Details

Time bar (total: 2.3s)

analyze2.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
50%12.5%37.5%4
50%6.2%43.8%5
50%3.1%46.9%6
50%1.6%48.5%7
50%0.8%49.2%8
50%0.4%49.6%9
50%0.2%49.8%10
50%0.1%49.9%11
50%0%50%12
50%0%50%13
50%0%50%14

sample21.0ms

Algorithm
intervals
Results
7.0ms60×body1280valid
4.0ms135×body80valid
3.0ms33×body640valid
1.0ms20×body320valid
0.0ms8×body160valid

simplify2.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
077
177

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.0b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
1 → 18
Calls
1 calls:
7.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series9.0ms

Counts
1 → 3
Calls
1 calls:
9.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify39.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
05323324

prune39.0ms

Filtered
15 candidates to 21 candidates (-40.0%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New20121
Fresh000
Picked011
Done000
Total20222

Merged error: 0.2b

Counts
22 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 55
Calls
2 calls:
7.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series16.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
11.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify41.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
05645850

prune115.0ms

Filtered
43 candidates to 61 candidates (-41.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New54761
Fresh000
Picked011
Done011
Total54963

Merged error: 0.0b

Counts
63 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
7.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
29.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms
(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

series55.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
17.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
18.0ms
(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify123.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0495211205
1495211205

prune575.0ms

Filtered
150 candidates to 457 candidates (-204.7%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New4525457
Fresh336
Picked101
Done022
Total45610466

Merged error: 0b

Counts
466 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b
(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
0.3b
(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
74×*-un-lft-identity
32×distribute-lft-out
30×add-sqr-sqrt
28×sqrt-div
21×pow1
16×add-cube-cbrt
15×swap-sqr
14×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×sqrt-pow1 pow1/2
9×associate-*r* associate-*l*
8×frac-times associate-/r/
5×pow-prod-up
4×associate-*r/ associate-*l/ add-log-exp unswap-sqr
3×times-frac pow-prod-down pow-sqr associate-/l*
2×cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod
1×pow2 frac-2neg pow-plus sqrt-unprod clear-num associate-/r* rem-square-sqrt *-commutative div-inv
Counts
4 → 135
Calls
4 calls:
7.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
7.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
19.0ms
(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
20.0ms
(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

series38.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
12.0ms
(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
6.0ms
(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify35.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
054182090

prune211.0ms

Filtered
83 candidates to 147 candidates (-77.1%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1461147
Fresh167
Picked011
Done022
Total14710157

Merged error: 0b

Counts
157 → 10

regimes122.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
099
199

end0.0ms

analyze2.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
50%12.5%37.5%4
50%6.2%43.8%5
50%3.1%46.9%6
50%1.6%48.5%7
50%0.8%49.2%8
50%0.4%49.6%9
50%0.2%49.8%10
50%0.1%49.9%11
50%0%50%12
50%0%50%13
50%0%50%14

sample601.0ms

Algorithm
intervals
Results
212.0ms1727×body1280valid
125.0ms1311×body640valid
106.0ms4013×body80valid
52.0ms633×body320valid
15.0ms316×body160valid
0.0ms1×body80nan

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