Details

Time bar (total: 6.7s)

analyze125.0ms (1.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
37.5%37.5%25.1%2
37.5%18.7%43.8%3
46.8%9.4%43.8%4
51.5%4.7%43.8%5
51.5%2.3%46.1%6
52.7%1.2%46.1%7
53.3%0.6%46.1%8
53.3%0.3%46.4%9
53.4%0.1%46.4%10
53.5%0.1%46.4%11
53.5%0%46.5%12
53.5%0%46.5%13
53.5%0%46.5%14
Compiler

Compiled 71 to 33 computations (53.5% saved)

sample35.0ms (0.5%)

Algorithm
intervals
Results
22.0ms256×body128valid
3.0ms256×pre128true
Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify103.0ms (1.5%)

Algorithm
egg-herbie
Rules
1509×associate-/l*_binary64
1334×associate-/r*_binary64
744×distribute-lft-out_binary64
549×unswap-sqr_binary64
452×associate-*r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 7 (0.0ms)

IterNodesCost
03277
17362
221845
377341
4139441
5304041
6337941
7354339
8213639
9262239
10267039
11494139

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 2
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
0.5b
(fabs.f64 (/.f64 (+.f64 (+.f64 (+.f64 (*.f64 2 x) (*.f64 2/3 (pow.f64 x 3))) (*.f64 1/5 (pow.f64 x 5))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 PI.f64)))
Compiler

Compiled 214 to 128 computations (40.2% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.1b
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
0.2b
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b
(sqrt.f64 PI.f64)

rewrite308.0ms (4.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
119×add-exp-log_binary64
80×pow1_binary64
79×add-cbrt-cube_binary64
78×prod-exp_binary64
48×cbrt-unprod_binary64
Counts
4 → 153
Calls

4 calls:

30.0ms
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
13.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
13.0ms
(*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 9104 to 3105 computations (65.9% saved)

series51.0ms (0.8%)

Error
0.0b
Counts
4 → 9
Calls

4 calls:

16.0ms
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
15.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
13.0ms
(*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 1251 to 652 computations (47.9% saved)

simplify129.0ms (1.9%)

Algorithm
egg-herbie
Rules
589×associate-/l*_binary64
360×associate-*r*_binary64
329×unswap-sqr_binary64
328×associate-*l*_binary64
236×associate-/r/_binary64
Counts
162 → 138
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02092395
13901751
215291466
332241437
448661403
548991403

prune133.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1380138
Fresh011
Picked011
Done000
Total1382140
Error
0.0b
Counts
140 → 2
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
0.5b
(fabs.f64 (/.f64 (+.f64 (+.f64 (+.f64 (*.f64 2 x) (*.f64 2/3 (pow.f64 x 3))) (*.f64 1/5 (pow.f64 x 5))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 PI.f64)))
Compiler

Compiled 4211 to 1773 computations (57.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 1/5 (pow.f64 x 5))
0.2b
(*.f64 2/3 (pow.f64 x 3))
0.3b
(/.f64 (+.f64 (+.f64 (+.f64 (*.f64 2 x) (*.f64 2/3 (pow.f64 x 3))) (*.f64 1/5 (pow.f64 x 5))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 PI.f64))
1.0b
(sqrt.f64 PI.f64)

rewrite199.0ms (3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
40×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
27×add-cube-cbrt_binary64
19×associate-*r*_binary64
18×times-frac_binary64
Counts
4 → 110
Calls

4 calls:

13.0ms
(/.f64 (+.f64 (+.f64 (+.f64 (*.f64 2 x) (*.f64 2/3 (pow.f64 x 3))) (*.f64 1/5 (pow.f64 x 5))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 PI.f64))
6.0ms
(*.f64 2/3 (pow.f64 x 3))
5.0ms
(*.f64 1/5 (pow.f64 x 5))
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 3611 to 2757 computations (23.6% saved)

series66.0ms (1%)

Error
0.0b
Counts
4 → 18
Calls

4 calls:

32.0ms
(/.f64 (+.f64 (+.f64 (+.f64 (*.f64 2 x) (*.f64 2/3 (pow.f64 x 3))) (*.f64 1/5 (pow.f64 x 5))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 PI.f64))
10.0ms
(*.f64 1/5 (pow.f64 x 5))
10.0ms
(*.f64 2/3 (pow.f64 x 3))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 836 to 704 computations (15.8% saved)

simplify191.0ms (2.9%)

Algorithm
egg-herbie
Rules
508×unswap-sqr_binary64
507×distribute-rgt-in_binary64
490×distribute-lft-in_binary64
398×*-commutative_binary64
202×log-prod_binary64
Counts
128 → 90
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01973778
14193465
212253363
335813363
446193355
549143355
648333355

prune102.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New86490
Fresh000
Picked011
Done101
Total87592
Error
0b
Counts
92 → 5
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7)))))
56.5b
(fabs.f64 (*.f64 1/21 (*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 x 7))))
0.5b
(fabs.f64 (/.f64 (+.f64 (+.f64 (+.f64 (*.f64 2 x) (*.f64 2/3 (pow.f64 x 3))) (*.f64 1/5 (pow.f64 x 5))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 PI.f64)))
0.4b
(fabs.f64 (/.f64 (/.f64 (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64))))
1.4b
(fabs.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7)))) (cbrt.f64 (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7))))) (fabs.f64 (cbrt.f64 PI.f64))) (/.f64 (cbrt.f64 (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (cbrt.f64 PI.f64)))))
Compiler

