Details

Time bar (total: 2.9s)

analyze263.0ms (9.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%50%25%4
25%37.5%37.5%5
25%31.2%43.8%6
25%28.1%46.9%7
25%26.5%48.5%8
25%25.8%49.2%9
25%25.4%49.6%10
25%25.2%49.8%11
25%25.1%49.9%12
25%25%50%13
25%25%50%14
Compiler

Compiled 10 to 8 computations (20% saved)

sample53.0ms (1.8%)

Algorithm
intervals
Results
19.0ms123×body2048nan
11.0ms256×body128valid
7.0ms62×body1024nan
3.0ms13×body256nan
3.0ms28×body512nan
0.0ms15×body128nan
Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify263.0ms (9.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (100.0ms)

IterNodesCost
0560414

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.1b

Counts
2 → 1
Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(-.f64 (*.f64 x x) 1)
0.0b
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
28.0b
(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite25.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64_423
add-sqr-sqrt_binary64_445
add-log-exp_binary64_462
sqrt-prod_binary64_439
add-cube-cbrt_binary64_458
pow1_binary64_484 difference-of-squares_binary64_392
cancel-sign-sub-inv_binary64_389 add-exp-log_binary64_461 add-cbrt-cube_binary64_459
sqrt-div_binary64_440 flip3--_binary64_427 difference-of-sqr-1_binary64_393 flip--_binary64_398
sub-neg_binary64_416 flip-+_binary64_397 diff-log_binary64_515 +-commutative_binary64_353 distribute-lft-out_binary64_374 rem-sqrt-square_binary64_436 flip3-+_binary64_426 pow1/2_binary64_503 sqrt-pow1_binary64_441 sum-log_binary64_514
Counts
3 → 47
Calls

3 calls:

8.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
6.0ms
(sqrt.f64 (-.f64 (*.f64 x x) 1))
5.0ms
(-.f64 (*.f64 x x) 1)

series160.0ms (5.5%)

Counts
3 → 9
Calls

3 calls:

61.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
56.0ms
(-.f64 (*.f64 x x) 1)
43.0ms
(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify71.0ms (2.5%)

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
04877706
14877706

prune48.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New55156
Fresh000
Picked011
Done000
Total55257

Merged error: 0b

Counts
57 → 2
Compiler

Compiled 790 to 519 computations (34.3% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.5b
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite23.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64_445
15×sqrt-prod_binary64_439
12×sqrt-div_binary64_440
11×*-un-lft-identity_binary64_423
10×associate-*r*_binary64_363
associate-*l*_binary64_364
add-cube-cbrt_binary64_458 pow1_binary64_484
frac-times_binary64_433 flip-+_binary64_397 flip3-+_binary64_426 add-exp-log_binary64_461 add-cbrt-cube_binary64_459 add-log-exp_binary64_462 unswap-sqr_binary64_391
pow-prod-down_binary64_494 flip3--_binary64_427 flip--_binary64_398
associate-*r/_binary64_365 associate-*l/_binary64_366 difference-of-squares_binary64_392 pow1/2_binary64_503 sqrt-pow1_binary64_441
prod-exp_binary64_472 +-commutative_binary64_353 distribute-lft-out_binary64_374 *-commutative_binary64_354 distribute-lft-out--_binary64_375 sqrt-unprod_binary64_443 difference-of-sqr-1_binary64_393 sum-log_binary64_514 cbrt-unprod_binary64_456
Counts
2 → 54
Calls

2 calls:

15.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
3.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

series123.0ms (4.3%)

Counts
2 → 6
Calls

2 calls:

68.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
55.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify61.0ms (2.1%)

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049601195
149601195

prune63.0ms (2.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New60060
Fresh000
Picked011
Done011
Total60262

Merged error: 0b

Counts
62 → 2
Compiler

Compiled 1149 to 866 computations (24.6% saved)

regimes27.0ms (0.9%)

Compiler

Compiled 99 to 79 computations (20.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02319
12319

end0.0ms (0%)

sample1.7s (58.6%)

Algorithm
intervals
Results
644.0ms4108×body2048nan
352.0ms8000×body128valid
242.0ms1963×body1024nan
98.0ms1033×body512nan
32.0ms520×body256nan
17.0ms506×body128nan
1.0msbody4096nan
Compiler

Compiled 43 to 36 computations (16.3% saved)

Profiling

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