Details

Time bar (total: 5.2s)

analyze113.0ms (2.1%)

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)

sample43.0ms (0.8%)

Algorithm
intervals
Results
29.0ms256×body128valid
3.0ms256×pre128true
Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify97.0ms (1.9%)

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)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

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 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)

rewrite625.0ms (11.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
181×add-exp-log_binary64
128×prod-exp_binary64
107×add-cbrt-cube_binary64
70×cbrt-unprod_binary64
51×pow1_binary64
Counts
4 → 183
Calls

4 calls:

84.0ms
(*.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)))
28.0ms
(*.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)))))
14.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 14915 to 5013 computations (66.4% saved)

series93.0ms (1.8%)

Error
0b
Counts
4 → 9
Calls

4 calls:

53.0ms
(*.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)))))
18.0ms
(*.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)))
16.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 1006 to 584 computations (41.9% saved)

simplify230.0ms (4.4%)

Algorithm
egg-herbie
Rules
582×associate-*l*_binary64
539×unswap-sqr_binary64
270×cancel-sign-sub-inv_binary64
255×*-commutative_binary64
206×distribute-rgt-neg-in_binary64
Counts
192 → 168
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03528086
19506124
228345339
348955339
448885339

prune175.0ms (3.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1662168
Fresh101
Picked101
Done000
Total1682170
Error
0b
Counts
170 → 2
Alt Table
StatusErrorProgram
0.5b
(fabs.f64 (/.f64 (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (*.f64 (fabs.f64 x) (+.f64 (*.f64 2/3 (*.f64 x x)) 2)))) (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 (pow.f64 (fabs.f64 x) 7) 21))))
Compiler

Compiled 5907 to 2936 computations (50.3% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

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)))
0.1b
(*.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 (pow.f64 (fabs.f64 x) 7) 21)))
0.1b
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b
(sqrt.f64 PI.f64)

rewrite364.0ms (6.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
119×add-exp-log_binary64
76×prod-exp_binary64
75×add-cbrt-cube_binary64
48×associate-*l*_binary64
46×add-sqr-sqrt_binary64
Counts
4 → 170
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 (pow.f64 (fabs.f64 x) 7) 21)))
32.0ms
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
14.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 10653 to 4681 computations (56.1% saved)

series93.0ms (1.8%)

Error
0b
Counts
4 → 9
Calls

4 calls:

58.0ms
(*.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 (pow.f64 (fabs.f64 x) 7) 21)))
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)))
14.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 796 to 558 computations (29.9% saved)

simplify249.0ms (4.8%)

Algorithm
egg-herbie
Rules
474×associate-*r*_binary64
415×associate-*l*_binary64
358×unswap-sqr_binary64
294×cancel-sign-sub-inv_binary64
210×*-commutative_binary64
Counts
179 → 155
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03146583
18645829
232525164
347775076
449045074
549195074

prune174.0ms (3.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1550155
Fresh011
Picked011
Done000
Total1552157
Error
0b
Counts
157 → 2
Alt Table
StatusErrorProgram
0.5b
(fabs.f64 (/.f64 (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (*.f64 (fabs.f64 x) (+.f64 (*.f64 2/3 (*.f64 x x)) 2)))) (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 (pow.f64 (fabs.f64 x) 7) 21))))
Compiler

Compiled 4976 to 2898 computations (41.8% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite176.0ms (3.4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
37×add-sqr-sqrt_binary64
25×add-cube-cbrt_binary64 *-un-lft-identity_binary64
18×times-frac_binary64
16×add-exp-log_binary64
15×sqrt-prod_binary64
Counts
4 → 104
Calls

4 calls:

14.0ms
(/.f64 (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (*.f64 (fabs.f64 x) (+.f64 (*.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64))
7.0ms
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
6.0ms
(*.f64 2/3 (*.f64 x x))
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 3905 to 2432 computations (37.7% saved)

series103.0ms (2%)

Error
0b
Counts
4 → 12
Calls

4 calls:

64.0ms
(/.f64 (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (*.f64 (fabs.f64 x) (+.f64 (*.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64))
17.0ms
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
12.0ms
(*.f64 2/3 (*.f64 x x))
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 888 to 682 computations (23.2% saved)

simplify176.0ms (3.4%)

Algorithm
egg-herbie
Rules
759×associate-*l*_binary64
651×associate-*r*_binary64
380×distribute-rgt-in_binary64
357×distribute-lft-in_binary64
165×times-frac_binary64
Counts
116 → 91
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02013980
14323751
211783189
342803189
449993189
548863189

prune98.0ms (1.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New91091
Fresh000
Picked011
Done011
Total91293
Error
0b
Counts
93 → 2
Alt Table
StatusErrorProgram
0.5b
(fabs.f64 (/.f64 (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (*.f64 (fabs.f64 x) (+.f64 (*.f64 2/3 (*.f64 x x)) 2)))) (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 (pow.f64 (fabs.f64 x) 7) 21))))
Compiler

Compiled 2474 to 1651 computations (33.3% saved)

regimes1.1s (20.9%)

Accuracy

Total 0.1b remaining (73.7%)

Threshold costs 0.1b (73.7%)

Compiler

Compiled 23014 to 15953 computations (30.7% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
fabs-mul_binary64
1-exp_binary64 fabs-div_binary64 sqr-abs_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03066
14666
25066
34766

end1.0ms (0%)

Compiler

Compiled 42 to 29 computations (31% saved)

sample1.3s (23.9%)

Algorithm
intervals
Results
760.0ms8000×body128valid
95.0ms8002×pre128true
0.0msbody128invalid
Compiler

Compiled 193 to 114 computations (40.9% saved)

Profiling

Loading profile data...