Details

Time bar (total: 11.7s)

analyze2.7s (22.8%)

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)

sample230.0ms (2%)

Algorithm
intervals
Results
126.0ms129×body2048valid
41.0ms89×body1024valid
9.0ms24×body1024overflowed
7.0ms311×pre128true
5.0ms18×body512valid
4.0msbody2048overflowed
3.0ms13×body512overflowed
3.0msbody4096valid
1.0ms14×body128valid
1.0msbody256valid
1.0msbody128overflowed
1.0msbody2048invalid
1.0msbody256overflowed
Compiler

Compiled 64 to 46 computations (28.1% saved)

simplify23.0ms (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
43.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
43.1b
(/.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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(expm1.f64 (*.f64 eps (+.f64 a b)))
0.1b
(*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))
0.7b
(*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b)))
40.9b
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series374.0ms (3.2%)

Counts
4 → 144
Calls

4 calls:

288.0ms
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
37.0ms
(*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b)))
30.0ms
(*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))
19.0ms
(expm1.f64 (*.f64 eps (+.f64 a b)))

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube_binary64
20×add-exp-log_binary64
12×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
4 → 74
Calls

4 calls:

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)))
0.0ms
(expm1.f64 (*.f64 eps (+.f64 a b)))

simplify143.0ms (1.2%)

Algorithm
egg-herbie
Rules
828×fma-def_binary64
622×times-frac_binary64
470×associate-/l*_binary64
249×*-commutative_binary64
191×+-commutative_binary64
Counts
218 → 229
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
06468872
121668105
253258105

prune186.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2245229
Fresh000
Picked101
Done000
Total2255230
Error
0.0b
Counts
230 → 5
Alt Table
StatusErrorProgram
53.0b
(cbrt.f64 (pow.f64 (/.f64 (*.f64 eps (expm1.f64 (*.f64 (+.f64 a b) eps))) (*.f64 (expm1.f64 (*.f64 b eps)) (expm1.f64 (*.f64 a eps)))) 3))
5.3b
(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))))
57.2b
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (-.f64 (fma.f64 eps (*.f64 b (exp.f64 (*.f64 a eps))) (*.f64 1/2 (*.f64 (*.f64 eps eps) (*.f64 (exp.f64 (*.f64 a eps)) (*.f64 b b))))) (fma.f64 b eps (*.f64 1/2 (*.f64 (*.f64 eps eps) (*.f64 b b))))))
43.1b
(/.f64 1 (/.f64 (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))) (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
44.0b
(/.f64 (*.f64 eps (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
Compiler

Compiled 11578 to 3927 computations (66.1% saved)

localize13.0ms (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))
6.3b
(*.f64 a (*.f64 eps eps))
6.5b
(*.f64 b (*.f64 eps eps))

series70.0ms (0.6%)

Counts
4 → 120
Calls

4 calls:

31.0ms
(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))))
20.0ms
(fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a))
11.0ms
(*.f64 a (*.f64 eps eps))
8.0ms
(*.f64 b (*.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 b (*.f64 eps eps))
4.0ms
(*.f64 a (*.f64 eps eps))
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))))
0.0ms
(fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a))

simplify96.0ms (0.8%)

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
Fresh224
Picked101
Done000
Total1243127
Error
0.0b
Counts
127 → 3
Alt Table
StatusErrorProgram
57.2b
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (-.f64 (fma.f64 eps (*.f64 b (exp.f64 (*.f64 a eps))) (*.f64 1/2 (*.f64 (*.f64 eps eps) (*.f64 (exp.f64 (*.f64 a eps)) (*.f64 b b))))) (fma.f64 b eps (*.f64 1/2 (*.f64 (*.f64 eps eps) (*.f64 b b))))))
2.6b
(+.f64 (/.f64 1 b) (/.f64 1 a))
44.0b
(/.f64 (*.f64 eps (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
Compiler

Compiled 3152 to 1528 computations (51.5% 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%)

Counts
1 → 6
Calls

1 calls:

6.0ms
(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite13.0ms (0.1%)

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:

11.0ms
(+.f64 (/.f64 1 b) (/.f64 1 a))

simplify118.0ms (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

prune28.0ms (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
57.2b
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (-.f64 (fma.f64 eps (*.f64 b (exp.f64 (*.f64 a eps))) (*.f64 1/2 (*.f64 (*.f64 eps eps) (*.f64 (exp.f64 (*.f64 a eps)) (*.f64 b b))))) (fma.f64 b eps (*.f64 1/2 (*.f64 (*.f64 eps eps) (*.f64 b b))))))
2.6b
(+.f64 (/.f64 1 b) (/.f64 1 a))
44.0b
(/.f64 (*.f64 eps (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
Compiler

Compiled 669 to 470 computations (29.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3)
0.7b
(*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b)))
22.0b
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3))
40.9b
(/.f64 (*.f64 eps (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series435.0ms (3.7%)

Counts
3 → 108
Calls

3 calls:

336.0ms
(/.f64 (*.f64 eps (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
83.0ms
(pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3)
16.0ms
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×add-exp-log_binary64
14×add-cbrt-cube_binary64
12×cbrt-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
3 → 71
Calls

3 calls:

6.0ms
(/.f64 (*.f64 eps (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
1.0ms
(pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3)
1.0ms
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3))

simplify171.0ms (1.5%)

Algorithm
egg-herbie
Rules
897×fma-def_binary64
618×times-frac_binary64
265×*-commutative_binary64
211×+-commutative_binary64
178×associate-+r+_binary64
Counts
179 → 170
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
07128528
123777884
249817880
349647880

prune188.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2300230
Fresh011
Picked011
Done011
Total2303233
Error
0.0b
Counts
233 → 3
Alt Table
StatusErrorProgram
57.2b
(/.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))) (-.f64 (fma.f64 eps (*.f64 b (exp.f64 (*.f64 a eps))) (*.f64 1/2 (*.f64 (*.f64 eps eps) (*.f64 (exp.f64 (*.f64 a eps)) (*.f64 b b))))) (fma.f64 b eps (*.f64 1/2 (*.f64 (*.f64 eps eps) (*.f64 b b))))))
2.6b
(+.f64 (/.f64 1 b) (/.f64 1 a))
44.0b
(/.f64 (*.f64 eps (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (+.f64 a b) eps)) 3))) (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))))
Compiler

Compiled 13312 to 5389 computations (59.5% saved)

regimes430.0ms (3.7%)

Accuracy

Total 0.3b remaining (89.9%)

Threshold costs 0.3b (89.9%)

Counts
100 → 3
Compiler

Compiled 8926 to 5660 computations (36.6% saved)

bsearch4.0ms (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
039128
155128
258128
356128

end12.0ms (0.1%)

Remove

(sort a b)

Compiler

Compiled 255 to 144 computations (43.5% saved)

sample6.3s (54.2%)

Algorithm
intervals
Results
3.5s4012×body2048valid
1.2s2446×body1024valid
236.0ms9632×pre128true
226.0ms762×body512valid
211.0ms540×body1024overflowed
200.0ms352×body2048overflowed
74.0ms288×body512overflowed
48.0ms246×body256valid
46.0ms523×body128valid
26.0ms301×body128overflowed
25.0ms148×body256overflowed
14.0ms11×body4096valid
2.0msbody2048invalid
Compiler

Compiled 203 to 122 computations (39.9% saved)

Profiling

Loading profile data...