Details

Time bar (total: 2.5s)

sample36.0ms

Algorithm
intervals
Results
7.0ms54×body1280valid
6.0ms245×body80nan
4.0ms43×body640valid
4.0ms134×body80valid
2.0ms22×body320valid
0.0ms3×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0107
1107

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.5b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
1.7b
(- (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))

series13.0ms

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

simplify30.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
05141523

prune66.0ms

Filtered
30 candidates to 41 candidates (-36.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New39241
Fresh000
Picked101
Done000
Total40242

Merged error: 0.1b

Counts
42 → 2

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 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
16×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 71
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
11.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series18.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
5.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify58.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
050701035

prune138.0ms

Filtered
59 candidates to 80 candidates (-35.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New74680
Fresh101
Picked011
Done000
Total75782

Merged error: 0.0b

Counts
82 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
13×cbrt-prod
10×associate-*r*
9×times-frac sqrt-prod
8×add-exp-log add-cbrt-cube
6×pow1 cbrt-div
4×flip3-+ flip-+ add-log-exp
3×associate-*l* associate-/r* distribute-lft-out associate-/l* unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 86
Calls
4 calls:
9.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
8.0ms
(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
3.0ms
(cbrt (+ 1.0 x))
3.0ms
(cbrt (+ 1.0 x))

series68.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
11.0ms
(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
6.0ms
(cbrt (+ 1.0 x))
6.0ms
(cbrt (+ 1.0 x))

simplify65.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
048512085
148512085

prune286.0ms

Filtered
80 candidates to 98 candidates (-22.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New96298
Fresh055
Picked011
Done011
Total969105

Merged error: 0.0b

Counts
105 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×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 → 250
Calls
4 calls:
10.0ms
(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
10.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
37.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

series55.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
9.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
16.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

simplify85.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049574249
149574249

prune426.0ms

Filtered
142 candidates to 262 candidates (-84.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2593262
Fresh066
Picked101
Done202
Total2629271

Merged error: 0b

Counts
271 → 9

regimes59.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01631
11631

end0.0ms

sample963.0ms

Algorithm
intervals
Results
226.0ms1756×body1280valid
205.0ms8097×body80nan
129.0ms1275×body640valid
106.0ms4012×body80valid
47.0ms637×body320valid
16.0ms320×body160valid

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