Compiled 2506 to 1927 computations (23.1% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7))))
0.1b
(*.f64 1/21 (pow.f64 x 7))
0.1b
(*.f64 1/5 (pow.f64 x 5))
0.2b
(*.f64 2/3 (pow.f64 x 3))

rewrite252.0ms (3.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
49×add-sqr-sqrt_binary64
29×associate-*r*_binary64
25×associate-*l*_binary64
24×*-un-lft-identity_binary64
23×add-cube-cbrt_binary64
Counts
4 → 122
Calls

4 calls:

17.0ms
(*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7))))
6.0ms
(*.f64 2/3 (pow.f64 x 3))
5.0ms
(*.f64 1/5 (pow.f64 x 5))
5.0ms
(*.f64 1/21 (pow.f64 x 7))
Compiler

Compiled 4088 to 3335 computations (18.4% saved)

series74.0ms (1.1%)

Error
0b
Counts
4 → 21
Calls

4 calls:

32.0ms
(*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7))))
13.0ms
(*.f64 1/21 (pow.f64 x 7))
11.0ms
(*.f64 1/5 (pow.f64 x 5))
10.0ms
(*.f64 2/3 (pow.f64 x 3))
Compiler

Compiled 1030 to 874 computations (15.1% saved)

simplify194.0ms (2.9%)

Algorithm
egg-herbie
Rules
457×unswap-sqr_binary64
342×log-prod_binary64
333×exp-prod_binary64
246×associate-+l+_binary64
240×associate-*l*_binary64
Counts
143 → 97
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02293860
15453299
218073221
333563221
445473211
549493211
650283211

prune119.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New96197
Fresh213
Picked011
Done011
Total984102
Error
0b
Counts
102 → 4
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7)))))
0.5b
(fabs.f64 (/.f64 (+.f64 (+.f64 (+.f64 (*.f64 2 x) (*.f64 2/3 (pow.f64 x 3))) (*.f64 1/5 (pow.f64 x 5))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 PI.f64)))
1.0b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))) (*.f64 (+.f64 (*.f64 1/21 (pow.f64 x 7)) (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 x 2)))) (sqrt.f64 (/.f64 1 (cbrt.f64 PI.f64))))))
0.4b
(fabs.f64 (/.f64 (/.f64 (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64))))
Compiler

Compiled 2579 to 2088 computations (19% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 2/3 (pow.f64 x 3))
0.3b
(/.f64 (/.f64 (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64)))
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)

rewrite590.0ms (8.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
564×sqrt-prod_binary64
549×times-frac_binary64
305×add-sqr-sqrt_binary64
296×*-un-lft-identity_binary64
296×add-cube-cbrt_binary64
Counts
4 → 391
Calls

4 calls:

25.0ms
(/.f64 (/.f64 (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64)))
7.0ms
(*.f64 2/3 (pow.f64 x 3))
1.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 15678 to 10393 computations (33.7% saved)

series52.0ms (0.8%)

Error
0b
Counts
4 → 15
Calls

4 calls:

34.0ms
(/.f64 (/.f64 (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64)))
10.0ms
(*.f64 2/3 (pow.f64 x 3))
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 715 to 586 computations (18% saved)

simplify909.0ms (13.6%)

Algorithm
egg-herbie
Rules
486×unswap-sqr_binary64
425×times-frac_binary64
378×associate-/r*_binary64
377×associate-/l/_binary64
374×*-commutative_binary64
Counts
406 → 349
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
036231313
177629928
2163529188
3408629053
4494929053
5497029053

prune199.0ms (3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New3490349
Fresh011
Picked011
Done022
Total3494353
Error
0b
Counts
353 → 4
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7)))))
0.5b
(fabs.f64 (/.f64 (+.f64 (+.f64 (+.f64 (*.f64 2 x) (*.f64 2/3 (pow.f64 x 3))) (*.f64 1/5 (pow.f64 x 5))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 PI.f64)))
1.0b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))) (*.f64 (+.f64 (*.f64 1/21 (pow.f64 x 7)) (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 x 2)))) (sqrt.f64 (/.f64 1 (cbrt.f64 PI.f64))))))
0.4b
(fabs.f64 (/.f64 (/.f64 (+.f64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 2 x))) (*.f64 1/21 (pow.f64 x 7))) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64))))
Compiler

Compiled 6084 to 4229 computations (30.5% saved)

regimes1.5s (21.8%)

Accuracy

Total 0.1b remaining (80.6%)

Threshold costs 0.1b (80.6%)

Compiler

Compiled 33176 to 22921 computations (30.9% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02869
14169
24069

end4.0ms (0.1%)

Compiler

Compiled 43 to 36 computations (16.3% saved)

sample1.3s (19.3%)

Algorithm
intervals
Results
739.0ms8000×body128valid
88.0ms8000×pre128true
Compiler

Compiled 238 to 170 computations (28.6% saved)

Profiling

Loading profile data...