Details

Time bar (total: 4.8s)

sample31.0ms

Algorithm
intervals
Results
7.0ms281×body80nan
6.0ms49×body1280valid
4.0ms42×body640valid
3.0ms133×body80valid
1.0ms19×body320valid
1.0ms13×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: 29.4b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.3b
(- (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 → 35
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series101.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify58.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune84.0ms

Filtered
41 candidates to 28 candidates (68.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New37441
Fresh000
Picked101
Done000
Total38442

Merged error: 0.2b

Counts
42 → 4

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)))

rewrite22.0ms

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

series240.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(sqrt (+ x 1.0))
61.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
144.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify40.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0341624
11239566
25001533

prune148.0ms

Filtered
80 candidates to 53 candidates (66.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New72880
Fresh213
Picked011
Done000
Total741084

Merged error: 0.0b

Counts
84 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

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:
9.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series794.0ms

Counts
4 → 12
Calls
4 calls:
346.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
143.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
139.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
166.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify114.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06472845
131522529
250022489

prune640.0ms

Filtered
262 candidates to 136 candidates (51.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2575262
Fresh358
Picked101
Done101
Total26210272

Merged error: 0.0b

Counts
272 → 10

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))))

rewrite91.0ms

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)))
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
27.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series801.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
159.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
322.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
139.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify145.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
010338862
141207704
250017681

prune458.0ms

Filtered
457 candidates to 148 candidates (32.4%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New4552457
Fresh189
Picked011
Done000
Total45611467

Merged error: 0b

Counts
467 → 11

regimes40.0ms

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
01112
11112

end0.0ms

sample898.0ms

Algorithm
intervals
Results
214.0ms8286×body80nan
213.0ms1791×body1280valid
123.0ms1225×body640valid
105.0ms4107×body80valid
44.0ms596×body320valid
14.0ms281×body160valid