Details

Time bar (total: 19.4s)

analyze765.0ms (3.9%)

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
0%99.9%0.1%4
12.5%87.4%0.1%5
18.7%81.2%0.1%6
28.1%71.8%0.1%7
32.8%67.1%0.1%8
38.2%61.7%0.1%9
41%58.9%0.1%10
43.9%56%0.1%11
45.4%54.5%0.1%12
46.9%53%0.1%13
47.7%52.2%0.1%14
Compiler

Compiled 19 to 9 computations (52.6% saved)

sample3.9s (20%)

Results
2.2s3934×body8192exit
763.0ms6800×body128valid
445.0ms4000×body128invalid
191.0ms683×body512valid
150.0ms749×body256valid
9.0ms24×body1024valid
Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify79.0ms (0.4%)

Algorithm
egg-herbie
Rules
568×neg-mul-1_binary64
503×fma-def_binary64
491×fma-neg_binary64
484×div-sub_binary64
416×distribute-neg-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0923
12223
25823
315221
433818
5109018
6290218
7369518
8470618
9488118

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
12.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
12.1b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
13.1b
(-.f64 wj (/.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))))
Compiler

Compiled 94 to 48 computations (48.9% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
0.0b
(/.f64 x (exp.f64 wj))
4.8b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series45.0ms (0.2%)

Counts
3 → 52
Calls

3 calls:

18.0ms
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
14.0ms
(/.f64 x (exp.f64 wj))
13.0ms
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

rewrite35.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity_binary64
49×add-sqr-sqrt_binary64
38×times-frac_binary64
24×add-cube-cbrt_binary64
10×difference-of-squares_binary64
Counts
3 → 100
Calls

3 calls:

13.0ms
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
13.0ms
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
3.0ms
(/.f64 x (exp.f64 wj))

simplify108.0ms (0.6%)

Algorithm
egg-herbie
Rules
643×fma-neg_binary64
444×fma-def_binary64
331×distribute-rgt-in_binary64
292×associate--l+_binary64
278×distribute-lft-in_binary64
Counts
152 → 152
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02283154
15833016
216042995
347982993
452982993

prune109.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1493152
Fresh101
Picked011
Done000
Total1504154
Error
0.1b
Counts
154 → 4
Alt Table
StatusErrorProgram
40.1b
(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
1.9b
(-.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
12.1b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
39.7b
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
Compiler

Compiled 3269 to 1428 computations (56.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
0.0b
(-.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
0.1b
(*.f64 8/3 (pow.f64 wj 3))
5.7b
(*.f64 x (*.f64 wj wj))

series55.0ms (0.3%)

Counts
4 → 72
Calls

4 calls:

27.0ms
(-.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
18.0ms
(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
8.0ms
(*.f64 x (*.f64 wj wj))
3.0ms
(*.f64 8/3 (pow.f64 wj 3))

rewrite21.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt_binary64
19×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
14×add-exp-log_binary64
13×associate-*r*_binary64
Counts
4 → 96
Calls

4 calls:

7.0ms
(*.f64 8/3 (pow.f64 wj 3))
5.0ms
(*.f64 x (*.f64 wj wj))
4.0ms
(-.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
0.0ms
(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))

simplify116.0ms (0.6%)

Algorithm
egg-herbie
Rules
806×fma-def_binary64
521×distribute-rgt-in_binary64
507×distribute-lft-in_binary64
479×fma-neg_binary64
401×cancel-sign-sub-inv_binary64
Counts
168 → 173
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01913853
14093376
214383085
349853004
451893004

prune193.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1712173
Fresh022
Picked011
Done011
Total1716177
Error
0.1b
Counts
177 → 6
Alt Table
StatusErrorProgram
54.8b
(fma.f64 wj wj (*.f64 (*.f64 wj wj) (-.f64 (*.f64 5/2 x) (*.f64 (fma.f64 x 8/3 1) wj))))
1.9b
(-.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
40.1b
(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
12.1b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
3.3b
(fma.f64 (*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
39.7b
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
Compiler

