Details

Time bar (total: 15.2s)

sample31.0ms

Algorithm
intervals
Results
8.0ms66×body1280valid
6.0ms245×body80nan
4.0ms138×body80valid
2.0ms21×body640valid
2.0ms22×body320valid
0.0ms9×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done12
212
111
06

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1))
2.9b
(- (sqrt (+ x 1)) (sqrt x))

rewrite64.0ms

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 insert-posit16 distribute-lft-out
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 37
Calls
2 calls:
5.0ms
(sqrt (+ x 1))
58.0ms
(- (sqrt (+ x 1)) (sqrt x))

series120.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(sqrt (+ x 1))
80.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify2.0s

Counts
43 → 43
Iterations
IterNodes
done5000
42095
3848
2350
1165
081

prune160.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))
0.1b
(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
74×*-un-lft-identity
32×distribute-lft-out
28×sqrt-prod
24×times-frac
17×add-sqr-sqrt
16×add-cube-cbrt
6×associate-/r*
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×insert-posit16
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
3 → 83
Calls
3 calls:
6.0ms
(sqrt (+ x 1))
18.0ms
(+ (sqrt (+ x 1)) (sqrt x))
37.0ms
(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

series168.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(sqrt (+ x 1))
53.0ms
(+ (sqrt (+ x 1)) (sqrt x))
90.0ms
(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.1s

Counts
92 → 92
Iterations
IterNodes
done5003
43628
31475
2606
1273
0133

prune319.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(/ (+ 1 0) (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
0.3b
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
78×*-un-lft-identity
34×distribute-lft-out
30×add-sqr-sqrt
28×sqrt-div
21×pow1
16×add-cube-cbrt
15×flip3-+ swap-sqr flip-+
11×add-cbrt-cube add-exp-log
10×sqrt-pow1 pow1/2
9×associate-*r* associate-*l*
8×frac-times associate-/r/
5×pow-prod-up
4×times-frac associate-*l/ associate-*r/ insert-posit16 associate-/l* add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod associate-/l/
1×pow2 clear-num associate-/r* rem-square-sqrt frac-2neg pow-plus sqrt-unprod *-commutative div-inv
Counts
4 → 143
Calls
4 calls:
34.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
23.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
52.0ms
(/ (+ 1 0) (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
127.0ms
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series437.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
133.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
117.0ms
(/ (+ 1 0) (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
67.0ms
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify3.1s

Counts
155 → 155
Iterations
IterNodes
done5000
33006
2967
1394
0165

prune531.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(/ (+ 1 0) (* (* 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
0.3b
(* (* 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

rewrite372.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
30×sqrt-prod
28×sqrt-div
23×add-exp-log
18×add-cbrt-cube
16×associate-*r/
15×flip3-+ flip-+
14×distribute-lft-out
12×add-sqr-sqrt
11×pow1
10×prod-exp add-cube-cbrt
9×associate-*r*
8×frac-times associate-/r/
6×cbrt-unprod
4×times-frac div-exp associate-*l/ insert-posit16 associate-/l* add-log-exp
3×cbrt-undiv pow-prod-down
2×rem-sqrt-square sqrt-pow1 pow1/2 1-exp associate-/l/
1×clear-num associate-/r* frac-2neg swap-sqr associate-*l* *-commutative div-inv
Counts
4 → 110
Calls
4 calls:
29.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
23.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
165.0ms
(/ (+ 1 0) (* (* 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
153.0ms
(* (* 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
132.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
95.0ms
(/ (+ 1 0) (* (* 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
77.0ms
(* (* 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify2.3s

Counts
122 → 122
Iterations
IterNodes
done5003
33249
21062
1461
0166

prune472.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes41.0ms

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
done13
113
09

end0.0ms

sample2.0s

Algorithm
intervals
Results
640.0ms4077×body80valid
471.0ms7851×body80nan
378.0ms1731×body1280valid
185.0ms1233×body640valid
105.0ms636×body320valid
24.0ms323×body160valid