Details

Time bar (total: 2.7s)

sample59.0ms

Algorithm
intervals
Results
15.0ms69×body1280valid
13.0ms276×body80nan
6.0ms33×body640valid
6.0ms121×body80valid
3.0ms27×body320valid
0.0ms6×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0717
1717

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.1b

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))

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))

simplify46.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04975523
14975523

prune76.0ms

Filtered
30 candidates to 41 candidates (-36.7%)
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))
0.2b
(/ 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))
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series19.0ms

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 (18.0ms)

IterNodesCost
050381051

prune152.0ms

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

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New73780
Fresh303
Picked011
Done000
Total76884

Merged error: 0.0b

Counts
84 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
62×add-sqr-sqrt
46×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
28×add-cube-cbrt
20×pow1/2
18×swap-sqr
10×associate-*r* associate-*l*
9×flip3-+ times-frac pow-prod-up flip-+ unswap-sqr
8×add-exp-log add-cbrt-cube distribute-lft-out
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
3×associate-/r* associate-/l*
2×associate-*r/ associate-*l/ associate-/r/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 161
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ 1.0 x)))
5.0ms
(sqrt (sqrt (+ 1.0 x)))
19.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
16.0ms
(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series26.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (sqrt (+ 1.0 x)))
6.0ms
(sqrt (sqrt (+ 1.0 x)))
10.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
4.0ms
(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify70.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049411700
149411700

prune243.0ms

Filtered
91 candidates to 173 candidates (-90.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1730173
Fresh066
Picked011
Done011
Total1738181

Merged error: 0.0b

Counts
181 → 8

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)))
0.1b
(/ 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))))

rewrite103.0ms

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:
8.0ms
(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))))
31.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series62.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
19.0ms
(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
19.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify119.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0507311200

prune554.0ms

Filtered
151 candidates to 457 candidates (-202.6%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New4552457
Fresh235
Picked011
Done022
Total4578465

Merged error: 0b

Counts
465 → 8

regimes57.0ms

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 (1.0ms)

IterNodesCost
099
199

end0.0ms

sample952.0ms

Algorithm
intervals
Results
214.0ms1717×body1280valid
203.0ms8017×body80nan
122.0ms1261×body640valid
106.0ms4087×body80valid
52.0ms642×body320valid
14.0ms293×body160valid

Profiling

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