Details

Time bar (total: 2.7s)

analyze2.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 50.021364%

Guaranteed chance to sample good point: 99.993897%

sample21.0ms

Algorithm
intervals
Results
6.0ms47×body1280valid
4.0ms136×body80valid
3.0ms34×body640valid
2.0ms24×body320valid
1.0ms15×body160valid

simplify5.0ms

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: 29.1b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
4.7b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite13.0ms

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))
9.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series13.0ms

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

simplify37.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0282318
11037308
25001297

prune75.0ms

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

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New37441
Fresh000
Picked101
Done000
Total38442

Merged error: 0.1b

Counts
42 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

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:
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
3.0ms
(sqrt (+ x 1.0))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series21.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
3.0ms
(sqrt (+ x 1.0))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify65.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0514800
12206753
25001721

prune160.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New81889
Fresh213
Picked011
Done000
Total831093

Merged error: 0.0b

Counts
93 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
25×add-sqr-sqrt
19×add-cube-cbrt
13×cbrt-prod
12×times-frac
10×associate-*r*
9×sqrt-prod
8×add-exp-log add-cbrt-cube
7×distribute-lft-out
6×pow1 cbrt-div
5×flip3-+ flip-+
4×associate-/l* add-log-exp
3×associate-*l* associate-/r* unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 92
Calls
4 calls:
12.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
8.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))

series70.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
10.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
6.0ms
(cbrt (+ x 1.0))
6.0ms
(cbrt (+ x 1.0))

simplify126.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09311718
149451624
250011624

prune364.0ms

Filtered
86 candidates to 104 candidates (-20.9%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1031104
Fresh178
Picked011
Done011
Total10410114

Merged error: 0.0b

Counts
114 → 10

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

rewrite117.0ms

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)))
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
34.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series57.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
17.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
19.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify122.0ms

Algorithm
egg-herbie
Counts
559 → 559
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0130411535
150019913

prune618.0ms

Filtered
153 candidates to 559 candidates (-265.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New5545559
Fresh527
Picked101
Done022
Total5609569

Merged error: 0b

Counts
569 → 9

regimes113.0ms

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
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 50.021364%

Guaranteed chance to sample good point: 99.993897%

sample608.0ms

Algorithm
intervals
Results
213.0ms1734×body1280valid
120.0ms1212×body640valid
114.0ms4064×body80valid
47.0ms625×body320valid
20.0ms365×body160valid
0.0ms1×body80nan

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