Details

Time bar (total: 10.7s)

analyze819.0ms (7.6%)

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)

sample4.0s (37.5%)

Results
2.2s3990×body8192exit
816.0ms6736×body128valid
504.0ms4090×body128invalid
233.0ms779×body512valid
148.0ms708×body256valid
12.0ms33×body1024valid
Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify78.0ms (0.7%)

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

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
15.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
15.5b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
15.8b
(-.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 (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 x (exp.f64 wj))
0.0b
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
5.6b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series45.0ms (0.4%)

Counts
3 → 52
Calls

3 calls:

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

rewrite34.0ms (0.3%)

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:

14.0ms
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
12.0ms
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
3.0ms
(/.f64 x (exp.f64 wj))

simplify108.0ms (1%)

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 → 154
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02283154
15833016
216042995
347982993
452982993

prune109.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1513154
Fresh101
Picked101
Done000
Total1533156
Error
0.1b
Counts
156 → 3
Alt Table
StatusErrorProgram
1.7b
(-.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)))
7.3b
(*.f64 1 (+.f64 (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 wj (/.f64 wj (+.f64 wj 1)))))
35.3b
(/.f64 (-.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
Compiler

Compiled 3318 to 1444 computations (56.5% saved)

localize17.0ms (0.2%)

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))
6.3b
(*.f64 x (*.f64 wj wj))

series62.0ms (0.6%)

Counts
4 → 72
Calls

4 calls:

29.0ms
(-.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)))
19.0ms
(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))
6.0ms
(*.f64 8/3 (pow.f64 wj 3))

rewrite18.0ms (0.2%)

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:

5.0ms
(*.f64 8/3 (pow.f64 wj 3))
4.0ms
(*.f64 x (*.f64 wj wj))
3.0ms
(-.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))

simplify114.0ms (1.1%)

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

prune249.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1703173
Fresh022
Picked011
Done000
Total1706176
Error
0.1b
Counts
176 → 6
Alt Table
StatusErrorProgram
53.6b
(fma.f64 wj wj (*.f64 (*.f64 wj wj) (-.f64 (*.f64 5/2 x) (*.f64 (fma.f64 x 8/3 1) wj))))
1.7b
(-.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)))
28.2b
(*.f64 (sqrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (sqrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
7.3b
(*.f64 1 (+.f64 (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 wj (/.f64 wj (+.f64 wj 1)))))
35.3b
(/.f64 (-.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
3.1b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
Compiler

Compiled 6568 to 3608 computations (45.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
0.5b
(*.f64 (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
0.6b
(cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))
4.6b
(*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))

series1.2s (11.1%)

Counts
4 → 96
Calls

4 calls:

911.0ms
(*.f64 (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
239.0ms
(cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))
26.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
13.0ms
(*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))

rewrite82.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
68×cbrt-div_binary64
36×add-sqr-sqrt_binary64
34×flip--_binary64
34×flip3--_binary64
32×frac-times_binary64
Counts
4 → 164
Calls

4 calls:

21.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
15.0ms
(*.f64 (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
5.0ms
(*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))
4.0ms
(cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))

simplify366.0ms (3.4%)

Algorithm
egg-herbie
Rules
527×*-commutative_binary64
371×+-commutative_binary64
340×fma-def_binary64
301×associate-+r+_binary64
168×associate-*r/_binary64
Counts
260 → 360
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0143136488
1506836488

prune2.1s (19.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New6173620
Fresh134
Picked101
Done011
Total6197626
Error
0.1b
Counts
626 → 7
Alt Table
StatusErrorProgram
53.6b
(fma.f64 wj wj (*.f64 (*.f64 wj wj) (-.f64 (*.f64 5/2 x) (*.f64 (fma.f64 x 8/3 1) wj))))
1.7b
(-.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)))
31.3b
(exp.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))) (log.f64 (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))))
28.7b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (cbrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))) (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))) (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))))
51.0b
(pow.f64 (*.f64 (*.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))) (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 (*.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) 1/3)
7.3b
(*.f64 1 (+.f64 (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 wj (/.f64 wj (+.f64 wj 1)))))
35.3b
(/.f64 (-.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
Compiler

Compiled 96877 to 66484 computations (31.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1)))
0.0b
(/.f64 wj (+.f64 wj 1))
0.0b
(*.f64 (exp.f64 wj) (+.f64 wj 1))
5.3b
(-.f64 wj (/.f64 wj (+.f64 wj 1)))

series38.0ms (0.4%)

Counts
4 → 60
Calls

4 calls:

30.0ms
(/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1)))
2.0ms
(*.f64 (exp.f64 wj) (+.f64 wj 1))
2.0ms
(-.f64 wj (/.f64 wj (+.f64 wj 1)))
2.0ms
(/.f64 wj (+.f64 wj 1))

rewrite42.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
104×*-un-lft-identity_binary64
75×add-sqr-sqrt_binary64
68×add-cube-cbrt_binary64
64×times-frac_binary64
54×prod-diff_binary64
Counts
4 → 176
Calls

4 calls:

12.0ms
(-.f64 wj (/.f64 wj (+.f64 wj 1)))
6.0ms
(/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1)))
6.0ms
(*.f64 (exp.f64 wj) (+.f64 wj 1))
4.0ms
(/.f64 wj (+.f64 wj 1))

simplify142.0ms (1.3%)

Algorithm
egg-herbie
Rules
813×fma-neg_binary64
476×distribute-rgt-in_binary64
264×cancel-sign-sub-inv_binary64
182×distribute-rgt-neg-in_binary64
159×sub-neg_binary64
Counts
236 → 262
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03415313
18523689
225353170
345413167
448863167

prune276.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2611262
Fresh415
Picked011
Done101
Total2663269
Error
0.0b
Counts
269 → 3
Alt Table
StatusErrorProgram
0.8b
(*.f64 1 (+.f64 (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 (fma.f64 wj wj (pow.f64 wj 4)) (pow.f64 wj 3))))
7.3b
(*.f64 1 (+.f64 (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 wj (/.f64 wj (+.f64 wj 1)))))
35.3b
(/.f64 (-.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
Compiler

Compiled 8241 to 5027 computations (39% saved)

regimes647.0ms (6%)

Accuracy

Total 1.1b remaining (93.7%)

Threshold costs 0b (0%)

Counts
166 → 1
Compiler

Compiled 12327 to 8130 computations (34% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
*-lft-identity_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01628
12428
22828
33028
43128
53028

end83.0ms (0.8%)

Compiler

Compiled 125 to 77 computations (38.4% saved)

Profiling

Loading profile data...