Details

Time bar (total: 2.8s)

analyze264.0ms (9.3%)

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)

sample51.0ms (1.8%)

Algorithm
intervals
Results
18.0ms121×body2048nan
11.0ms256×body128valid
7.0ms60×body1024nan
3.0ms36×body512nan
1.0ms19×body256nan
1.0ms16×body128nan
0.0msbody4096nan
Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify269.0ms (9.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (101.0ms)

IterNodesCost
0560414

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.1b

Counts
2 → 1
Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
29.9b
(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite15.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64_423 sqrt-prod_binary64_439
add-sqr-sqrt_binary64_445
add-log-exp_binary64_462
add-cube-cbrt_binary64_458 pow1_binary64_484
sqrt-div_binary64_440 add-exp-log_binary64_461 difference-of-squares_binary64_392 add-cbrt-cube_binary64_459
flip-+_binary64_397 +-commutative_binary64_353 distribute-lft-out_binary64_374 rem-sqrt-square_binary64_436 flip3--_binary64_427 flip3-+_binary64_426 pow1/2_binary64_503 sqrt-pow1_binary64_441 difference-of-sqr-1_binary64_393 flip--_binary64_398 sum-log_binary64_514
Counts
2 → 30
Calls

2 calls:

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

series104.0ms (3.7%)

Counts
2 → 6
Calls

2 calls:

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

simplify50.0ms (1.8%)

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
04922536
14922536

prune33.0ms (1.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New35136
Fresh000
Picked101
Done000
Total36137

Merged error: 0b

Counts
37 → 1
Compiler

Compiled 550 to 367 computations (33.3% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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)))

rewrite30.0ms (1%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64_445
19×sqrt-prod_binary64_439
15×*-un-lft-identity_binary64_423
14×sqrt-div_binary64_440
10×associate-*r*_binary64_363
add-cube-cbrt_binary64_458 pow1_binary64_484
associate-*l*_binary64_364
flip-+_binary64_397 flip3-+_binary64_426 add-exp-log_binary64_461 add-cbrt-cube_binary64_459 add-log-exp_binary64_462
frac-times_binary64_433 unswap-sqr_binary64_391
pow-prod-down_binary64_494 flip3--_binary64_427 pow1/2_binary64_503 sqrt-pow1_binary64_441 flip--_binary64_398
distribute-lft-out_binary64_374 associate-*r/_binary64_365 associate-*l/_binary64_366 difference-of-squares_binary64_392
prod-exp_binary64_472 +-commutative_binary64_353 rem-sqrt-square_binary64_436 *-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
3 → 70
Calls

3 calls:

17.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
4.0ms
(sqrt.f64 (+.f64 x 1))
3.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

series155.0ms (5.5%)

Counts
3 → 9
Calls

3 calls:

67.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
63.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
25.0ms
(sqrt.f64 (+.f64 x 1))

simplify82.0ms (2.9%)

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
048931454
148931454

prune85.0ms (3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New79079
Fresh000
Picked011
Done000
Total79180

Merged error: 0b

Counts
80 → 1
Compiler

Compiled 1515 to 1142 computations (24.6% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02319
12319

end0.0ms (0%)

sample1.7s (59.2%)

Algorithm
intervals
Results
623.0ms4018×body2048nan
348.0ms8000×body128valid
250.0ms2067×body1024nan
95.0ms1035×body512nan
32.0ms485×body256nan
19.0ms528×body128nan
2.0ms10×body4096nan
Compiler

Compiled 34 to 29 computations (14.7% saved)

Profiling

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