Details

Time bar (total: 6.7s)

analyze6.0ms (0.1%)

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)

sample1.7s (26%)

Results
1.6s8256×body128valid
0.0msbody128invalid
Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify107.0ms (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

prune6.0ms (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)

localize27.0ms (0.4%)

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

series118.0ms (1.8%)

Counts
4 → 36
Calls

4 calls:

100.0ms
(*.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)))))
10.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms
(*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms
(sqrt.f64 (PI.f64))

rewrite66.0ms (1%)

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:

24.0ms
(*.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)))))
10.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
6.0ms
(*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
1.0ms
(sqrt.f64 (PI.f64))

simplify157.0ms (2.3%)

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

prune403.0ms (6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3071308
Fresh011
Picked011
Done000
Total3073310
Error
0b
Counts
310 → 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))))
0.1b
(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))))))
0.7b
(fabs.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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))))))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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)))))))))
Compiler

Compiled 24281 to 9176 computations (62.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(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)))))
0.2b
(*.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))

series18.0ms (0.3%)

Counts
3 → 24
Calls

3 calls:

9.0ms
(/.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)))
5.0ms
(*.f64 2/3 (pow.f64 x 3))
4.0ms
(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)))))

rewrite14.0ms (0.2%)

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:

5.0ms
(*.f64 2/3 (pow.f64 x 3))
3.0ms
(/.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)))
0.0ms
(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)))))

simplify102.0ms (1.5%)

Algorithm
egg-herbie
Rules
642×associate-*l*_binary64
599×associate-*r*_binary64
300×fma-def_binary64
205×cancel-sign-sub-inv_binary64
199×exp-prod_binary64
Counts
108 → 145
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01633453
13173236
27953122
334593122
448643122

prune194.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1610161
Fresh011
Picked011
Done011
Total1613164
Error
0b
Counts
164 → 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))))
0.1b
(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))))))
0.7b
(fabs.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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))))))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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)))))))))
Compiler

Compiled 5325 to 3881 computations (27.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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)))))))
0.5b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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))))))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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))))))))
1.0b
(sqrt.f64 (PI.f64))

series465.0ms (7%)

Counts
3 → 36
Calls

3 calls:

355.0ms
(*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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)))))))
83.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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))))))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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))))))))
27.0ms
(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

rewrite79.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
223×add-sqr-sqrt_binary64
146×rem-sqrt-square_binary64
98×mul-fabs_binary64
86×times-frac_binary64
84×sqrt-prod_binary64
Counts
3 → 158
Calls

3 calls:

18.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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))))))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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))))))))
12.0ms
(*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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)))))))
0.0ms
(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

simplify287.0ms (4.3%)

Algorithm
egg-herbie
Rules
676×sqr-pow_binary64
405×unswap-sqr_binary64
370×fma-def_binary64
361×*-commutative_binary64
329×associate-/l/_binary64
Counts
194 → 165
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01338038
12617457
28917346
317597019
429307019
536186887
643286887
753316887

prune516.0ms (7.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2950295
Fresh000
Picked011
Done022
Total2953298
Error
0b
Counts
298 → 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))))
0.1b
(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))))))
0.7b
(fabs.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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))))))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (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)))))))))
Compiler

Compiled 20211 to 13348 computations (34% saved)

regimes2.2s (33.1%)

Accuracy

Total 0.1b remaining (70.3%)

Threshold costs 0.1b (70.3%)

Counts
205 → 1
Compiler

Compiled 56546 to 38202 computations (32.4% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02869
14169
24069

end129.0ms (1.9%)

Compiler

Compiled 238 to 166 computations (30.3% saved)

Profiling

Loading profile data...