Details

Time bar (total: 3.8s)

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)

sample48.0ms (1.3%)

Algorithm
intervals
Results
9.0ms30×body512valid
8.0ms66×body1024valid
5.0ms138×body128valid
1.0ms18×body256valid
1.0msbody2048valid
Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify11.0ms (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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
29.5b
Counts
2 → 1
Alt Table
StatusErrorProgram
29.5b
(-.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))
3.7b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series24.0ms (0.6%)

Counts
2 → 5
Calls

2 calls:

16.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
7.0ms
(sqrt.f64 (+.f64 x 1))

rewrite18.0ms (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:

9.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
2.0ms
(sqrt.f64 (+.f64 x 1))

simplify153.0ms (4%)

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 (3.4%)

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
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
29.7b
(+.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (sqrt.f64 (cbrt.f64 x))))
Compiler

Compiled 1908 to 1014 computations (46.9% saved)

localize8.0ms (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)))

series32.0ms (0.8%)

Counts
3 → 6
Calls

3 calls:

15.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms
(sqrt.f64 (+.f64 1 x))

rewrite26.0ms (0.7%)

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:

11.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
6.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
2.0ms
(sqrt.f64 (+.f64 1 x))

simplify134.0ms (3.5%)

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

prune115.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New86995
Fresh101
Picked101
Done000
Total88997
Error
0.0b
Counts
97 → 9
Alt Table
StatusErrorProgram
9.4b
(/.f64 1 (+.f64 (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
9.3b
(*.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)))))
9.3b
(cbrt.f64 (*.f64 (*.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
14.4b
(/.f64 1 (+.f64 (/.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (-.f64 (fma.f64 x x 1) x))) (sqrt.f64 x)))
9.2b
(*.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 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.2b
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (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))))
0.5b
(/.f64 1 (+.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
Compiler

Compiled 1992 to 1440 computations (27.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series175.0ms (4.6%)

Counts
3 → 14
Calls

3 calls:

86.0ms
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
85.0ms
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
5.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

rewrite11.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
12×sqrt-prod_binary64
times-frac_binary64
Counts
3 → 67
Calls

3 calls:

4.0ms
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
3.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.0ms
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))

simplify99.0ms (2.6%)

Algorithm
egg-herbie
Rules
911×fma-def_binary64
652×times-frac_binary64
572×fma-neg_binary64
338×associate-/l*_binary64
259×associate-/r*_binary64
Counts
81 → 113
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01321459
12701361
25871255
315521216
442291216
548401216
648841216

prune336.0ms (8.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2141215
Fresh088
Picked011
Done000
Total21410224
Error
0.0b
Counts
224 → 10
Alt Table
StatusErrorProgram
9.2b
(*.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 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
9.4b
(/.f64 1 (+.f64 (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
9.3b
(*.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)))))
9.3b
(cbrt.f64 (*.f64 (*.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
14.4b
(/.f64 1 (+.f64 (/.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (-.f64 (fma.f64 x x 1) x))) (sqrt.f64 x)))
0.4b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.2b
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (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))))
0.5b
(/.f64 1 (+.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
Compiler

Compiled 5358 to 4083 computations (23.8% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))
0.2b
(*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))))
0.2b
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
0.3b
(cbrt.f64 (sqrt.f64 (+.f64 1 x)))

series204.0ms (5.4%)

Counts
4 → 37
Calls

4 calls:

185.0ms
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
10.0ms
(*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))))
5.0ms
(sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))
5.0ms
(cbrt.f64 (sqrt.f64 (+.f64 1 x)))

rewrite36.0ms (1%)

Algorithm
rewrite-expression-head
Rules
91×add-sqr-sqrt_binary64
75×sqrt-prod_binary64
64×cbrt-prod_binary64
33×*-un-lft-identity_binary64
28×unswap-sqr_binary64
Counts
4 → 161
Calls

4 calls:

14.0ms
(*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))))
3.0ms
(sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))
3.0ms
(cbrt.f64 (sqrt.f64 (+.f64 1 x)))
2.0ms
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))

simplify160.0ms (4.2%)

Algorithm
egg-herbie
Rules
778×fma-neg_binary64
694×fma-def_binary64
399×associate-*l*_binary64
377×associate-*r*_binary64
305×times-frac_binary64
Counts
198 → 261
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02926442
16575488
215544347
346184343
452044343

prune554.0ms (14.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3023305
Fresh268
Picked101
Done101
Total3069315
Error
0.0b
Counts
315 → 9
Alt Table
StatusErrorProgram
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (*.f64 (cbrt.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (+.f64 1 x))))))) (sqrt.f64 x)))
0.9b
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))))) (sqrt.f64 x)))
9.2b
(*.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)))))
9.3b
(*.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 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
9.3b
(cbrt.f64 (*.f64 (*.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (+.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 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) 3) (sqrt.f64 x)))
0.5b
(/.f64 1 (+.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
Compiler

Compiled 10332 to 8215 computations (20.5% saved)

regimes542.0ms (14.3%)

Accuracy

Total 0.1b remaining (73.7%)

Threshold costs 0.1b (73.7%)

Counts
264 → 1
Compiler

Compiled 11499 to 9030 computations (21.5% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11418
21318

end0.0ms (0%)

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample950.0ms (25%)

Algorithm
intervals
Results
278.0ms2018×body1024valid
156.0ms4252×body128valid
101.0ms1014×body512valid
35.0ms218×body2048valid
33.0ms498×body256valid
0.0msbody128nan
Compiler

Compiled 270 to 209 computations (22.6% saved)

Profiling

Loading profile data...