Compiled 6450 to 3517 computations (45.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 (*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
0.5b
(*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))))
0.6b
(cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))
5.7b
(*.f64 x (*.f64 wj wj))

series8.6s (44.1%)

Counts
3 → 72
Calls

3 calls:

8.4s
(fma.f64 (*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
154.0ms
(*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))))
55.0ms
(cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
19×cbrt-prod_binary64
12×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
10×pow1_binary64
Counts
3 → 65
Calls

3 calls:

4.0ms
(*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))))
1.0ms
(cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))
0.0ms
(fma.f64 (*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))

simplify181.0ms (0.9%)

Algorithm
egg-herbie
Rules
730×fma-def_binary64
625×associate-/l*_binary64
267×*-commutative_binary64
164×+-commutative_binary64
137×sub-neg_binary64
Counts
137 → 233
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
073313270
1261011912
2509911912

prune884.0ms (4.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New4701471
Fresh033
Picked101
Done022
Total4716477
Error
0.1b
Counts
477 → 6
Alt Table
StatusErrorProgram
54.8b
(fma.f64 wj wj (*.f64 (*.f64 wj wj) (-.f64 (*.f64 5/2 x) (*.f64 (fma.f64 x 8/3 1) wj))))
1.9b
(-.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
40.1b
(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
56.2b
(fma.f64 (pow.f64 (pow.f64 wj 4) 1/3) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
12.1b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
39.7b
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
Compiler

Compiled 41776 to 24732 computations (40.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 x (exp.f64 wj))
0.0b
(pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)
2.9b
(+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3))
29.7b
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))

series2.7s (13.9%)

Counts
3 → 72
Calls

3 calls:

2.5s
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
175.0ms
(+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3))
41.0ms
(pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)

rewrite120.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
133×*-un-lft-identity_binary64
83×times-frac_binary64
83×add-sqr-sqrt_binary64
53×cube-prod_binary64
53×unpow-prod-down_binary64
Counts
3 → 168
Calls

3 calls:

43.0ms
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
38.0ms
(+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3))
11.0ms
(pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)

simplify269.0ms (1.4%)

Algorithm
egg-herbie
Rules
452×+-commutative_binary64
410×associate-+r+_binary64
318×*-commutative_binary64
317×fma-def_binary64
198×associate-/r*_binary64
Counts
240 → 210
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0125129969
1499329969

prune679.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New3252327
Fresh123
Picked101
Done022
Total3276333
Error
0.1b
Counts
333 → 6
Alt Table
StatusErrorProgram
54.8b
(fma.f64 wj wj (*.f64 (*.f64 wj wj) (-.f64 (*.f64 5/2 x) (*.f64 (fma.f64 x 8/3 1) wj))))
51.8b
(/.f64 (fma.f64 (pow.f64 (sqrt.f64 wj) 3) (pow.f64 (sqrt.f64 wj) 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
1.9b
(-.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
49.8b
(exp.f64 (log.f64 (/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))))
56.2b
(fma.f64 (pow.f64 (pow.f64 wj 4) 1/3) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
12.1b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
Compiler

Compiled 42338 to 22906 computations (45.9% saved)

regimes371.0ms (1.9%)

Accuracy

Total 0.3b remaining (74.7%)

Threshold costs 0.3b (74.7%)

Counts
90 → 2
Compiler

Compiled 6450 to 4029 computations (37.5% saved)

bsearch4.0ms (0%)

Compiler

Compiled 18 to 8 computations (55.6% saved)

simplify8.0ms (0%)

Algorithm
egg-herbie
Rules
19×+-commutative_binary64
18×distribute-rgt-neg-in_binary64
18×sub-neg_binary64
17×cancel-sign-sub-inv_binary64
16×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03385
15285
26985
38585
411085
512685
613985
715785
817085
917985
1018185
1117785

end152.0ms (0.8%)

Compiler

Compiled 309 to 180 computations (41.7% saved)

Profiling

Loading profile data...