Details

Time bar (total: 16.1s)

sample48.0ms

Algorithm
intervals
Results
9.0ms61×body640valid
7.0ms223×body80nan
7.0ms35×body1280valid
5.0ms130×body80valid
2.0ms20×body320valid
1.0ms10×body160valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
3.2b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite247.0ms

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:
15.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
113.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series314.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(/ 1.0 (sqrt (+ x 1.0)))
62.0ms
(/ 1.0 (sqrt x))
164.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.7s

Counts
748 → 748
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
069140576
1156435138
2491927357
done500027357

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 18.9b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
3.1b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite128.0ms

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:
73.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
31.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
18.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series620.0ms

Counts
3 → 9
Calls
3 calls:
396.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
78.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
145.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.8s

Counts
88 → 88
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01871602
15481499
226811201
done50001197

prune337.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.9b

localize26.0ms

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))))
0.1b
(/ (/ (- (* (* 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)))
2.0b
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

rewrite284.0ms

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:
117.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
95.0ms
(/ (/ (- (* (* 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))))
30.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
33.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

series1.3s

Counts
4 → 12
Calls
4 calls:
542.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x)) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
657.0ms
(/ (/ (- (* (* 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))))
73.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
5.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* (* 1.0 1.0) x))

simplify461.0ms

Counts
145 → 145
Iterations

Useful iterations: done (456.0ms)

IterNodesCost
02964063
19143406
done50002860

prune560.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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)))

rewrite192.0ms

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:
56.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
43.0ms
(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
58.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
31.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series956.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
188.0ms
(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
621.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
84.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.9s

Counts
141 → 141
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02682572
17612246
243841891
done50001887

prune374.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes67.0ms

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
01226
11726
done1726

end0.0ms

sample1.9s

Algorithm
intervals
Results
637.0ms1887×body640valid
416.0ms7921×body80nan
258.0ms1212×body1280valid
185.0ms3985×body80valid
106.0ms603×body320valid
22.0ms313×body160valid