Details

Time bar (total: 17.1s)

sample30.0ms

Algorithm
intervals
Results
6.0ms334×body80nan
5.0ms63×body1280valid
2.0ms130×body80valid
2.0ms32×body640valid
1.0ms17×body320valid
1.0ms14×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104
done104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite49.0ms

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:
6.0ms
(sqrt (+ x 1.0))
42.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series104.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(sqrt (+ x 1.0))
73.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify57.0ms

Counts
41 → 41
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
0182265
1544243
22020233
35002232
done5002232

prune84.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

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)))

rewrite79.0ms

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:
6.0ms
(sqrt (+ x 1.0))
28.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
41.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series238.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
67.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify39.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0341624
11239566
25001533
done5001533

prune161.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

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)))
0.1b
(/ 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))))

rewrite270.0ms

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:
36.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
36.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
117.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series792.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
164.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
328.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
137.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify122.0ms

Counts
457 → 457
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
010338862
141207704
250017681
done50017681

prune558.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
21584×sqrt-prod
14985×*-un-lft-identity
14958×times-frac
5512×distribute-lft-out
5341×add-sqr-sqrt
5339×add-cube-cbrt
438×associate-/l*
404×sqrt-div
370×associate-/r/
186×flip3-+ flip-+
185×div-inv
33×associate-/r*
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×pow1
4×sqrt-pow1 add-log-exp
3×frac-2neg clear-num
2×rem-sqrt-square pow1/2 associate-/l/
Counts
4 → 5792
Calls
4 calls:
38.0ms
(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
42.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
117.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
335.0ms
(/ (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
300.0ms
(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
628.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
541.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
138.0ms
(/ (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.5s

Counts
5804 → 5804
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
05001217621
done5001217621

prune9.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095
195
done95

end0.0ms

sample726.0ms

Algorithm
intervals
Results
142.0ms1713×body1280valid
138.0ms8104×body80nan
92.0ms1318×body640valid
80.0ms4060×body80valid
30.0ms605×body320valid
10.0ms304×body160valid