Details

Time bar (total: 8.1s)

analyze37.0ms (0.5%)

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)

sample53.0ms (0.7%)

Algorithm
intervals
Results
17.0ms60×body1024valid
10.0ms133×body128valid
7.0ms35×body512valid
3.0ms23×body256valid
2.0msbody2048valid
Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify22.0ms (0.3%)

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%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
31.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
31.1b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 24 to 18 computations (25% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
3.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series46.0ms (0.6%)

Counts
2 → 5
Calls

2 calls:

30.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
16.0ms
(sqrt.f64 (+.f64 x 1))

rewrite39.0ms (0.5%)

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:

16.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms
(sqrt.f64 (+.f64 x 1))

simplify234.0ms (2.9%)

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

prune183.0ms (2.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New96298
Fresh000
Picked101
Done000
Total97299
Error
0.2b
Counts
99 → 2
Alt Table
StatusErrorProgram
31.1b
(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)))
Compiler

Compiled 1894 to 1008 computations (46.8% saved)

localize13.0ms (0.2%)

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)))

series58.0ms (0.7%)

Counts
3 → 6
Calls

3 calls:

25.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
19.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
13.0ms
(sqrt.f64 (+.f64 1 x))

rewrite48.0ms (0.6%)

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:

16.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
13.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
9.0ms
(sqrt.f64 (+.f64 1 x))

simplify200.0ms (2.5%)

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

prune238.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New88795
Fresh101
Picked011
Done000
Total89897
Error
0.0b
Counts
97 → 8
Alt Table
StatusErrorProgram
0.3b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
10.2b
(*.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 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)))))
10.2b
(*.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)))))
10.3b
(cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.7b
(*.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)))))
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b
(/.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))))
Compiler

Compiled 1944 to 1400 computations (28% saved)

localize15.0ms (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))))

series70.0ms (0.9%)

Counts
4 → 18
Calls

4 calls:

28.0ms
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
20.0ms
(+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))
14.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
8.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

rewrite115.0ms (1.4%)

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:

30.0ms
(/.f64 1 (+.f64 (*.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 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
23.0ms
(+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))
6.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

simplify239.0ms (3%)

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

prune767.0ms (9.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2642266
Fresh066
Picked011
Done011
Total26410274
Error
0.0b
Counts
274 → 10
Alt Table
StatusErrorProgram
0.3b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
10.2b
(*.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 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)))))
0.7b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
0.3b
(/.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))))
14.1b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (/.f64 (sqrt.f64 (hypot.f64 1 (pow.f64 x 3/2))) (sqrt.f64 (sqrt.f64 (-.f64 (fma.f64 x x 1) x))))) (sqrt.f64 x)))
10.2b
(*.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)))))
10.3b
(cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.7b
(*.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)))))
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
Compiler

Compiled 6900 to 5317 computations (22.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series128.0ms (1.6%)

Counts
3 → 3
Calls

3 calls:

56.0ms
(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
44.0ms
(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
28.0ms
(/.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))))

rewrite289.0ms (3.6%)

Algorithm
rewrite-expression-head
Rules
733×*-un-lft-identity_binary64
694×sqrt-prod_binary64
594×times-frac_binary64
276×distribute-lft-out_binary64
259×add-sqr-sqrt_binary64
Counts
3 → 451
Calls

3 calls:

50.0ms
(/.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))))
17.0ms
(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
13.0ms
(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify1.2s (14.6%)

Algorithm
egg-herbie
Rules
453×fma-def_binary64
452×distribute-rgt-in_binary64
411×distribute-lft-in_binary64
348×associate-/l/_binary64
341×associate-/l*_binary64
Counts
454 → 339
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
016018625
132917661
258816355
3120615865
4269014861
5450213993
6490413993
7487913993

prune1.3s (16.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4015406
Fresh617
Picked101
Done112
Total4097416
Error
0b
Counts
416 → 7
Alt Table
StatusErrorProgram
0.4b
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
0.8b
(*.f64 (/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2)) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
10.3b
(cbrt.f64 (/.f64 1 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)))
10.2b
(*.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 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)))))
0.3b
(/.f64 (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (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)))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
Compiler

Compiled 13795 to 10006 computations (27.5% saved)

regimes904.0ms (11.2%)

Accuracy

Total 0.1b remaining (81.2%)

Threshold costs 0.1b (81.2%)

Counts
231 → 1
Compiler

Compiled 12854 to 9694 computations (24.6% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
11214
21114

end1.0ms (0%)

Compiler

Compiled 10 to 8 computations (20% saved)

sample1.8s (22.6%)

Algorithm
intervals
Results
564.0ms1993×body1024valid
327.0ms4345×body128valid
209.0ms963×body512valid
79.0ms219×body2048valid
72.0ms480×body256valid
0.0msbody128nan
Compiler

Compiled 211 to 159 computations (24.6% saved)

Profiling

Loading profile data...