Details

Time bar (total: 16.7s)

sample70.0ms

Algorithm
intervals
Results
15.0ms72×body640valid
13.0ms309×body80nan
11.0ms38×body1280valid
7.0ms117×body80valid
4.0ms23×body320valid
1.0ms6×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.4b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite252.0ms

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:
13.0ms
(/ 1.0 (sqrt (+ x 1.0)))
10.0ms
(/ 1.0 (sqrt x))
136.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series392.0ms

Counts
3 → 9
Calls
3 calls:
108.0ms
(/ 1.0 (sqrt (+ x 1.0)))
54.0ms
(/ 1.0 (sqrt x))
231.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.4s

Counts
748 → 748
Iterations

Useful iterations: done (2.4s)

IterNodesCost
069140576
1151035050
2295326090
done500020519

prune988.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 22.4b

localize12.0ms

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))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.4b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite146.0ms

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:
71.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
36.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
33.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series610.0ms

Counts
3 → 9
Calls
3 calls:
343.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
105.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
162.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.9s

Counts
88 → 88
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01871602
15211487
217811167
done50011116

prune337.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 21.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
0.1b
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
1.7b
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

rewrite320.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
22×add-sqr-sqrt
18×times-frac
16×*-un-lft-identity
14×add-cube-cbrt
12×cbrt-undiv div-exp associate-/l*
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-+
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 → 128
Calls
4 calls:
111.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
119.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
42.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
39.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

series992.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
721.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
76.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
4.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

simplify2.3s

Counts
140 → 140
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02883978
18403760
238322747
done50002704

prune569.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt x) (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
0.2b
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
25×*-un-lft-identity
24×add-sqr-sqrt
18×times-frac sqrt-prod
16×add-cube-cbrt
12×cbrt-undiv div-exp associate-/l*
10×associate-*r/
8×pow1 associate-/r/
7×associate-*r* prod-exp cbrt-unprod
6×fma-def flip3-+ associate-*l* flip-+ add-log-exp
5×distribute-lft-out
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 → 128
Calls
4 calls:
20.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
32.0ms
(/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
52.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
34.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
97.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
204.0ms
(/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
681.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.5s

Counts
140 → 140
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02672572
17162230
228281845
done50011806

prune434.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01224
11424
done1424

end0.0ms

sample2.1s

Algorithm
intervals
Results
487.0ms4128×body80valid
407.0ms1807×body640valid
362.0ms8101×body80nan
331.0ms1143×body1280valid
141.0ms609×body320valid
25.0ms313×body160valid