Details

Time bar (total: 4.4s)

analyze3.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
50%12.5%37.5%4
50%6.2%43.8%5
50%3.1%46.9%6
50%1.6%48.5%7
50%0.8%49.2%8
50%0.4%49.6%9
50%0.2%49.8%10
50%0.1%49.9%11
50%0%50%12
50%0%50%13
50%0%50%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.4s (31.4%)

Results
578.0ms2033×body1024valid
386.0ms4421×body128valid
228.0ms1054×body512valid
82.0ms211×body2048valid
80.0ms537×body256valid
0.0msbody128invalid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.2%)

Algorithm
egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
14×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32311
43011
54711
67211
79211
810911
911911
1012311
1112511
1211111

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
31.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
31.3b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
5.1b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series24.0ms (0.5%)

Counts
2 → 5
Calls

2 calls:

15.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
8.0ms
(sqrt.f64 (+.f64 x 1))

rewrite17.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
64×sqrt-prod_binary64
57×*-un-lft-identity_binary64
45×add-sqr-sqrt_binary64
42×prod-diff_binary64
33×add-cube-cbrt_binary64
Counts
2 → 95
Calls

2 calls:

8.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms
(sqrt.f64 (+.f64 x 1))

simplify155.0ms (3.5%)

Algorithm
egg-herbie
Rules
1110×fma-neg_binary64
566×unswap-sqr_binary64
455×cancel-sign-sub-inv_binary64
444×fma-def_binary64
429×associate-*l*_binary64
Counts
100 → 98
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01192533
12241344
25921128
325271125
440991093
543811093
646631093
749491093
847301093

prune129.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New94498
Fresh000
Picked101
Done000
Total95499
Error
0.1b
Counts
99 → 4
Alt Table
StatusErrorProgram
31.3b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
31.3b
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
31.2b
(+.f64 (fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
Compiler

Compiled 1992 to 1060 computations (46.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series30.0ms (0.7%)

Counts
3 → 6
Calls

3 calls:

13.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms
(sqrt.f64 (+.f64 1 x))

rewrite22.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity_binary64
28×sqrt-prod_binary64
22×distribute-lft-out_binary64
22×add-sqr-sqrt_binary64
18×times-frac_binary64
Counts
3 → 91
Calls

3 calls:

8.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
7.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms
(sqrt.f64 (+.f64 1 x))

simplify131.0ms (3%)

Algorithm
egg-herbie
Rules
888×fma-neg_binary64
558×cancel-sign-sub-inv_binary64
538×times-frac_binary64
389×associate-*l*_binary64
311×associate-*r*_binary64
Counts
97 → 95
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0961310
12031217
24441211
311331207
425561207
542291207
649561207
749981207
848371207

prune144.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New90595
Fresh213
Picked011
Done000
Total92799
Error
0.0b
Counts
99 → 7
Alt Table
StatusErrorProgram
0.4b
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 x) 3))) (+.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.4b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
31.3b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
0.3b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
Compiler

Compiled 1844 to 1330 computations (27.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))
0.1b
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.2b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

series38.0ms (0.9%)

Counts
4 → 18
Calls

4 calls:

13.0ms
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
12.0ms
(+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))
8.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
5.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

rewrite55.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
102×sqrt-prod_binary64
74×add-sqr-sqrt_binary64
42×*-un-lft-identity_binary64
36×sqrt-pow1_binary64
30×pow1_binary64
Counts
4 → 171
Calls

4 calls:

14.0ms
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
14.0ms
(+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))
12.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
3.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

simplify127.0ms (2.9%)

Algorithm
egg-herbie
Rules
729×times-frac_binary64
590×fma-neg_binary64
555×fma-def_binary64
279×cancel-sign-sub-inv_binary64
216×unswap-sqr_binary64
Counts
189 → 220
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02012748
14302530
211182395
327282341
446442341
548412341

prune359.0ms (8.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2642266
Fresh055
Picked101
Done011
Total2658273
Error
0.0b
Counts
273 → 8
Alt Table
StatusErrorProgram
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
0.5b
(/.f64 1 (+.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
0.4b
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
10.0b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 x) 3))) (+.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.4b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
31.3b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
0.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
Compiler

Compiled 6771 to 5233 computations (22.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.2b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
0.2b
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
0.2b
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))))

series27.0ms (0.6%)

Counts
3 → 17
Calls

3 calls:

13.0ms
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
8.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))))
6.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

rewrite109.0ms (2.5%)

Algorithm
rewrite-expression-head
Rules
174×sqrt-div_binary64
143×sqrt-prod_binary64
134×sqrt-pow1_binary64
118×add-sqr-sqrt_binary64
72×pow1_binary64
Counts
3 → 223
Calls

3 calls:

28.0ms
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
26.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))))
15.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify210.0ms (4.7%)

Algorithm
egg-herbie
Rules
658×times-frac_binary64
515×fma-def_binary64
445×fma-neg_binary64
253×*-commutative_binary64
232×cancel-sign-sub-inv_binary64
Counts
240 → 290
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02645068
16044301
213774080
329124022
446704016
549614016
648404016

prune789.0ms (17.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New4271428
Fresh066
Picked011
Done011
Total4279436
Error
0.0b
Counts
436 → 9
Alt Table
StatusErrorProgram
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
10.2b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 x 3/2))) (+.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))))) (-.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))))
10.0b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 x) 3))) (+.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.5b
(/.f64 1 (+.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
0.4b
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.4b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
31.3b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
0.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
Compiler

Compiled 14340 to 11474 computations (20% saved)

regimes413.0ms (9.4%)

Accuracy

Total 0.1b remaining (76.9%)

Threshold costs 0.1b (76.9%)

Counts
207 → 1
Compiler

Compiled 8870 to 6733 computations (24.1% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11418
21318

end206.0ms (4.7%)

Compiler

Compiled 304 to 239 computations (21.4% saved)

Profiling

Loading profile data...