Details

Time bar (total: 7.8s)

analyze155.0ms (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)

sample81.0ms (1%)

Algorithm
intervals
Results
61.0ms256×body128valid
5.0ms256×pre128true
Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify148.0ms (1.9%)

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

prune10.0ms (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)

localize54.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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))

series61.0ms (0.8%)

Counts
4 → 36
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)))
17.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
14.0ms
(*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.0ms
(sqrt.f64 (PI.f64))

rewrite115.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
119×add-exp-log_binary64
80×pow1_binary64
79×add-cbrt-cube_binary64
78×prod-exp_binary64
48×cbrt-unprod_binary64
Counts
4 → 161
Calls

4 calls:

46.0ms
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
19.0ms
(*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
17.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms
(sqrt.f64 (PI.f64))

simplify163.0ms (2.1%)

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
197 → 196
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02172703
13982049
215411726
332831697
449591697

prune590.0ms (7.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2393242
Fresh011
Picked101
Done000
Total2404244
Error
0.0b
Counts
244 → 4
Alt Table
StatusErrorProgram
1.1b
(fabs.f64 (*.f64 (/.f64 1 (expm1.f64 (log1p.f64 (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
(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 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
0.2b
(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 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (pow.f64 x 4))) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
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))))
Compiler

Compiled 17723 to 6548 computations (63.1% saved)

localize59.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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))

prune544.0ms (7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1951196
Fresh213
Picked011
Done000
Total1973200
Error
0.0b
Counts
200 → 3
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 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
1.1b
(fabs.f64 (*.f64 (/.f64 1 (expm1.f64 (log1p.f64 (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 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
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))))
Compiler

Compiled 12750 to 6229 computations (51.1% saved)

localize31.0ms (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))))
0.2b
(*.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))

series26.0ms (0.3%)

Counts
3 → 24
Calls

3 calls:

14.0ms
(/.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)))
6.0ms
(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))

rewrite26.0ms (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 (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)))
8.0ms
(*.f64 2/3 (pow.f64 x 3))
1.0ms
(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))

simplify218.0ms (2.8%)

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

prune378.0ms (4.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1292131
Fresh011
Picked011
Done011
Total1295134
Error
0b
Counts
134 → 5
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3)))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5))))))
1.7b
(fabs.f64 (*.f64 (/.f64 (*.f64 (cbrt.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)))))) (cbrt.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))))))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (/.f64 (cbrt.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)))))) (cbrt.f64 (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 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
1.1b
(fabs.f64 (*.f64 (/.f64 1 (expm1.f64 (log1p.f64 (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 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
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))))
Compiler

Compiled 4479 to 3272 computations (26.9% saved)

localize40.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series61.0ms (0.8%)

Counts
3 → 24
Calls

3 calls:

29.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5))))
26.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
6.0ms
(*.f64 1/5 (pow.f64 x 5))

rewrite59.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt_binary64
35×associate-*l*_binary64
32×sqrt-prod_binary64
26×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
Counts
3 → 105
Calls

3 calls:

27.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5))))
12.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
7.0ms
(*.f64 1/5 (pow.f64 x 5))

simplify216.0ms (2.8%)

Algorithm
egg-herbie
Rules
679×fma-def_binary64
459×associate-/l*_binary64
435×sqr-pow_binary64
350×*-commutative_binary64
223×exp-prod_binary64
Counts
129 → 142
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01593232
13062800
28962788
316482788
424772788
544482788
650982788

prune629.0ms (8.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1802182
Fresh202
Picked011
Done022
Total1825187
Error
0b
Counts
187 → 5
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3)))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (PI.f64)))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (PI.f64)))) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5)))))))
0.1b
(fabs.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3)))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5))))))
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 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
0.1b
(fabs.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3)))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))) (*.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 (PI.f64)))) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5)))))))
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))))
Compiler

Compiled 7047 to 5609 computations (20.4% saved)

regimes1.8s (23.2%)

Accuracy

Total 0.1b remaining (79.7%)

Threshold costs 0.1b (79.7%)

Counts
114 → 1
Compiler

Compiled 27316 to 18328 computations (32.9% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02660
13460
23360

end2.0ms (0%)

Compiler

Compiled 38 to 32 computations (15.8% saved)

sample2.3s (29.5%)

Algorithm
intervals
Results
1.6s8000×body128valid
127.0ms8000×pre128true
Compiler

Compiled 303 to 209 computations (31% saved)

Profiling

Loading profile data...