Details

Time bar (total: 2.8s)

analyze278.0ms

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

sample60.0ms

Algorithm
intervals
Results
21.0ms97×body2560nan
12.0ms76×body1280nan
10.0ms256×body80valid
4.0ms30×body640nan
3.0ms30×body320nan
1.0ms10×body160nan
0.0msbody80nan

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
089
189

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.1b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.0b
(- (* x x) 1.0)
30.8b
(sqrt (- (* x x) 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt add-log-exp
*-un-lft-identity
pow1 add-cube-cbrt sqrt-prod
add-exp-log add-cbrt-cube
flip3-- sqrt-div flip-- difference-of-squares
+-commutative sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log sum-log flip-+ distribute-lft-out
Counts
3 → 40
Calls
3 calls:
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(- (* x x) 1.0)
4.0ms
(sqrt (- (* x x) 1.0))

series14.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(- (* x x) 1.0)
4.0ms
(sqrt (- (* x x) 1.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
04889464
14889464

prune83.0ms

Filtered
40 candidates to 49 candidates (-22.5%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New48149
Fresh000
Picked101
Done000
Total49150

Merged error: 0b

Counts
50 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
10×*-un-lft-identity
associate-*r*
associate-*l*
pow1 add-cube-cbrt
add-exp-log frac-times flip3-+ add-cbrt-cube flip-+ add-log-exp unswap-sqr
flip3-- pow-prod-down flip--
sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
+-commutative sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 53
Calls
2 calls:
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series21.0ms

Counts
2 → 6
Calls
2 calls:
9.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify41.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
05012893

prune132.0ms

Filtered
44 candidates to 59 candidates (-34.1%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New59059
Fresh000
Picked011
Done000
Total59160

Merged error: 0b

Counts
60 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01314
11314

end0.0ms

analyze277.0ms

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

sample1.8s

Algorithm
intervals
Results
590.0ms3034×body2560nan
397.0ms2510×body1280nan
321.0ms8000×body80valid
154.0ms1209×body640nan
60.0ms629×body320nan
22.0ms332×body160nan
10.0ms301×body80nan

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