Details

Time bar (total: 2.2s)

analyze2.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
50%12.5%37.5%4
50%6.2%43.8%5
50%3.1%46.9%6
50%1.6%48.5%7
50%0.8%49.2%8
50%0.4%49.6%9
50%0.2%49.8%10
50%0.1%49.9%11
50%0%50%12
50%0%50%13
50%0%50%14

sample23.0ms

Algorithm
intervals
Results
8.0ms61×body1280valid
5.0ms45×body640valid
3.0ms123×body80valid
1.0ms19×body320valid
0.0ms8×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0717
1717

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.6b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.0b
(- (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 → 34
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:
4.0ms
(sqrt (+ x 1.0))
10.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify46.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04975520
14975520

prune69.0ms

Filtered
30 candidates to 40 candidates (-33.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New37340
Fresh000
Picked101
Done000
Total38341

Merged error: 0.1b

Counts
41 → 3

localize6.0ms

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

series18.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify27.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
050381051

prune133.0ms

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

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New74680
Fresh202
Picked011
Done000
Total76783

Merged error: 0.0b

Counts
83 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 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))

rewrite25.0ms

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)))
7.0ms
(* (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)))
10.0ms
(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
6.0ms
(cbrt (+ 1.0 x))
6.0ms
(cbrt (+ 1.0 x))

simplify58.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
057602085

prune292.0ms

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

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New95398
Fresh235
Picked101
Done011
Total987105

Merged error: 0.0b

Counts
105 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.1b
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b
(/ 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)))))

rewrite79.0ms

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))))
9.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
36.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

series54.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
9.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
13.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
12.0ms
(* (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
049524249
149524249

prune434.0ms

Filtered
143 candidates to 262 candidates (-83.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2602262
Fresh145
Picked011
Done011
Total2618269

Merged error: 0.0b

Counts
269 → 8

regimes49.0ms

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
099
199

end0.0ms

sample640.0ms

Algorithm
intervals
Results
231.0ms1699×body1280valid
137.0ms1287×body640valid
116.0ms4130×body80valid
45.0ms576×body320valid
16.0ms308×body160valid
0.0ms7×body80nan

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