Details

Time bar (total: 3.1s)

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)

sample1.8s (57.6%)

Results
830.0ms2118×body1024valid
417.0ms4416×body128valid
223.0ms1003×body512valid
187.0ms505×body256valid
74.0ms214×body2048valid
0.0ms1×body128invalid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify14.0ms (0.4%)

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 (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
33.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶33.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓2.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series13.0ms (0.4%)

Counts
1 → 1
Calls

1 calls:

13.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite58.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
832×prod-diff_binary64
742×log1p-expm1-u_binary64
742×expm1-log1p-u_binary64
89×egg-rr
72×add-sqr-sqrt_binary64
Counts
1 → 89
Calls

1 calls:

56.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
115111
2184111
3601511

simplify9.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
1×1-exp_binary64
Counts
90 → 90
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011
141
231

prune104.0ms (3.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New82890
Fresh000
Picked101
Done000
Total83891
Error
32.5b
Counts
91 → 8
Alt Table
StatusErrorProgram
▶33.4b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
35.0b
1
34.0b
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
34.7b
(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (*.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))
33.8b
(+.f64 (fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
33.9b
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
34.6b
(+.f64 (fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (*.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (*.f64 x x))) (*.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x))))))
34.0b
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
Compiler

Compiled 2392 to 1327 computations (44.5% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓0.0b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓2.4b
(+.f64 x (-.f64 1 x))

series17.0ms (0.6%)

Counts
3 → 14
Calls

3 calls:

9.0ms
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
7.0ms
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
1.0ms
(+.f64 x (-.f64 1 x))

rewrite93.0ms (3%)

Algorithm
1×batch-egg-rewrite
Rules
689×fma-def_binary64
347×fma-neg_binary64
277×egg-rr
199×expm1-udef_binary64
199×log1p-udef_binary64
Counts
3 → 277
Calls

3 calls:

85.0ms
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
85.0ms
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
85.0ms
(+.f64 x (-.f64 1 x))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01038
123229
2319429
3495529

simplify11.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
1×1-exp_binary64
Counts
291 → 278
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0114
1414
2314

prune205.0ms (6.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2762278
Fresh527
Picked101
Done000
Total2824286
Error
0.2b
Counts
286 → 4
Alt Table
StatusErrorProgram
34.0b
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
33.4b
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 x 1) (-.f64 x (hypot.f64 x (sqrt.f64 x)))))
33.9b
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
▶0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Compiler

Compiled 6135 to 3833 computations (37.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.3%)

Counts
1 → 1
Calls

1 calls:

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

rewrite47.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
845×log1p-expm1-u_binary64
845×expm1-log1p-u_binary64
84×add-sqr-sqrt_binary64
79×add-cbrt-cube_binary64
79×add-log-exp_binary64
Counts
1 → 26
Calls

1 calls:

47.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
117614
2214214
3509614

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
1×1-exp_binary64
Counts
27 → 27
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011
141
231

prune83.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New71677
Fresh303
Picked101
Done000
Total75681
Error
0.0b
Counts
81 → 6
Alt Table
StatusErrorProgram
18.9b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))
0.2b
(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
33.0b
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
▶0.2b
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
0.4b
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
Compiler

Compiled 1331 to 961 computations (27.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓0.1b
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
✓0.3b
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)

series31.0ms (1%)

Counts
3 → 3
Calls

3 calls:

15.0ms
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
9.0ms
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
7.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite63.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
439×fma-def_binary64
414×log-prod_binary64
218×fma-neg_binary64
171×expm1-udef_binary64
171×log1p-udef_binary64
Counts
3 → 109
Calls

3 calls:

61.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
61.0ms
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
61.0ms
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01039
121339
2244239
3494039

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
1×1-exp_binary64
Counts
112 → 110
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
013
143
233

prune136.0ms (4.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1082110
Fresh055
Picked011
Done000
Total1088116
Error
0b
Counts
116 → 8
Alt Table
StatusErrorProgram
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
0.3b
(sqrt.f64 (*.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (*.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
18.9b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))
0.2b
(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
0.4b
(sqrt.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2)))
33.0b
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
✓0.2b
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
0.4b
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
Compiler

Compiled 1937 to 1442 computations (25.6% saved)

regimes229.0ms (7.5%)

Accuracy

Total 0.2b remaining (87.6%)

Threshold costs 0.2b (87.6%)

Counts
125 → 1
Compiler

Compiled 4237 to 3238 computations (23.6% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
11620
21520

end128.0ms (4.2%)

Compiler

Compiled 176 to 141 computations (19.9% saved)

Profiling

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