Details

Time bar (total: 6.2s)

sample30.0ms

Algorithm
intervals
Results
7.0ms56×body1280valid
6.0ms250×body80nan
4.0ms139×body80valid
4.0ms38×body640valid
1.0ms19×body320valid
0.0ms4×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.1b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
1.5b
(- (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))
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series102.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(sqrt (+ x 1.0))
71.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify62.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune70.0ms

Filtered
41 candidates to 28 candidates (68.3%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New39241
Fresh000
Picked101
Done000
Total40242

Merged error: 0.2b

Counts
42 → 2

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite24.0ms

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))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series234.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(sqrt (+ x 1.0))
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
139.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify42.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0341624
11239566
25001533

prune141.0ms

Filtered
80 candidates to 53 candidates (66.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New74680
Fresh101
Picked011
Done000
Total75782

Merged error: 0.0b

Counts
82 → 7

localize8.0ms

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)))
0.2b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (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 (+ x 1.0)) (sqrt x)))
11.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
33.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series806.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
158.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
341.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
141.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify148.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
010338862
141207704
250017681

prune471.0ms

Filtered
457 candidates to 145 candidates (31.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New4534457
Fresh235
Picked011
Done011
Total4559464

Merged error: 0.0b

Counts
464 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
1330×sqrt-prod
1020×*-un-lft-identity
972×times-frac
431×add-sqr-sqrt
425×add-cube-cbrt
340×distribute-lft-out
270×cbrt-prod
58×sqrt-div
42×associate-/l*
28×associate-/r/
17×flip3-+ flip-+
14×div-inv
12×associate-*l* associate-/r*
11×add-exp-log add-cbrt-cube
6×pow1 cbrt-div
4×add-log-exp
3×cbrt-undiv div-exp associate-*r* unswap-sqr
2×pow1/3 associate-*l/
1×frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod associate-/l/
Counts
4 → 638
Calls
4 calls:
14.0ms
(* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
41.0ms
(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
8.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

series1.5s

Counts
4 → 12
Calls
4 calls:
299.0ms
(* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
614.0ms
(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
300.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
294.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify176.0ms

Algorithm
egg-herbie
Counts
650 → 650
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0168717538
1500116373

prune1.2s

Filtered
650 candidates to 240 candidates (36.9%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New6482650
Fresh066
Picked011
Done022
Total64811659

Merged error: 0b

Counts
659 → 11

regimes43.0ms

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
095
195

end0.0ms

sample889.0ms

Algorithm
intervals
Results
212.0ms1717×body1280valid
202.0ms8106×body80nan
120.0ms1209×body640valid
107.0ms4106×body80valid
48.0ms625×body320valid
17.0ms343×body160valid

Profiling

Loading profile data...