Details

Time bar (total: 4.4s)

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)

sample1.5s (34.7%)

Results
619.0ms2089×body1024valid
414.0ms4402×body128valid
284.0ms1007×body512valid
83.0ms534×body256valid
81.0ms224×body2048valid
0.0ms3×body128invalid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify14.0ms (0.3%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
29.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶29.6b
(-.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))
✓4.2b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series23.0ms (0.5%)

Counts
2 → 5
Calls

2 calls:

17.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
7.0ms
(sqrt.f64 (+.f64 x 1))

rewrite19.0ms (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))
3.0ms
(sqrt.f64 (+.f64 x 1))

simplify150.0ms (3.4%)

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

prune116.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New95398
Fresh000
Picked101
Done000
Total96399
Error
0.1b
Counts
99 → 3
Alt Table
StatusErrorProgram
29.8b
(+.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (sqrt.f64 (cbrt.f64 x))))
▶0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
29.6b
(/.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (*.f64 (sqrt.f64 x) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Compiler

Compiled 1956 to 1046 computations (46.5% saved)

localize5.0ms (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)))

series67.0ms (1.5%)

Counts
3 → 6
Calls

3 calls:

46.0ms
(sqrt.f64 (+.f64 1 x))
12.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 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 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
7.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
2.0ms
(sqrt.f64 (+.f64 1 x))

simplify128.0ms (2.9%)

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

prune127.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New87895
Fresh202
Picked011
Done000
Total89998
Error
0.0b
Counts
98 → 9
Alt Table
StatusErrorProgram
10.2b
(/.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)))
▶0.3b
(*.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)))))
0.8b
(*.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)))))
9.3b
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
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)))
0.4b
(/.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))))
0.7b
(/.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))))
✓0.2b
(/.f64 1 (+.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)))))
Compiler

Compiled 1936 to 1400 computations (27.7% saved)

localize12.0ms (0.3%)

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 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 (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)))))

series38.0ms (0.9%)

Counts
2 → 2
Calls

2 calls:

26.0ms
(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
12.0ms
(*.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)))))

rewrite77.0ms (1.8%)

Algorithm
1×rewrite-expression-head
Rules
258×sqrt-prod_binary64
236×*-un-lft-identity_binary64
148×times-frac_binary64
144×add-sqr-sqrt_binary64
84×distribute-lft-out_binary64
Counts
2 → 204
Calls

2 calls:

31.0ms
(*.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)))))
8.0ms
(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

simplify219.0ms (5%)

Algorithm
1×egg-herbie
Rules
635×unswap-sqr_binary64
539×times-frac_binary64
411×div-sub_binary64
403×fma-def_binary64
378×associate-/l*_binary64
Counts
206 → 200
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
01114253
11864015
24933961
312303833
425213833
542433833
642563829
749263829
847883829

prune627.0ms (14.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3723375
Fresh347
Picked011
Done101
Total3768384
Error
0b
Counts
384 → 8
Alt Table
StatusErrorProgram
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 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (*.f64 (sqrt.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))))))
▶0.2b
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))
0.8b
(*.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)))))
✓0.3b
(*.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 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
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)))
0.8b
(*.f64 (pow.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 5/2) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
Compiler

Compiled 11501 to 8499 computations (26.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓0.3b
(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series41.0ms (0.9%)

Counts
2 → 2
Calls

2 calls:

25.0ms
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))
16.0ms
(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite38.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
57×*-un-lft-identity_binary64
24×sqrt-prod_binary64
24×distribute-lft-out_binary64
17×pow1_binary64
15×add-sqr-sqrt_binary64
Counts
2 → 83
Calls

2 calls:

16.0ms
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))
15.0ms
(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify117.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
606×distribute-rgt-in_binary64
583×distribute-lft-in_binary64
315×fma-def_binary64
271×times-frac_binary64
267×exp-prod_binary64
Counts
85 → 109
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01142287
12902023
29941593
333761570
445091472
549921472
648311472

prune283.0ms (6.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2072209
Fresh426
Picked101
Done101
Total2134217
Error
0b
Counts
217 → 4
Alt Table
StatusErrorProgram
0.0b
(pow.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) (+.f64 1 x)) (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (/.f64 -1 2))
0.8b
(*.f64 (pow.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 5/2) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
10.2b
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3)) (sqrt.f64 x))) (/.f64 -1 2))
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)))))
Compiler

Compiled 5548 to 3958 computations (28.7% saved)

regimes621.0ms (14.2%)

Accuracy

Total 0.1b remaining (84.7%)

Threshold costs 0.1b (84.7%)

Counts
330 → 1
Compiler

Compiled 14641 to 11064 computations (24.4% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01432
11832
21632

end99.0ms (2.2%)

Compiler

Compiled 153 to 110 computations (28.1% saved)

Profiling

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