Details

Time bar (total: 11.4s)

analyze463.0ms (4.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
50%50%0.1%2
50%50%0.1%3
50%50%0.1%4
50%50%0.1%5
62.4%37.5%0.1%6
62.4%37.5%0.1%7
68.7%31.2%0.1%8
68.7%31.2%0.1%9
71.8%28.1%0.1%10
71.8%28.1%0.1%11
73.4%26.5%0.1%12
73.4%26.5%0.1%13
74.1%25.8%0.1%14
Compiler

Compiled 19 to 9 computations (52.6% saved)

sample4.8s (42.7%)

Results
2.5s3823×body8192exit
1.0s6809×body128valid
702.0ms4007×body128invalid
278.0ms708×body512valid
170.0ms719×body256valid
7.0ms20×body1024valid
Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify99.0ms (0.9%)

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
9.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
10.8b
(-.f64 wj (/.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))))
9.6b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
Compiler

Compiled 94 to 48 computations (48.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 x (exp.f64 wj)) wj)
0.0b
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
0.0b
(/.f64 x (exp.f64 wj))
4.6b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series79.0ms (0.7%)

Counts
4 → 61
Calls

4 calls:

26.0ms
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
23.0ms
(/.f64 x (exp.f64 wj))
14.0ms
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
14.0ms
(-.f64 (/.f64 x (exp.f64 wj)) wj)

rewrite72.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt_binary64
95×*-un-lft-identity_binary64
75×times-frac_binary64
67×add-cube-cbrt_binary64
39×prod-diff_binary64
Counts
4 → 171
Calls

4 calls:

17.0ms
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
17.0ms
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
12.0ms
(-.f64 (/.f64 x (exp.f64 wj)) wj)
10.0ms
(/.f64 x (exp.f64 wj))

simplify220.0ms (1.9%)

Algorithm
egg-herbie
Rules
1035×fma-neg_binary64
613×times-frac_binary64
411×distribute-rgt-in_binary64
220×sub-neg_binary64
180×fma-def_binary64
Counts
232 → 240
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02964475
16944262
223674057
348964050
455334050

prune255.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2364240
Fresh101
Picked101
Done000
Total2384242
Error
0.1b
Counts
242 → 4
Alt Table
StatusErrorProgram
2.8b
(-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 x (fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2)))) (*.f64 (pow.f64 wj 3) (+.f64 (*.f64 8/3 x) 1)))
9.7b
(+.f64 wj (/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))))
39.2b
(/.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))))
28.9b
(/.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 5777 to 2176 computations (62.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 x (fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2)))) (*.f64 (pow.f64 wj 3) (+.f64 (*.f64 8/3 x) 1)))
0.0b
(fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2))
0.3b
(*.f64 8/3 x)
5.7b
(*.f64 (pow.f64 wj 3) (+.f64 (*.f64 8/3 x) 1))

series68.0ms (0.6%)

Counts
4 → 60
Calls

4 calls:

48.0ms
(-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 x (fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2)))) (*.f64 (pow.f64 wj 3) (+.f64 (*.f64 8/3 x) 1)))
13.0ms
(*.f64 (pow.f64 wj 3) (+.f64 (*.f64 8/3 x) 1))
5.0ms
(fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2))
2.0ms
(*.f64 8/3 x)

rewrite26.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
15×associate-*l*_binary64
12×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
11×add-exp-log_binary64
Counts
4 → 95
Calls

4 calls:

12.0ms
(*.f64 (pow.f64 wj 3) (+.f64 (*.f64 8/3 x) 1))
6.0ms
(-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 x (fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2)))) (*.f64 (pow.f64 wj 3) (+.f64 (*.f64 8/3 x) 1)))
3.0ms
(*.f64 8/3 x)
0.0ms
(fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2))

simplify146.0ms (1.3%)

Algorithm
egg-herbie
Rules
873×fma-neg_binary64
291×distribute-rgt-neg-in_binary64
263×associate-*r*_binary64
256×associate-*l*_binary64
249×distribute-lft-neg-in_binary64
Counts
155 → 174
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02203535
16253208
226442922
347082918
450942918

prune245.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1722174
Fresh033
Picked011
Done000
Total1726178
Error
0.1b
Counts
178 → 6
Alt Table
StatusErrorProgram
2.8b
(-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 x (fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2)))) (*.f64 (pow.f64 wj 3) (+.f64 (*.f64 8/3 x) 1)))
9.7b
(+.f64 wj (/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))))
25.7b
(/.f64 (fma.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6)))) (fma.f64 (fma.f64 8/3 x 1) (pow.f64 wj 3) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x))))
39.2b
(/.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))))
28.9b
(/.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))))
35.2b
(exp.f64 (log.f64 (-.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 (fma.f64 8/3 x 1) (pow.f64 wj 3)))))
Compiler

