Details

Time bar (total: 5.6s)

analyze114.0ms (2%)

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)

sample37.0ms (0.7%)

Algorithm
intervals
Results
24.0ms256×body128valid
3.0ms257×pre128true
0.0msbody128invalid
Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify97.0ms (1.7%)

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)

localize30.0ms (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 (*.f64 (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)

rewrite257.0ms (4.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
106×pow1_binary64
43×add-exp-log_binary64 add-cbrt-cube_binary64
42×pow-prod-up_binary64 pow-plus_binary64
24×prod-exp_binary64 cbrt-unprod_binary64
19×add-sqr-sqrt_binary64
Counts
4 → 139
Calls

4 calls:

14.0ms
(*.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))
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 7105 to 2462 computations (65.3% saved)

series47.0ms (0.8%)

Error
0.0b
Counts
4 → 9
Calls

4 calls:

14.0ms
(*.f64 (*.f64 (*.f64 (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)))
12.0ms
(*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 1286 to 675 computations (47.5% saved)

simplify130.0ms (2.3%)

Algorithm
egg-herbie
Rules
646×associate-/l*_binary64
427×*-commutative_binary64
349×associate-/l/_binary64
331×associate-/r*_binary64
227×associate-*r*_binary64
Counts
148 → 127
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01371497
12641100
210291004
31867967
43089947
54599947
64821947
74918947

prune123.0ms (2.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1261127
Fresh011
Picked101
Done000
Total1272129
Error
0.0b
Counts
129 → 2
Alt Table
StatusErrorProgram
0.8b
(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 (cbrt.f64 (pow.f64 x 12)) (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 3999 to 1685 computations (57.9% saved)

localize16.0ms (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)

rewrite189.0ms (3.4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
40×add-sqr-sqrt_binary64
27×add-cube-cbrt_binary64 *-un-lft-identity_binary64
19×associate-*r*_binary64
18×times-frac_binary64
16×add-exp-log_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))
7.0ms
(*.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)

series70.0ms (1.3%)

Error
0.0b
Counts
4 → 18
Calls

4 calls:

36.0ms
(/.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))
11.0ms
(*.f64 1/5 (pow.f64 x 5))
11.0ms
(*.f64 2/3 (pow.f64 x 3))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 836 to 704 computations (15.8% saved)

simplify193.0ms (3.4%)

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

prune290.0ms (5.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New88290
Fresh101
Picked011
Done000
Total89392
Error
0b
Counts
92 → 3
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)))))
36.9b
(fabs.f64 (cbrt.f64 (pow.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 PI.f64)) 3)))
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 2322 to 1779 computations (23.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite223.0ms (4%)

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:

21.0ms
(*.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))))
7.0ms
(*.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)

series82.0ms (1.5%)

Error
0b
Counts
4 → 21
Calls

4 calls:

36.0ms
(*.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))))
14.0ms
(*.f64 1/21 (pow.f64 x 7))
12.0ms
(*.f64 1/5 (pow.f64 x 5))
12.0ms
(*.f64 2/3 (pow.f64 x 3))
Compiler

Compiled 1030 to 874 computations (15.1% saved)

simplify205.0ms (3.6%)

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 → 99
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02293860
15453299
218073221
333563221
445473211
549493211
650283211

prune103.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New99099
Fresh011
Picked011
Done011
Total993102
Error
0b
Counts
102 → 3
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)))))
36.9b
(fabs.f64 (cbrt.f64 (pow.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 PI.f64)) 3)))
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 2510 to 2039 computations (18.8% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b
(/.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 PI.f64))
0.3b
(pow.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 PI.f64)) 3)
1.0b
(sqrt.f64 PI.f64)
36.9b
(cbrt.f64 (pow.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 PI.f64)) 3))

rewrite268.0ms (4.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
90×times-frac_binary64
75×add-sqr-sqrt_binary64
74×add-cube-cbrt_binary64 *-un-lft-identity_binary64
51×sqrt-prod_binary64
50×cbrt-prod_binary64
Counts
4 → 178
Calls

4 calls:

16.0ms
(pow.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 PI.f64)) 3)
15.0ms
(cbrt.f64 (pow.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 PI.f64)) 3))
15.0ms
(/.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 PI.f64))
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 6025 to 4681 computations (22.3% saved)

series165.0ms (2.9%)

Error
0b
Counts
4 → 36
Calls

4 calls:

52.0ms
(pow.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 PI.f64)) 3)
44.0ms
(cbrt.f64 (pow.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 PI.f64)) 3))
35.0ms
(/.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 PI.f64))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 1910 to 1643 computations (14% saved)

simplify340.0ms (6%)

Algorithm
egg-herbie
Rules
913×times-frac_binary64
644×log-prod_binary64
352×unswap-sqr_binary64
148×sqr-pow_binary64
147×associate-*r*_binary64
Counts
214 → 166
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
026412946
170311716
2229610971
3466110971
4562310971

prune116.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1660166
Fresh000
Picked011
Done022
Total1663169
Error
0b
Counts
169 → 3
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)))))
36.9b
(fabs.f64 (cbrt.f64 (pow.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 PI.f64)) 3)))
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 3059 to 2418 computations (21% saved)

regimes1.2s (20.7%)

Accuracy

Total 0.1b remaining (68.9%)

Threshold costs 0.1b (68.9%)

Compiler

Compiled 30126 to 17664 computations (41.4% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
fabs-mul_binary64
1-exp_binary64 fabs-div_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02542
13842
24242
34042

end1.0ms (0%)

Compiler

Compiled 28 to 24 computations (14.3% saved)

sample1.3s (23.3%)

Algorithm
intervals
Results
790.0ms8000×body128valid
98.0ms8001×pre128true
0.0msbody128invalid
Compiler

Compiled 183 to 129 computations (29.5% saved)

Profiling

Loading profile data...