Details

Time bar (total: 2.4s)

sample27.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.993897%

Results
7.0ms53×body1280valid
5.0ms49×body640valid
3.0ms116×body80valid
2.0ms30×body320valid
0.0ms8×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: 33.3b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms

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))

series13.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(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

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))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ (+ 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:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
14.0ms
(/ (+ 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)))

simplify65.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0514800
12206753
25001721

prune162.0ms

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

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New80989
Fresh123
Picked011
Done000
Total811293

Merged error: 0.0b

Counts
93 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 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:
13.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
7.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))

series64.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ (+ 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))

simplify127.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09311718
149451624
250011624

prune373.0ms

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

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1031104
Fresh1910
Picked011
Done011
Total10412116

Merged error: 0.0b

Counts
116 → 12

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)))
0.1b
(/ (+ 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))))

rewrite65.0ms

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)))
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(/ (+ 1.0 0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
21.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series35.0ms

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))))

simplify109.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06981775
134731578
250021527

prune253.0ms

Filtered
86 candidates to 151 candidates (-75.6%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1492151
Fresh189
Picked101
Done112
Total15211163

Merged error: 0.0b

Counts
163 → 11

regimes157.0ms

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

sample689.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.993897%

Results
234.0ms1713×body1280valid
137.0ms1271×body640valid
118.0ms4069×body80valid
53.0ms643×body320valid
16.0ms304×body160valid
0.0ms1×body80nan

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