Details

Time bar (total: 4.8s)

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 (32.9%)

Results
1.5s8256×body128valid
0.0msbody128invalid
Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify106.0ms (2.2%)

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 (0.1%)

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)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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 (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))

series34.0ms (0.7%)

Counts
4 → 36
Calls

4 calls:

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)))
10.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
8.0ms
(*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms
(sqrt.f64 (PI.f64))

rewrite61.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
115×add-exp-log_binary64
78×add-cbrt-cube_binary64
75×prod-exp_binary64
53×pow1_binary64
45×cbrt-unprod_binary64
Counts
4 → 153
Calls

4 calls:

27.0ms
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (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))
1.0ms
(sqrt.f64 (PI.f64))

simplify136.0ms (2.8%)

Algorithm
egg-herbie
Rules
504×associate-/l*_binary64
471×fma-def_binary64
345×associate-/r*_binary64
331×unswap-sqr_binary64
310×associate-*r*_binary64
Counts
189 → 194
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02172646
13962039
213721782
329771752
446191719
549961719
648911719

prune391.0ms (8.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2793282
Fresh011
Picked101
Done000
Total2804284
Error
0.0b
Counts
284 → 4
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 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (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))))
5.5b
(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (log.f64 (exp.f64 (pow.f64 (fabs.f64 x) 3))))) (*.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))))))
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))))))
Compiler

Compiled 20573 to 7402 computations (64% saved)

localize29.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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 (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))

prune394.0ms (8.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2362238
Fresh213
Picked011
Done000
Total2384242
Error
0.0b
Counts
242 → 4
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 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (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 (*.f64 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
5.5b
(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (log.f64 (exp.f64 (pow.f64 (fabs.f64 x) 3))))) (*.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 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (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 16465 to 7708 computations (53.2% saved)

localize14.0ms (0.3%)

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))

series17.0ms (0.4%)

Counts
3 → 24
Calls

3 calls:

10.0ms
(/.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)))
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)))))
3.0ms
(*.f64 2/3 (pow.f64 x 3))

rewrite13.0ms (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:

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)))))

simplify110.0ms (2.3%)

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

prune192.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1583161
Fresh202
Picked011
Done011
Total1605165
Error
0b
Counts
165 → 5
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 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
1.2b
(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))))) (expm1.f64 (log1p.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 (*.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 1/5 (pow.f64 x 5) (*.f64 1/21 (pow.f64 x 7))))))
0.4b
(fabs.f64 (/.f64 (/.f64 (fma.f64 1/5 (pow.f64 x 5) (fma.f64 1/21 (pow.f64 x 7) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (fabs.f64 (cbrt.f64 (PI.f64)))) (sqrt.f64 (cbrt.f64 (PI.f64)))))
Compiler

Compiled 5367 to 3935 computations (26.7% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series22.0ms (0.5%)

Counts
3 → 24
Calls

3 calls:

11.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 x 5) (*.f64 1/21 (pow.f64 x 7))))
6.0ms
(*.f64 1/21 (pow.f64 x 7))
5.0ms
(fma.f64 1/5 (pow.f64 x 5) (*.f64 1/21 (pow.f64 x 7)))

rewrite15.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64
19×associate-*l*_binary64
16×sqrt-prod_binary64
16×*-un-lft-identity_binary64
15×add-cube-cbrt_binary64
Counts
3 → 76
Calls

3 calls:

7.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/5 (pow.f64 x 5) (*.f64 1/21 (pow.f64 x 7))))
4.0ms
(*.f64 1/21 (pow.f64 x 7))
0.0ms
(fma.f64 1/5 (pow.f64 x 5) (*.f64 1/21 (pow.f64 x 7)))

simplify75.0ms (1.5%)

Algorithm
egg-herbie
Rules
947×distribute-lft-in_binary64
945×distribute-rgt-in_binary64
474×fma-def_binary64
454×associate-*l*_binary64
385×associate-*r*_binary64
Counts
100 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01202194
12141937
25941925
317581925
455711925

prune256.0ms (5.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1510151
Fresh022
Picked011
Done022
Total1515156
Error
0b
Counts
156 → 5
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 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
1.2b
(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))))) (expm1.f64 (log1p.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 (*.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 1/5 (pow.f64 x 5) (*.f64 1/21 (pow.f64 x 7))))))
0.4b
(fabs.f64 (/.f64 (/.f64 (fma.f64 1/5 (pow.f64 x 5) (fma.f64 1/21 (pow.f64 x 7) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (fabs.f64 (cbrt.f64 (PI.f64)))) (sqrt.f64 (cbrt.f64 (PI.f64)))))
Compiler

Compiled 5770 to 4604 computations (20.2% saved)

regimes1.2s (24.3%)

Accuracy

Total 0.1b remaining (83.5%)

Threshold costs 0.1b (83.5%)

Counts
137 → 1
Compiler

Compiled 37281 to 24193 computations (35.1% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02544
13144
23044

end154.0ms (3.2%)

Compiler

Compiled 229 to 171 computations (25.3% saved)

Profiling

Loading profile data...