Details

Time bar (total: 7.4s)

analyze185.0ms (2.5%)

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)

sample94.0ms (1.3%)

Algorithm
intervals
Results
72.0ms256×body128valid
5.0ms256×pre128true
Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify117.0ms (1.6%)

Algorithm
egg-herbie
Rules
1509×associate-/l*_binary64
766×distribute-rgt-out_binary64
744×distribute-lft-out_binary64
549×unswap-sqr_binary64
497×associate-/r*_binary64
Counts
1 → 2
Iterations

Useful iterations: 7 (0.0ms)

IterNodesCost
03275
17459
223941
392837
4154937
5319537
6353437
7369833
8228933
9277533
10282333
11480733
12532433

prune11.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.5b
(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
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))))))
Compiler

Compiled 272 to 147 computations (46% saved)

localize48.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.1b
(*.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)))))
0.1b
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b
(sqrt.f64 (PI.f64))

series196.0ms (2.6%)

Counts
4 → 36
Calls

4 calls:

163.0ms
(*.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)))))
19.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
13.0ms
(*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms
(sqrt.f64 (PI.f64))

rewrite98.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt_binary64
39×add-exp-log_binary64
38×add-cbrt-cube_binary64
36×associate-*l*_binary64
35×pow1_binary64
Counts
4 → 155
Calls

4 calls:

35.0ms
(*.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)))))
20.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
9.0ms
(*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
2.0ms
(sqrt.f64 (PI.f64))

simplify254.0ms (3.4%)

Algorithm
egg-herbie
Rules
519×associate-*r*_binary64
418×associate-*l*_binary64
389×cancel-sign-sub-inv_binary64
313×fma-neg_binary64
213×*-commutative_binary64
Counts
191 → 220
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02867308
18705784
235105032
349125032

prune698.0ms (9.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New3062308
Fresh011
Picked101
Done000
Total3073310
Error
0b
Counts
310 → 3
Alt Table
StatusErrorProgram
0.7b
(fabs.f64 (*.f64 (/.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))) (sqrt.f64 (sqrt.f64 (PI.f64))))))
0.5b
(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
Compiler

Compiled 24263 to 9179 computations (62.2% saved)

localize34.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))
0.1b
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.1b
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
0.1b
(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

series243.0ms (3.3%)

Counts
4 → 36
Calls

4 calls:

107.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
55.0ms
(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
54.0ms
(fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))
27.0ms
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))

rewrite35.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt_binary64
19×associate-*l*_binary64
18×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
16×sqrt-prod_binary64
Counts
4 → 92
Calls

4 calls:

12.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
9.0ms
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
1.0ms
(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
1.0ms
(fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))

simplify271.0ms (3.7%)

Algorithm
egg-herbie
Rules
692×distribute-rgt-in_binary64
691×distribute-lft-in_binary64
547×associate-*l*_binary64
469×associate-*r*_binary64
180×exp-prod_binary64
Counts
128 → 114
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01564064
12723814
28473802
345783802
449953802
549893802

prune211.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1131114
Fresh112
Picked011
Done000
Total1143117
Error
0b
Counts
117 → 3
Alt Table
StatusErrorProgram
0.5b
(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
0.5b
(fabs.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))) (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))))
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
Compiler

Compiled 4508 to 3131 computations (30.5% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
0.1b
(*.f64 2/3 (pow.f64 x 3))
0.3b
(/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64)))
1.0b
(sqrt.f64 (PI.f64))

series29.0ms (0.4%)

Counts
3 → 24
Calls

3 calls:

16.0ms
(/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64)))
7.0ms
(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
5.0ms
(*.f64 2/3 (pow.f64 x 3))

rewrite24.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64
22×*-un-lft-identity_binary64
22×add-cube-cbrt_binary64
18×times-frac_binary64
12×associate-*r*_binary64
Counts
3 → 84
Calls

3 calls:

8.0ms
(*.f64 2/3 (pow.f64 x 3))
5.0ms
(/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64)))
1.0ms
(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))

simplify253.0ms (3.4%)

Algorithm
egg-herbie
Rules
651×associate-*l*_binary64
610×associate-*r*_binary64
285×log-prod_binary64
262×fma-def_binary64
184×swap-sqr_binary64
Counts
108 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01613342
13053139
27963025
334383025
448513025
548763025

prune274.0ms (3.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1301131
Fresh101
Picked011
Done011
Total1313134
Error
0b
Counts
134 → 3
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (+.f64 (*.f64 1/5 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5))) (+.f64 (*.f64 2/3 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))) (+.f64 (*.f64 2 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)) (*.f64 1/21 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))))))
0.5b
(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
Compiler

Compiled 4202 to 3098 computations (26.3% saved)

localize37.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series86.0ms (1.2%)

Counts
4 → 0
Calls

4 calls:

24.0ms
(*.f64 2/3 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3)))
23.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))
21.0ms
(*.f64 1/5 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5)))
18.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)

rewrite74.0ms (1%)

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt_binary64
41×sqrt-prod_binary64
38×associate-*l*_binary64
31×*-un-lft-identity_binary64
31×add-exp-log_binary64
Counts
4 → 140
Calls

4 calls:

20.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))
13.0ms
(*.f64 1/5 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5)))
12.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
11.0ms
(*.f64 2/3 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3)))

simplify217.0ms (2.9%)

Algorithm
egg-herbie
Rules
499×associate-/l*_binary64
471×*-commutative_binary64
376×fma-def_binary64
291×associate-*r*_binary64
272×associate-*l/_binary64
Counts
140 → 162
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01652522
13312376
211312376
319622376
444692302
548772302
649012302

prune543.0ms (7.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1620162
Fresh000
Picked011
Done022
Total1623165
Error
0b
Counts
165 → 3
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (+.f64 (*.f64 1/5 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5))) (+.f64 (*.f64 2/3 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))) (+.f64 (*.f64 2 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)) (*.f64 1/21 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))))))
0.5b
(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
Compiler

Compiled 8129 to 6508 computations (19.9% saved)

regimes743.0ms (10%)

Accuracy

Total 0.1b remaining (89.3%)

Threshold costs 0.1b (89.3%)

Counts
43 → 1
Compiler

Compiled 8401 to 6015 computations (28.4% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02966
14166
24066

end2.0ms (0%)

Compiler

Compiled 41 to 34 computations (17.1% saved)

sample2.6s (35%)

Algorithm
intervals
Results
1.8s8000×body128valid
150.0ms8001×pre128true
0.0msbody128invalid
Compiler

Compiled 208 to 145 computations (30.3% saved)

Profiling

Loading profile data...