Details

Time bar (total: 2.8s)

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

sample32.0ms

Algorithm
intervals
Results
7.0ms60×body1280valid
4.0ms46×body640valid
3.0ms116×body80valid
2.0ms22×body320valid
1.0ms12×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0717
1717

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.5b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
33.5b
(- (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 → 34
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:
3.0ms
(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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New38240
Fresh000
Picked101
Done000
Total39241

Merged error: 0.2b

Counts
41 → 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)))

rewrite21.0ms

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))
9.0ms
(/ 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)))

simplify25.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (17.0ms)

IterNodesCost
050381051

prune174.0ms

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

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New72880
Fresh101
Picked011
Done000
Total73982

Merged error: 0.0b

Counts
82 → 9

localize11.0ms

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))

rewrite28.0ms

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:
10.0ms
(/ 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))

series65.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 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))
7.0ms
(cbrt (+ 1.0 x))

simplify58.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
057602085

prune287.0ms

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

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New97198
Fresh167
Picked011
Done011
Total989107

Merged error: 0.0b

Counts
107 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
11.0ms
(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
26.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series61.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
23.0ms
(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
18.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify120.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0507311200

prune754.0ms

Filtered
153 candidates to 457 candidates (-198.7%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New4543457
Fresh426
Picked011
Done022
Total4588466

Merged error: 0b

Counts
466 → 8

regimes55.0ms

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

sample812.0ms

Algorithm
intervals
Results
206.0ms1661×body1280valid
119.0ms1223×body640valid
99.0ms4116×body80valid
45.0ms646×body320valid
16.0ms354×body160valid

Profiling

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