Details

Time bar (total: 4.8s)

analyze3.0ms (0.1%)

Algorithm
1×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 (29.3%)

Results
585.0ms2061×body1024valid
392.0ms4403×body128valid
242.0ms1014×body512valid
80.0ms560×body256valid
79.0ms218×body2048valid
0.0ms1×body128invalid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify11.0ms (0.2%)

Algorithm
1×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))
✓2.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series25.0ms (0.5%)

Counts
2 → 5
Calls

2 calls:

18.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
7.0ms
(sqrt.f64 (+.f64 x 1))

rewrite18.0ms (0.4%)

Algorithm
1×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))
2.0ms
(sqrt.f64 (+.f64 x 1))

simplify152.0ms (3.2%)

Algorithm
1×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

prune104.0ms (2.1%)

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
29.6b
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
29.5b
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
29.5b
(-.f64 (hypot.f64 (sqrt.f64 x) 1) (sqrt.f64 x))
▶0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
Compiler

Compiled 1940 to 1042 computations (46.3% saved)

localize9.0ms (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 (0.6%)

Counts
3 → 6
Calls

3 calls:

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

rewrite22.0ms (0.5%)

Algorithm
1×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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
2.0ms
(sqrt.f64 (+.f64 1 x))

simplify142.0ms (3%)

Algorithm
1×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

prune137.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New86995
Fresh303
Picked101
Done000
Total90999
Error
0.0b
Counts
99 → 9
Alt Table
StatusErrorProgram
10.1b
(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)))))
9.6b
(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 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.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)))
0.3b
(/.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))))
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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
15.8b
(/.f64 1 (+.f64 (/.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (-.f64 (fma.f64 x x 1) x))) (sqrt.f64 x)))
9.9b
(*.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)))))
0.5b
(/.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)

localize9.0ms (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)))

series97.0ms (2%)

Counts
3 → 14
Calls

3 calls:

81.0ms
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
12.0ms
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
4.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

rewrite11.0ms (0.2%)

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

3 calls:

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

Algorithm
1×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

prune327.0ms (6.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2141215
Fresh268
Picked011
Done000
Total2168224
Error
0.0b
Counts
224 → 8
Alt Table
StatusErrorProgram
10.1b
(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)))))
9.6b
(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 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.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)))
▶0.3b
(/.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))))
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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
9.9b
(*.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 (*.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)))
Compiler

Compiled 5288 to 4029 computations (23.8% saved)

localize8.0ms (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)))
✓0.1b
(/.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))))

series61.0ms (1.3%)

Counts
3 → 3
Calls

3 calls:

26.0ms
(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
21.0ms
(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
14.0ms
(/.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))))

rewrite137.0ms (2.8%)

Algorithm
1×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:

23.0ms
(/.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))))
10.0ms
(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
6.0ms
(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify561.0ms (11.6%)

Algorithm
1×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

prune706.0ms (14.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4033406
Fresh246
Picked101
Done011
Total4068414
Error
0b
Counts
414 → 8
Alt Table
StatusErrorProgram
0.3b
(/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (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))) (*.f64 (*.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)))
10.1b
(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)))))
0.3b
(/.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)))
✓0.2b
(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
9.9b
(*.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)))))
0.5b
(/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3))
0.4b
(/.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
Compiler

Compiled 13808 to 10020 computations (27.4% saved)

regimes569.0ms (11.8%)

Accuracy

Total 0.1b remaining (82%)

Threshold costs 0.1b (82%)

Counts
304 → 1
Compiler

Compiled 13855 to 10613 computations (23.4% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11418
21318

end156.0ms (3.2%)

Compiler

Compiled 228 to 177 computations (22.4% saved)

Profiling

Loading profile data...