Details

Time bar (total: 18.5s)

sample49.0ms

Algorithm
intervals
Results
9.0ms63×body1280valid
9.0ms282×body80nan
6.0ms46×body640valid
4.0ms116×body80valid
2.0ms20×body320valid
1.0ms11×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.1b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite84.0ms

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:
6.0ms
(sqrt (+ x 1.0))
77.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series151.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(sqrt (+ x 1.0))
98.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.5s

Counts
41 → 41
Iterations
IterNodes
done5000
32862
2671
1193
086

prune145.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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)))

rewrite110.0ms

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:
13.0ms
(sqrt (+ x 1.0))
48.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
45.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series315.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(sqrt (+ x 1.0))
90.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
175.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify770.0ms

Counts
80 → 80
Iterations
IterNodes
done5000
21548
1371
0156

prune328.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite276.0ms

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:
46.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms
(sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))
41.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
121.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.5s

Counts
4 → 12
Calls
4 calls:
207.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
236.0ms
(sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))
492.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
571.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify2.0s

Counts
457 → 457
Iterations
IterNodes
done5000
24280
11140
0478

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite995.0ms

Algorithm
rewrite-expression-head
Rules
2154×sqrt-prod
1514×*-un-lft-identity
1308×times-frac
665×add-sqr-sqrt
564×distribute-lft-out
527×add-cube-cbrt
330×associate-*r*
51×sqrt-div
48×associate-/r/
42×associate-/l*
36×associate-*l* unswap-sqr
27×associate-/r*
24×flip3-+ flip-+ div-inv
15×add-cbrt-cube add-exp-log
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×clear-num frac-2neg
2×sqrt-undiv prod-exp cbrt-unprod
1×frac-times sqrt-unprod pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 910
Calls
4 calls:
65.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
50.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
607.0ms
(* (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (/ (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
130.0ms
(/ (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

series2.1s

Counts
4 → 12
Calls
4 calls:
499.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
543.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
185.0ms
(* (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (/ (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
867.0ms
(/ (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

simplify1.5s

Counts
922 → 922
Iterations
IterNodes
done5000
11716
0719

prune3.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes87.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done9
19
07

end0.0ms

sample2.0s

Algorithm
intervals
Results
399.0ms8079×body80nan
390.0ms1247×body640valid
380.0ms1686×body1280valid
259.0ms4121×body80valid
81.0ms663×body320valid
23.0ms283×body160valid