Details

Time bar (total: 2.5s)

analyze266.0ms

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

sample57.0ms

Algorithm
intervals
Results
17.0ms89×body2560nan
12.0ms72×body1280nan
10.0ms256×body80valid
6.0ms50×body640nan
2.0ms17×body320nan
1.0ms16×body160nan
0.0msbody80nan

simplify157.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (154.0ms)

IterNodesCost
050309

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.4b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
28.3b
(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64 sqrt-prod_binary64
add-sqr-sqrt_binary64
add-log-exp_binary64
pow1_binary64 add-cube-cbrt_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 difference-of-squares_binary64 sqrt-div_binary64
flip3-+_binary64 pow1/2_binary64 flip3--_binary64 distribute-lft-out_binary64 difference-of-sqr-1_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 +-commutative_binary64 flip--_binary64 flip-+_binary64 sum-log_binary64
Counts
2 → 30
Calls
2 calls:
7.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 x x) 1))

series10.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify42.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
04983354
14983354

prune34.0ms

Filtered
29 candidates to 36 candidates (-24.1%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New35136
Fresh000
Picked101
Done000
Total36137

Merged error: 0b

Counts
37 → 1

localize8.0ms

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)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
15×sqrt-prod_binary64
12×sqrt-div_binary64
11×*-un-lft-identity_binary64
10×associate-*r*_binary64
associate-*l*_binary64
pow1_binary64 add-cube-cbrt_binary64
flip3-+_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 unswap-sqr_binary64 flip-+_binary64 frac-times_binary64
pow-prod-down_binary64 flip3--_binary64 flip--_binary64
pow1/2_binary64 associate-*r/_binary64 sqrt-pow1_binary64 difference-of-squares_binary64 associate-*l/_binary64
cbrt-unprod_binary64 distribute-lft-out_binary64 difference-of-sqr-1_binary64 sqrt-unprod_binary64 prod-exp_binary64 distribute-lft-out--_binary64 +-commutative_binary64 sum-log_binary64 *-commutative_binary64
Counts
2 → 54
Calls
2 calls:
3.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
13.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

series16.0ms

Counts
2 → 6
Calls
2 calls:
6.0ms
(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
9.0ms
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

simplify46.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
05012756

prune58.0ms

Filtered
45 candidates to 60 candidates (-33.3%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New60060
Fresh000
Picked011
Done000
Total60161

Merged error: 0b

Counts
61 → 1

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02212
12212

end0.0ms

sample1.8s

Algorithm
intervals
Results
588.0ms2965×body2560nan
417.0ms2469×body1280nan
327.0ms8000×body80valid
169.0ms1273×body640nan
64.0ms649×body320nan
23.0ms311×body160nan
10.0ms299×body80nan

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