Details

Time bar (total: 2.4s)

analyze2.0ms

Algorithm
search

sample22.0ms

Algorithm
intervals
Results
8.0ms70×body1280valid
3.0ms127×body80valid
3.0ms34×body640valid
1.0ms16×body320valid
0.0ms9×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.9b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.1b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-exp-log sqrt-div add-cbrt-cube distribute-lft-out
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+
Counts
2 → 35
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series17.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(sqrt (+ x 1.0))
14.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify30.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0282318
11037308
25001297

prune72.0ms

Filtered
31 candidates to 41 candidates (-32.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New38341
Fresh000
Picked101
Done000
Total39342

Merged error: 0.2b

Counts
42 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
74×*-un-lft-identity
32×distribute-lft-out
28×sqrt-prod
24×times-frac
17×add-sqr-sqrt
16×add-cube-cbrt
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 80
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series20.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
5.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
11.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify64.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0514800
12206753
25001721

prune151.0ms

Filtered
59 candidates to 89 candidates (-50.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New81889
Fresh202
Picked011
Done000
Total83992

Merged error: 0.0b

Counts
92 → 9

localize9.0ms

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)))
0.2b
(/ (+ 1.0 0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
78×*-un-lft-identity
34×distribute-lft-out
30×add-sqr-sqrt
28×sqrt-div
21×pow1
16×add-cube-cbrt
15×flip3-+ swap-sqr 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×times-frac associate-*r/ associate-*l/ associate-/l* add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod associate-/l/
1×pow2 frac-2neg pow-plus sqrt-unprod clear-num associate-/r* rem-square-sqrt *-commutative div-inv
Counts
4 → 139
Calls
4 calls:
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
21.0ms
(/ (+ 1.0 0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
20.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series36.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms
(/ (+ 1.0 0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
6.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify103.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
06981775
134731578
250021527

prune289.0ms

Filtered
84 candidates to 151 candidates (-79.8%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1465151
Fresh257
Picked011
Done011
Total14812160

Merged error: 0.0b

Counts
160 → 12

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))))

rewrite86.0ms

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)))
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
27.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series57.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
26.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify107.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
012619013
150017878

prune579.0ms

Filtered
151 candidates to 457 candidates (-202.6%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New4525457
Fresh639
Picked101
Done022
Total45910469

Merged error: 0.0b

Counts
469 → 10

regimes63.0ms

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
0126
1166
2166

end0.0ms

analyze2.0ms

Algorithm
search

sample605.0ms

Algorithm
intervals
Results
227.0ms1784×body1280valid
123.0ms1277×body640valid
102.0ms3967×body80valid
46.0ms652×body320valid
15.0ms320×body160valid
0.0ms1×body80nan

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