Details

Time bar (total: 17.8s)

sample70.0ms

Algorithm
intervals
Results
26.0ms72×body640valid
11.0ms309×body80nan
9.0ms38×body1280valid
6.0ms117×body80valid
3.0ms23×body320valid
0.0ms6×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

localize10.0ms

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))))

rewrite275.0ms

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:
29.0ms
(/ 1.0 (sqrt (+ x 1.0)))
13.0ms
(/ 1.0 (sqrt x))
135.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series419.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(/ 1.0 (sqrt (+ x 1.0)))
78.0ms
(/ 1.0 (sqrt x))
223.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.5s

Counts
748 → 748
Iterations

Useful iterations: done (2.4s)

IterNodesCost
069140576
1151035050
2295326090
done500020519

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 22.4b

localize25.0ms

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))

rewrite133.0ms

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:
67.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
27.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
36.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series740.0ms

Counts
3 → 9
Calls
3 calls:
476.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
113.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
151.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify2.5s

Counts
88 → 88
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01871602
15211487
217811167
done50011116

prune419.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 21.8b

localize19.0ms

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)))

rewrite382.0ms

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:
150.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
136.0ms
(/ (/ (- (* (* 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))))
45.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
41.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
176.0ms
(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
757.0ms
(/ (/ (- (* (* 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))))
64.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
5.0ms
(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

simplify2.5s

Counts
140 → 140
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02883978
18403760
238322747
done50002704

prune589.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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)))

rewrite197.0ms

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:
22.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
28.0ms
(/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
86.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
57.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
101.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
206.0ms
(/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
791.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
67.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.6s

Counts
140 → 140
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02672572
17162230
228281845
done50011806

prune375.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01121
11321
done1321

end0.0ms

sample1.7s

Algorithm
intervals
Results
611.0ms1807×body640valid
299.0ms1143×body1280valid
296.0ms8101×body80nan
221.0ms4128×body80valid
62.0ms609×body320valid
21.0ms313×body160valid