Compiled 6426 to 3811 computations (40.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))
0.0b
(/.f64 x (exp.f64 wj))
0.2b
(/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj)))
5.3b
(+.f64 wj (/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))))

series112.0ms (1%)

Counts
3 → 72
Calls

3 calls:

53.0ms
(/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))
29.0ms
(/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj)))
29.0ms
(+.f64 wj (/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))))

rewrite101.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
231×times-frac_binary64
198×*-un-lft-identity_binary64
196×add-sqr-sqrt_binary64
91×add-cube-cbrt_binary64
42×difference-of-squares_binary64
Counts
3 → 216
Calls

3 calls:

29.0ms
(+.f64 wj (/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))))
16.0ms
(/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))
13.0ms
(/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj)))

simplify301.0ms (2.7%)

Algorithm
egg-herbie
Rules
519×distribute-rgt-in_binary64
233×associate-+r+_binary64
218×distribute-neg-in_binary64
200×+-commutative_binary64
175×sub-neg_binary64
Counts
288 → 300
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03458660
18928159
231937935
350837935

prune348.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New3371338
Fresh044
Picked011
Done011
Total3377344
Error
0.1b
Counts
344 → 7
Alt Table
StatusErrorProgram
35.4b
(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))))
2.8b
(-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 x (fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2)))) (*.f64 (pow.f64 wj 3) (+.f64 (*.f64 8/3 x) 1)))
9.7b
(+.f64 wj (/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))))
25.7b
(/.f64 (fma.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6)))) (fma.f64 (fma.f64 8/3 x 1) (pow.f64 wj 3) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x))))
39.2b
(/.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))))
28.9b
(/.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))))
35.2b
(exp.f64 (log.f64 (-.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 (fma.f64 8/3 x 1) (pow.f64 wj 3)))))
Compiler

Compiled 9531 to 4483 computations (53% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.6b
(fma.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6))))
1.8b
(*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6))
4.0b
(*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6)))
23.1b
(/.f64 (fma.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6)))) (fma.f64 (fma.f64 8/3 x 1) (pow.f64 wj 3) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x))))

series947.0ms (8.3%)

Counts
4 → 96
Calls

4 calls:

819.0ms
(/.f64 (fma.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6)))) (fma.f64 (fma.f64 8/3 x 1) (pow.f64 wj 3) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x))))
55.0ms
(fma.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6))))
40.0ms
(*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6)))
31.0ms
(*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6))

rewrite25.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
21×add-exp-log_binary64
16×*-un-lft-identity_binary64
16×add-cube-cbrt_binary64
13×add-cbrt-cube_binary64
Counts
4 → 87
Calls

4 calls:

10.0ms
(*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6)))
4.0ms
(*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6))
2.0ms
(/.f64 (fma.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6)))) (fma.f64 (fma.f64 8/3 x 1) (pow.f64 wj 3) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x))))
0.0ms
(fma.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 (fma.f64 8/3 x 1) (*.f64 (fma.f64 x -8/3 -1) (pow.f64 wj 6))))

simplify349.0ms (3.1%)

Algorithm
egg-herbie
Rules
779×times-frac_binary64
434×+-commutative_binary64
389×associate-+r+_binary64
347×fma-def_binary64
277×*-commutative_binary64
Counts
183 → 227
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0118320691
1383119955
2505519955

prune859.0ms (7.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2261227
Fresh404
Picked101
Done022
Total2313234
Error
0b
Counts
234 → 3
Alt Table
StatusErrorProgram
2.8b
(-.f64 (+.f64 (fma.f64 wj wj x) (*.f64 x (fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2)))) (*.f64 (pow.f64 wj 3) (+.f64 (*.f64 8/3 x) 1)))
9.7b
(+.f64 wj (/.f64 1 (/.f64 (+.f64 wj 1) (-.f64 (/.f64 x (exp.f64 wj)) wj))))
25.0b
(/.f64 (fma.f64 (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (*.f64 -64/9 (*.f64 (pow.f64 wj 6) (pow.f64 x 2)))) (fma.f64 (fma.f64 8/3 x 1) (pow.f64 wj 3) (fma.f64 x (*.f64 wj (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x))))
Compiler

Compiled 31817 to 21413 computations (32.7% saved)

regimes1.4s (12.6%)

Accuracy

Total 0.1b remaining (87.9%)

Threshold costs 0.1b (87.9%)

Counts
163 → 3
Compiler

Compiled 11094 to 7044 computations (36.5% saved)

bsearch66.0ms (0.6%)

Steps
ItersRangePoint
7
2.660218507564059e-12
3.9223141968496533e-10
3.8566291204319244e-10
8
-0.01567123490780688
-1.0998118616781996e-6
-2.6140157849411603e-6
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
mul-1-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03578
14878
25278
35578
45778
55578

end231.0ms (2%)

Compiler

Compiled 210 to 126 computations (40% saved)

Profiling

Loading profile data...