Details

Time bar (total: 3.1s)

sample30.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.987794%

Results
9.0ms65×body1280valid
5.0ms45×body640valid
3.0ms117×body80valid
1.0ms17×body320valid
1.0ms12×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.0b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.3b
(- (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))
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series14.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
10.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify32.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0282318
11037308
25001297

prune78.0ms

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

localize8.0ms

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)))

rewrite25.0ms

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)))

series18.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
5.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify67.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0514800
12206753
25001721

prune165.0ms

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

localize10.0ms

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

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
1122×*-un-lft-identity
900×sqrt-prod
774×times-frac
460×distribute-lft-out
294×add-sqr-sqrt
292×add-cube-cbrt
46×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
15×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 547
Calls
4 calls:
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
32.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series55.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms
(/ (+ 1.0 0) (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))))

simplify123.0ms

Algorithm
egg-herbie
Counts
559 → 559
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0130411535
150019913

prune682.0ms

Filtered
154 candidates to 559 candidates (-263.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New5545559
Fresh527
Picked101
Done011
Total5608568

Merged error: 0b

Counts
568 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
597×*-un-lft-identity
420×sqrt-prod
256×distribute-lft-out
247×times-frac
130×add-sqr-sqrt
99×add-cube-cbrt
71×swap-sqr
33×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 flip3-+ pow1/2 flip-+ unswap-sqr
8×associate-/l*
7×div-inv
5×sqrt-div pow-prod-up
4×associate-/l/ 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 → 316
Calls
4 calls:
12.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
46.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series50.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify163.0ms

Algorithm
egg-herbie
Counts
328 → 328
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
08273981
145313471
250013422

prune515.0ms

Filtered
151 candidates to 328 candidates (-117.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3280328
Fresh066
Picked011
Done011
Total3288336

Merged error: 0b

Counts
336 → 8

regimes60.0ms

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

sample722.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.987794%

Results
240.0ms1735×body1280valid
143.0ms1269×body640valid
125.0ms4087×body80valid
53.0ms627×body320valid
16.0ms282×body160valid
0.0ms1×body80nan

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