(+.f64 (*.f64 b 1/2) (+.f64 (*.f64 b (/.f64 -1/2 (+.f64 1 (exp.f64 a)))) 1))
Compiler

Compiled 1348 to 991 computations (26.5% saved)

simplify117.0ms (1.7%)

Algorithm
egg-herbie
Rules
796×distribute-rgt-in_binary64
749×distribute-lft-in_binary64
188×cancel-sign-sub-inv_binary64
143×exp-prod_binary64
138×times-frac_binary64
Counts
55 → 46
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01292089
14031947
212061773
346791773
450411773

prune38.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New45146
Fresh022
Picked101
Done000
Total46349
Error
0.2b
Counts
49 → 3
Alt Table
StatusErrorProgram
0.6b
(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (*.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 1 (*.f64 b (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))))))
29.9b
(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3)) (+.f64 (pow.f64 (exp.f64 a) 2) (*.f64 (exp.f64 b) (-.f64 (exp.f64 b) (exp.f64 a))))))
30.7b
(log.f64 (+.f64 1 (+.f64 b (+.f64 (exp.f64 a) (*.f64 b (*.f64 b (+.f64 1/2 (*.f64 b 1/6))))))))
Compiler

Compiled 1230 to 860 computations (30.1% saved)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (*.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 1 (*.f64 b (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))))))

rewrite28.0ms (0.4%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
associate-+l+_binary64
log-prod_binary64
*-un-lft-identity_binary64
associate-+r+_binary64
associate-+l-_binary64
Counts
1 → 19
Calls

1 calls:

5.0ms
(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (*.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 1 (*.f64 b (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))))))
Compiler

Compiled 801 to 555 computations (30.7% saved)

series93.0ms (1.3%)

Error
0.2b
Counts
1 → 13
Calls

1 calls:

88.0ms
(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (*.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 1 (*.f64 b (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))))))
Compiler

Compiled 771 to 578 computations (25% saved)

simplify96.0ms (1.4%)

Algorithm
egg-herbie
Rules
361×associate-*l*_binary64
341×distribute-rgt-in_binary64
335×associate-*r*_binary64
322×distribute-lft-in_binary64
270×distribute-rgt-neg-in_binary64
Counts
32 → 23
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0891527
12571443
27641275
332371275
445871275
549531275

prune18.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New23023
Fresh022
Picked011
Done000
Total23326
Error
0.2b
Counts
26 → 3
Alt Table
StatusErrorProgram
0.6b
(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (*.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 1 (*.f64 b (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))))))
29.9b
(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3)) (+.f64 (pow.f64 (exp.f64 a) 2) (*.f64 (exp.f64 b) (-.f64 (exp.f64 b) (exp.f64 a))))))
30.7b
(log.f64 (+.f64 1 (+.f64 b (+.f64 (exp.f64 a) (*.f64 b (*.f64 b (+.f64 1/2 (*.f64 b 1/6))))))))
Compiler

Compiled 634 to 437 computations (31.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(pow.f64 (exp.f64 b) 3)
0.9b
(/.f64 (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3)) (+.f64 (pow.f64 (exp.f64 a) 2) (*.f64 (exp.f64 b) (-.f64 (exp.f64 b) (exp.f64 a)))))
3.5b
(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3)) (+.f64 (pow.f64 (exp.f64 a) 2) (*.f64 (exp.f64 b) (-.f64 (exp.f64 b) (exp.f64 a))))))
5.0b
(-.f64 (exp.f64 b) (exp.f64 a))

rewrite142.0ms (2%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
108×*-un-lft-identity_binary64
54×times-frac_binary64
38×add-sqr-sqrt_binary64
36×add-cube-cbrt_binary64
35×distribute-lft-out_binary64
Counts
4 → 141
Calls

4 calls:

15.0ms
(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3)) (+.f64 (pow.f64 (exp.f64 a) 2) (*.f64 (exp.f64 b) (-.f64 (exp.f64 b) (exp.f64 a))))))
15.0ms
(/.f64 (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3)) (+.f64 (pow.f64 (exp.f64 a) 2) (*.f64 (exp.f64 b) (-.f64 (exp.f64 b) (exp.f64 a)))))
4.0ms
(-.f64 (exp.f64 b) (exp.f64 a))
4.0ms
(pow.f64 (exp.f64 b) 3)
Compiler

Compiled 4273 to 1875 computations (56.1% saved)

series2.5s (36.6%)

Error
0.2b
Counts
4 → 35
Calls

4 calls:

