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 (32.7%)

Results
645.0ms1994×body1024valid
382.0ms4489×body128valid
230.0ms1034×body512valid
81.0ms224×body2048valid
76.0ms515×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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
29.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
29.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 24 to 18 computations (25% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
2.7b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series31.0ms (0.7%)

Counts
2 → 5
Calls

2 calls:

16.0ms
(sqrt.f64 (+.f64 x 1))
15.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite19.0ms (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))

simplify151.0ms (3.4%)

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

prune130.0ms (2.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New95398
Fresh000
Picked101
Done000
Total96399
Error
0.2b
Counts
99 → 3
Alt Table
StatusErrorProgram
29.9b
(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)))
29.9b
(+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (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 1966 to 1042 computations (47% saved)

localize7.0ms (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)))

series31.0ms (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))

rewrite25.0ms (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:

7.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
7.0ms
(sqrt.f64 (+.f64 1 x))
6.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify136.0ms (3.1%)

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

prune124.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89695
Fresh022
Picked011
Done000
Total89998
Error
0.0b
Counts
98 → 9
Alt Table
StatusErrorProgram
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))))) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
29.9b
(+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (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)))))
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)))))
29.9b
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
9.5b
(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)))))
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
0.5b
(/.f64 1 (fma.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)))
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))))
Compiler

Compiled 1934 to 1384 computations (28.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series100.0ms (2.3%)

Counts
4 → 37
Calls

4 calls:

86.0ms
(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
5.0ms
(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
5.0ms
(sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
4.0ms
(cbrt.f64 (+.f64 1 x))

rewrite29.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity_binary64
29×add-sqr-sqrt_binary64
28×cbrt-prod_binary64
26×cbrt-div_binary64
21×add-cube-cbrt_binary64
Counts
4 → 133
Calls

4 calls:

8.0ms
(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
6.0ms
(sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
5.0ms
(cbrt.f64 (+.f64 1 x))
2.0ms
(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))

simplify180.0ms (4.1%)

Algorithm
egg-herbie
Rules
652×times-frac_binary64
561×fma-neg_binary64
391×fma-def_binary64
269×cancel-sign-sub-inv_binary64
264×associate-*l*_binary64
Counts
170 → 204
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02093488
14203111
29592778
326342494
444042333
547972333
649862333
749042333

prune488.0ms (11%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2833286
Fresh077
Picked011
Done011
Total28312295
Error
0.0b
Counts
295 → 12
Alt Table
StatusErrorProgram
9.5b
(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)))))
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 (cbrt.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 (fma.f64 (sqrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 4) (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)))) (sqrt.f64 (cbrt.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))))) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
29.9b
(+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (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)))))
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)))))
29.9b
(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)))
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
0.5b
(/.f64 1 (fma.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)))
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 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x))))
Compiler

Compiled 8783 to 6680 computations (23.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x)))
0.2b
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x))))
0.3b
(cbrt.f64 (sqrt.f64 (+.f64 1 x)))
0.3b
(cbrt.f64 (+.f64 1 x))

series17.0ms (0.4%)

Counts
3 → 28
Calls

3 calls:

7.0ms
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x)))
5.0ms
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x))))
5.0ms
(cbrt.f64 (sqrt.f64 (+.f64 1 x)))

rewrite46.0ms (1%)

Algorithm
rewrite-expression-head
Rules
68×cbrt-div_binary64
44×sqrt-div_binary64
35×cbrt-prod_binary64
34×flip-+_binary64
34×flip3-+_binary64
Counts
3 → 121
Calls

3 calls:

19.0ms
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x))))
9.0ms
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x)))
3.0ms
(cbrt.f64 (sqrt.f64 (+.f64 1 x)))

simplify156.0ms (3.5%)

Algorithm
egg-herbie
Rules
450×fma-def_binary64
380×fma-neg_binary64
338×times-frac_binary64
275×*-commutative_binary64
269×associate-/l*_binary64
Counts
149 → 220
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02383886
15853723
213593584
326473019
445363009
549673009
649023009

prune697.0ms (15.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3432345
Fresh369
Picked101
Done112
Total3489357
Error
0.0b
Counts
357 → 9
Alt Table
StatusErrorProgram
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))))) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
29.9b
(+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (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)))))
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)))))
29.9b
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
9.5b
(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)))))
0.2b
(/.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))))
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))) (*.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (*.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 1 x)))))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
Compiler

Compiled 13009 to 10123 computations (22.2% saved)

regimes406.0ms (9.2%)

Accuracy

Total 0.1b remaining (72.9%)

Threshold costs 0.1b (72.9%)

Counts
180 → 1
Compiler

Compiled 8534 to 6486 computations (24% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
11214
21114

end155.0ms (3.5%)

Compiler

Compiled 253 to 188 computations (25.7% saved)

Profiling

Loading profile data...