Details

Time bar (total: 37.2s)

sample37.0ms

Algorithm
intervals
Results
12.0ms253×body80nan
6.0ms54×body1280valid
3.0ms143×body80valid
3.0ms34×body640valid
1.0ms14×body320valid
1.0ms11×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06162
19162
210162
done10162

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.5b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite50.0ms

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-cbrt-cube sqrt-div add-exp-log distribute-lft-out
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 35
Calls
2 calls:
7.0ms
(sqrt (+ x 1.0))
41.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series147.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(sqrt (+ x 1.0))
108.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.8s

Counts
41 → 41
Iterations

Useful iterations: done (1.8s)

IterNodesCost
08612737
11939896
26719452
328629252
done50009211

prune190.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

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-cbrt-cube add-exp-log add-log-exp
4×pow1
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
3 → 71
Calls
3 calls:
6.0ms
(sqrt (+ x 1.0))
34.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
37.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series333.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(sqrt (+ x 1.0))
111.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
180.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.2s

Counts
80 → 80
Iterations

Useful iterations: done (1.2s)

IterNodesCost
015627666
137122028
2154821050
done500020890

prune344.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

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))))

rewrite344.0ms

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-cbrt-cube add-exp-log
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
58.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
31.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
61.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
136.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts
4 → 12
Calls
4 calls:
201.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
223.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
441.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
181.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify3.4s

Counts
457 → 457
Iterations

Useful iterations: done (3.3s)

IterNodesCost
0442299517
11072249725
24125245184
done5002243664

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b
(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)))))
0.2b
(/ 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)))))

rewrite2.4s

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-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
6×pow1
4×sqrt-pow1 add-log-exp
3×clear-num frac-2neg
2×rem-sqrt-square pow1/2 associate-/l/
Counts
4 → 5792
Calls
4 calls:
48.0ms
(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
535.0ms
(/ (/ (/ 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)))))
56.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
154.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series2.0s

Counts
4 → 12
Calls
4 calls:
425.0ms
(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
192.0ms
(/ (/ (/ 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)))))
501.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
852.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify7.9s

Counts
5804 → 5804
Iterations

Useful iterations: done (5.9s)

IterNodesCost
026855735226
done50005434542

prune13.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes48.0ms

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
07202
19202
done9202

end0.0ms

sample968.0ms

Algorithm
intervals
Results
305.0ms1750×body1280valid
210.0ms7946×body80nan
115.0ms4066×body80valid
107.0ms1314×body640valid
36.0ms560×body320valid
12.0ms310×body160valid