Details

Time bar (total: 15.0s)

sample47.0ms

Algorithm
intervals
Results
10.0ms135×body80valid
7.0ms245×body80nan
7.0ms56×body640valid
6.0ms41×body1280valid
1.0ms14×body320valid
1.0ms10×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.8b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
875×*-un-lft-identity
742×add-sqr-sqrt
712×add-cube-cbrt
594×prod-diff
562×sqrt-prod
73×distribute-lft-out
54×div-inv
46×sqrt-div associate-/r/
23×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-exp-log add-cbrt-cube
6×associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
3 → 739
Calls
3 calls:
21.0ms
(/ 1.0 (sqrt (+ x 1.0)))
12.0ms
(/ 1.0 (sqrt x))
112.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series360.0ms

Counts
3 → 9
Calls
3 calls:
111.0ms
(/ 1.0 (sqrt (+ x 1.0)))
51.0ms
(/ 1.0 (sqrt x))
198.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.7s

Counts
748 → 748
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
069140576
1156435138
2491927357
done500027357

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.7b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.8b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
11×*-un-lft-identity sqrt-prod
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt
7×pow1 associate-*r*
6×associate-*l*
5×add-log-exp
4×sqrt-div associate-*r/ unswap-sqr
3×expm1-log1p-u times-frac pow-prod-down log1p-expm1-u associate-/l*
2×cbrt-undiv flip3-- sqrt-pow1 flip3-+ pow1/2 div-exp prod-exp associate-/r/ flip-- cbrt-unprod flip-+ associate-/l/
1×sub-neg frac-2neg fma-neg sqrt-unprod diff-log div-sub prod-diff clear-num associate-/r* *-commutative div-inv distribute-lft-out
Counts
3 → 79
Calls
3 calls:
64.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
42.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
34.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series521.0ms

Counts
3 → 9
Calls
3 calls:
327.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
70.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
123.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.5s

Counts
88 → 88
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01871602
15481499
226811201
done50001197

prune337.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.2b
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
22×add-sqr-sqrt times-frac
16×*-un-lft-identity
14×add-cube-cbrt associate-/l*
12×cbrt-undiv div-exp
11×sqrt-prod
10×associate-*r/
8×pow1 associate-/r/
7×associate-*r* prod-exp cbrt-unprod
6×associate-*l* add-log-exp
5×flip3-+ flip-+ distribute-lft-out--
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv unswap-sqr
3×div-sub pow-prod-down associate-/l/
2×flip3-- frac-2neg sqrt-pow1 pow1/2 associate--l+ clear-num associate-/r* flip--
1×distribute-rgt-in sub-neg distribute-lft-in fma-neg sqrt-unprod diff-log prod-diff *-commutative distribute-lft-out
Counts
4 → 133
Calls
4 calls:
92.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
99.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
29.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
32.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

series720.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
511.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
63.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
3.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

simplify396.0ms

Counts
145 → 145
Iterations

Useful iterations: done (391.0ms)

IterNodesCost
02964063
19143406
done50002860

prune567.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
27×*-un-lft-identity
24×add-sqr-sqrt
19×sqrt-prod
18×times-frac
16×add-cube-cbrt
12×cbrt-undiv div-exp associate-/l*
10×associate-*r/
8×pow1 associate-/r/
7×fma-def associate-*r* prod-exp cbrt-unprod
6×flip3-+ associate-*l* flip-+ distribute-lft-out add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r*
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 129
Calls
4 calls:
35.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
31.0ms
(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
56.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
26.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series793.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
147.0ms
(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
517.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
63.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify2.0s

Counts
141 → 141
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02682572
17612246
243841891
done50001887

prune563.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01229
11729
done1729

end0.0ms

sample1.8s

Algorithm
intervals
Results
530.0ms1097×body1280valid
338.0ms7921×body80nan
305.0ms1843×body640valid
207.0ms4136×body80valid
57.0ms613×body320valid
20.0ms311×body160valid