Details

Time bar (total: 15.5s)

sample34.0ms

Algorithm
intervals
Results
9.0ms58×body1280valid
7.0ms276×body80nan
3.0ms133×body80valid
3.0ms33×body640valid
2.0ms25×body320valid
0.0ms7×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.7b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.4b
(- (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 → 19
Calls
1 calls:
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series70.0ms

Counts
1 → 3
Calls
1 calls:
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify48.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune40.0ms

Filtered
22 candidates to 14 candidates (63.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New19322
Fresh000
Picked011
Done000
Total19423

Merged error: 0.1b

Counts
23 → 4

localize11.0ms

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)))

rewrite19.0ms

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))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series199.0ms

Counts
2 → 6
Calls
2 calls:
65.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
134.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0295535
11077482
25002453

prune116.0ms

Filtered
61 candidates to 39 candidates (63.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New55661
Fresh202
Picked011
Done101
Total58765

Merged error: 0.0b

Counts
65 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

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 (+ x 1.0)) (sqrt x)))
11.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
33.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series785.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
159.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
329.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
135.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify142.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
010338862
141207704
250017681

prune488.0ms

Filtered
457 candidates to 146 candidates (31.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New4534457
Fresh235
Picked011
Done011
Total4559464

Merged error: 0b

Counts
464 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
21574×sqrt-prod
14984×*-un-lft-identity
14958×times-frac
5512×distribute-lft-out
5339×add-sqr-sqrt
5338×add-cube-cbrt
438×associate-/l*
402×sqrt-div
370×associate-/r/
186×flip3-+ flip-+
185×div-inv
33×associate-/r*
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
5×pow1
4×add-log-exp
3×frac-2neg clear-num
2×associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 5786
Calls
4 calls:
12.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
32.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
200.0ms
(/ (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
152.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
322.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
541.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
141.0ms
(/ (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.7s

Algorithm
egg-herbie
Counts
5798 → 5798
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
05001217546

prune8.1s

Filtered
5798 candidates to 1894 candidates (32.7%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New579805798
Fresh066
Picked011
Done022
Total579895807

Merged error: 0b

Counts
5807 → 9

regimes38.0ms

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
095
195

end0.0ms

sample913.0ms

Algorithm
intervals
Results
221.0ms1746×body1280valid
211.0ms7964×body80nan
123.0ms1203×body640valid
112.0ms4119×body80valid
48.0ms599×body320valid
17.0ms333×body160valid

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