2.3s
(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3)) (+.f64 (pow.f64 (exp.f64 a) 2) (*.f64 (exp.f64 b) (-.f64 (exp.f64 b) (exp.f64 a))))))
171.0ms
(/.f64 (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3)) (+.f64 (pow.f64 (exp.f64 a) 2) (*.f64 (exp.f64 b) (-.f64 (exp.f64 b) (exp.f64 a)))))
14.0ms
(-.f64 (exp.f64 b) (exp.f64 a))
11.0ms
(pow.f64 (exp.f64 b) 3)
Compiler

Compiled 15757 to 10869 computations (31% saved)

simplify203.0ms (2.9%)

Algorithm
egg-herbie
Rules
748×times-frac_binary64
642×associate-/l*_binary64
160×+-commutative_binary64
159×*-commutative_binary64
125×associate-+r+_binary64
Counts
176 → 132
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
068912556
1207912204
2502912204

prune154.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1311132
Fresh101
Picked011
Done011
Total1323135
Error
0.2b
Counts
135 → 3
Alt Table
StatusErrorProgram
1.2b
(-.f64 (+.f64 (*.f64 3 (/.f64 (*.f64 b (pow.f64 (exp.f64 a) 2)) (*.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)) (-.f64 (+.f64 1 (pow.f64 (exp.f64 a) 2)) (exp.f64 a))))) (+.f64 (*.f64 3 (+.f64 (/.f64 (*.f64 (exp.f64 a) b) (*.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)) (pow.f64 (-.f64 (+.f64 1 (pow.f64 (exp.f64 a) 2)) (exp.f64 a)) 2))) (/.f64 (*.f64 b (pow.f64 (exp.f64 a) 4)) (*.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)) (pow.f64 (-.f64 (+.f64 1 (pow.f64 (exp.f64 a) 2)) (exp.f64 a)) 2))))) (+.f64 (log.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)) (-.f64 (+.f64 1 (pow.f64 (exp.f64 a) 2)) (exp.f64 a)))) (+.f64 (/.f64 (*.f64 b (pow.f64 (exp.f64 a) 6)) (*.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)) (pow.f64 (-.f64 (+.f64 1 (pow.f64 (exp.f64 a) 2)) (exp.f64 a)) 2))) (*.f64 3 (/.f64 b (*.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)) (-.f64 (+.f64 1 (pow.f64 (exp.f64 a) 2)) (exp.f64 a))))))))) (+.f64 (*.f64 3 (*.f64 (/.f64 b (*.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)) (-.f64 (+.f64 1 (pow.f64 (exp.f64 a) 2)) (exp.f64 a)))) (exp.f64 a))) (+.f64 (/.f64 (*.f64 b (pow.f64 (exp.f64 a) 3)) (*.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)) (pow.f64 (-.f64 (+.f64 1 (pow.f64 (exp.f64 a) 2)) (exp.f64 a)) 2))) (+.f64 (*.f64 2 (/.f64 b (*.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)) (pow.f64 (-.f64 (+.f64 1 (pow.f64 (exp.f64 a) 2)) (exp.f64 a)) 2)))) (*.f64 3 (*.f64 (/.f64 b (pow.f64 (-.f64 (+.f64 1 (pow.f64 (exp.f64 a) 2)) (exp.f64 a)) 2)) (+.f64 (/.f64 (pow.f64 (exp.f64 a) 2) (+.f64 1 (pow.f64 (exp.f64 a) 3))) (/.f64 (pow.f64 (exp.f64 a) 5) (+.f64 1 (pow.f64 (exp.f64 a) 3))))))))))
29.9b
(log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3)) (+.f64 (pow.f64 (exp.f64 a) 2) (*.f64 (exp.f64 b) (-.f64 (exp.f64 b) (exp.f64 a))))))
0.6b
(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (*.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 1 (*.f64 b (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))))))
Compiler

Compiled 6639 to 3695 computations (44.3% saved)

regimes365.0ms (5.2%)

Accuracy

Total 0.4b remaining (39%)

Threshold costs 0.4b (39%)

Compiler

Compiled 10107 to 6915 computations (31.6% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
distribute-neg-frac_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01539
12439
23139
33339
43439
53239

end8.0ms (0.1%)

Compiler

Compiled 81 to 60 computations (25.9% saved)

sample2.4s (34.6%)

Algorithm
intervals
Results
1.0s1998×body1024valid
245.0ms910×body512valid
239.0ms4396×body128valid
137.0ms200×body2048valid
70.0ms496×body256valid
6.0ms136×body128overflowed
Compiler

Compiled 348 to 236 computations (32.2% saved)

Profiling

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