Details

Time bar (total: 3.5s)

analyze5.0ms (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)

sample1.6s (44.6%)

Results
1.5s8256×body128valid
0.0msbody128invalid
Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify101.0ms (2.9%)

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

prune5.0ms (0.2%)

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))))
0.2b
(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 (*.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)

localize22.0ms (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)))))
0.2b
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b
(sqrt.f64 (PI.f64))

series75.0ms (2.1%)

Counts
4 → 36
Calls

4 calls:

59.0ms
(*.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))
0.0ms
(sqrt.f64 (PI.f64))

rewrite40.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
274×log1p-expm1-u_binary64
274×expm1-log1p-u_binary64
268×add-cbrt-cube_binary64
267×add-log-exp_binary64
266×add-exp-log_binary64
Counts
4 → 61
Calls

4 calls:

39.0ms
(*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
39.0ms
(*.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)))))
39.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
38.0ms
(sqrt.f64 (PI.f64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03180
161263
2491963
000
100

simplify123.0ms (3.5%)

Algorithm
egg-herbie
Rules
2001×fma-def_binary64
777×*-commutative_binary64
687×associate-*l*_binary64
479×associate-*r*_binary64
450×sqr-pow_binary64
Counts
97 → 64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
025684
163684
2156684
3399660
4927660
52296660
62662660
72663660
82777660
92969660
103254660
114429660
124853660
134891660

prune99.0ms (2.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New89190
Fresh011
Picked101
Done000
Total90292
Error
0.0b
Counts
92 → 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))))
0.2b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
Compiler

Compiled 5443 to 2316 computations (57.4% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series97.0ms (2.7%)

Counts
4 → 0
Calls

4 calls:

58.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
15.0ms
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
14.0ms
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
9.0ms
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

rewrite70.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
466×log1p-udef_binary64
259×log1p-expm1-u_binary64
259×expm1-log1p-u_binary64
250×add-log-exp_binary64
249×add-cbrt-cube_binary64
Counts
4 → 54
Calls

4 calls:

68.0ms
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
68.0ms
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
68.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
68.0ms
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02569
156167
2480667
3537567
000
100

simplify6.0ms (0.2%)

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
100

prune61.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New54054
Fresh011
Picked011
Done000
Total54256
Error
0.0b
Counts
56 → 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))))
0.2b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
Compiler

Compiled 1849 to 1346 computations (27.2% saved)

localize14.0ms (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))

series15.0ms (0.4%)

Counts
3 → 24
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)))
3.0ms
(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
3.0ms
(*.f64 2/3 (pow.f64 x 3))

rewrite66.0ms (1.9%)

Algorithm
batch-egg-rewrite
Rules
326×log1p-udef_binary64
239×prod-diff_binary64
190×add-sqr-sqrt_binary64
184×log1p-expm1-u_binary64
184×expm1-log1p-u_binary64
Counts
3 → 70
Calls

3 calls:

65.0ms
(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
65.0ms
(*.f64 2/3 (pow.f64 x 3))
65.0ms
(/.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)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01956
140656
2425256
3501556
000
100

simplify133.0ms (3.7%)

Algorithm
egg-herbie
Rules
1073×fma-def_binary64
750×cube-prod_binary64
711×sqr-pow_binary64
690×unswap-sqr_binary64
582×fabs-mul_binary64
Counts
94 → 90
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
038627
1102627
2243535
3580475
41167465
51645465
61841465
72088465
82526465
92549465
102716465
112979465
123197465
133572465
144095465
154379465
164925465

prune109.0ms (3.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1081109
Fresh000
Picked011
Done011
Total1083111
Error
0b
Counts
111 → 3
Alt Table
StatusErrorProgram
1.3b
(fabs.f64 (*.f64 (/.f64 (pow.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)))))) 2) (cbrt.f64 (PI.f64))) (cbrt.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 (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))))
0.2b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
Compiler

Compiled 3101 to 2373 computations (23.5% saved)

localize23.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(cbrt.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))))
0.7b
(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))))))
1.0b
(sqrt.f64 (PI.f64))
1.0b
(cbrt.f64 (PI.f64))

series25.0ms (0.7%)

Counts
3 → 24
Calls

3 calls:

18.0ms
(cbrt.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))))
7.0ms
(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))))))
0.0ms
(cbrt.f64 (PI.f64))

rewrite72.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
239×prod-diff_binary64
212×add-sqr-sqrt_binary64
203×log1p-expm1-u_binary64
203×expm1-log1p-u_binary64
202×add-cbrt-cube_binary64
Counts
3 → 72
Calls

3 calls:

70.0ms
(cbrt.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))))
70.0ms
(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))))))
70.0ms
(cbrt.f64 (PI.f64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02264
145664
2474264
3491764
000
100

simplify61.0ms (1.7%)

Algorithm
egg-herbie
Rules
679×fma-def_binary64
570×unswap-sqr_binary64
451×associate-*l*_binary64
423×distribute-rgt-out_binary64
343×associate-*r*_binary64
Counts
96 → 120
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01211630
13311552
29241096
33571850
45418850

prune202.0ms (5.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1390139
Fresh000
Picked011
Done022
Total1393142
Error
0b
Counts
142 → 3
Alt Table
StatusErrorProgram
1.3b
(fabs.f64 (*.f64 (/.f64 (pow.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)))))) 2) (cbrt.f64 (PI.f64))) (cbrt.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 (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))))
0.2b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
Compiler

Compiled 7947 to 6169 computations (22.4% saved)

regimes362.0ms (10.2%)

Accuracy

Total 0.1b remaining (77.1%)

Threshold costs 0.1b (77.1%)

Counts
51 → 1
Compiler

Compiled 7444 to 5738 computations (22.9% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02650
13950
24050
33950

end161.0ms (4.6%)

Compiler

Compiled 168 to 134 computations (20.2% saved)

Profiling

Loading profile data...