Details

Time bar (total: 2.9s)

analyze283.0ms (9.8%)

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)

sample59.0ms (2.1%)

Algorithm
intervals
Results
21.0ms125×body2048nan
12.0ms256×body128valid
11.0ms85×body1024nan
3.0ms27×body512nan
1.0ms21×body256nan
1.0ms15×body128nan
Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify241.0ms (8.3%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (145.0ms)

IterNodesCost
0492214
1492214

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.6b

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)))
31.3b
(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite19.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64_419
add-sqr-sqrt_binary64_441
add-log-exp_binary64_458
sqrt-prod_binary64_435
add-cube-cbrt_binary64_454
difference-of-squares_binary64_388 pow1_binary64_480
add-cbrt-cube_binary64_455 add-exp-log_binary64_457 cancel-sign-sub-inv_binary64_385
sqrt-div_binary64_436 difference-of-sqr-1_binary64_389 flip3--_binary64_423 flip--_binary64_394
flip3-+_binary64_422 sub-neg_binary64_412 pow1/2_binary64_499 sum-log_binary64_510 distribute-lft-out_binary64_370 flip-+_binary64_393 diff-log_binary64_511 sqrt-pow1_binary64_437 rem-sqrt-square_binary64_432 +-commutative_binary64_349
Counts
3 → 47
Calls

3 calls:

7.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 x x) 1))
4.0ms
(-.f64 (*.f64 x x) 1)

series72.0ms (2.5%)

Counts
3 → 9
Calls

3 calls:

28.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
23.0ms
(-.f64 (*.f64 x x) 1)
20.0ms
(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify39.0ms (1.4%)

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
05277706

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 769 to 501 computations (34.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64_441
26×sqrt-prod_binary64_435
20×*-un-lft-identity_binary64_419
16×sqrt-div_binary64_436
10×add-cube-cbrt_binary64_454 associate-*r*_binary64_359 pow1_binary64_480
associate-*l*_binary64_360
add-log-exp_binary64_458 add-cbrt-cube_binary64_455 add-exp-log_binary64_457
flip3-+_binary64_422 flip-+_binary64_393
difference-of-squares_binary64_388 pow1/2_binary64_499 unswap-sqr_binary64_387 frac-times_binary64_429 flip3--_binary64_423 sqrt-pow1_binary64_437 flip--_binary64_394
pow-prod-down_binary64_490
associate-*l/_binary64_362 difference-of-sqr-1_binary64_389 distribute-lft-out_binary64_370 associate-*r/_binary64_361 distribute-lft-out--_binary64_371 rem-sqrt-square_binary64_432
sqrt-unprod_binary64_439 prod-exp_binary64_468 cbrt-unprod_binary64_452 sum-log_binary64_510 *-commutative_binary64_350 +-commutative_binary64_349
Counts
4 → 89
Calls

4 calls:

13.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
4.0ms
(sqrt.f64 (-.f64 x 1))
3.0ms
(sqrt.f64 (+.f64 x 1))
3.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

series93.0ms (3.2%)

Counts
4 → 12
Calls

4 calls:

36.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
28.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
15.0ms
(sqrt.f64 (-.f64 x 1))
14.0ms
(sqrt.f64 (+.f64 x 1))

simplify73.0ms (2.5%)

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
050081769

prune102.0ms (3.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1010101
Fresh000
Picked011
Done011
Total1012103

Merged error: 0b

Counts
103 → 2
Compiler

Compiled 1918 to 1437 computations (25.1% saved)

regimes26.0ms (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%)

sample1.8s (61.7%)

Algorithm
intervals
Results
658.0ms3902×body2048nan
365.0ms8000×body128valid
268.0ms2050×body1024nan
97.0ms986×body512nan
38.0ms550×body256nan
17.0ms494×body128nan
1.0msbody4096nan
Compiler

Compiled 43 to 36 computations (16.3% saved)

Profiling

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