Details

Time bar (total: 2.5s)

analyze3.0ms

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
6.0ms48×body1280valid
5.0ms47×body640valid
3.0ms133×body80valid
1.0ms18×body320valid
0.0ms10×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0717
1717

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.3b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.7b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite9.0ms

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:
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series14.0ms

Counts
1 → 3
Calls
1 calls:
14.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify29.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
05102335

prune42.0ms

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

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New18321
Fresh000
Picked101
Done000
Total19322

Merged error: 0.1b

Counts
22 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite21.0ms

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))
12.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series15.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify23.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 0 (17.0ms)

IterNodesCost
05138866

prune105.0ms

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

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New57461
Fresh202
Picked011
Done000
Total59564

Merged error: 0.0b

Counts
64 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 250
Calls
4 calls:
10.0ms
(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
10.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
39.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

series57.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
9.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
17.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

simplify86.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049524249
149524249

prune457.0ms

Filtered
142 candidates to 262 candidates (-84.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2593262
Fresh123
Picked101
Done011
Total2616267

Merged error: 0.0b

Counts
267 → 6

localize15.0ms

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

rewrite94.0ms

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:
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
12.0ms
(/ 1.0 (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))))

series65.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
25.0ms
(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
19.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify125.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
0507311200

prune567.0ms

Filtered
153 candidates to 457 candidates (-198.7%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New4561457
Fresh134
Picked011
Done011
Total4576463

Merged error: 0b

Counts
463 → 6

regimes44.0ms

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

sample604.0ms

Algorithm
intervals
Results
220.0ms1721×body1280valid
127.0ms1259×body640valid
109.0ms4151×body80valid
43.0ms592×body320valid
13.0ms277×body160valid
0.0ms3×body80nan

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