Details

Time bar (total: 12.6s)

sample53.0ms

Algorithm
intervals
Results
9.0ms245×body80nan
9.0ms56×body640valid
9.0ms41×body1280valid
6.0ms135×body80valid
2.0ms14×body320valid
1.0ms10×body160valid

simplify5.0ms

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))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
70×add-sqr-sqrt
69×times-frac
46×sqrt-prod
40×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l*
5×add-log-exp
4×div-inv
3×pow1
2×cbrt-undiv frac-2neg sqrt-div div-exp clear-num associate-/r/
1×sub-neg flip3-- flip3-+ diff-log frac-sub flip-- flip-+
Counts
3 → 117
Calls
3 calls:
19.0ms
(/ 1.0 (sqrt (+ x 1.0)))
12.0ms
(/ 1.0 (sqrt x))
93.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series354.0ms

Counts
3 → 9
Calls
3 calls:
114.0ms
(/ 1.0 (sqrt (+ x 1.0)))
67.0ms
(/ 1.0 (sqrt x))
173.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify874.0ms

Counts
126 → 126
Iterations

Useful iterations: done (868.0ms)

IterNodesCost
02011764
14281621
215601557
done50011553

prune522.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.7b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×sqrt-prod
17×add-exp-log add-cbrt-cube
16×*-un-lft-identity
7×pow1 add-cube-cbrt associate-*r*
6×associate-*r/ associate-*l*
5×prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv sqrt-div div-exp difference-of-squares unswap-sqr
3×pow-prod-down distribute-lft-out--
2×flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/ distribute-lft-out
1×sub-neg frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
3 → 77
Calls
3 calls:
79.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
41.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
59.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series551.0ms

Counts
3 → 9
Calls
3 calls:
348.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
103.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
100.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.7s

Counts
86 → 86
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01801446
15121316
230171085
done50011071

prune351.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
113×*-un-lft-identity
46×add-sqr-sqrt
39×sqrt-prod
37×times-frac distribute-lft-out
29×add-exp-log add-cbrt-cube
22×add-cube-cbrt
16×distribute-lft-out--
9×cbrt-undiv div-exp add-log-exp
8×pow1 prod-exp cbrt-unprod difference-of-squares
7×associate-*r* associate-/r* associate-/l*
6×associate-*l*
5×associate-*r/
4×sqrt-div associate-/r/ unswap-sqr
3×flip3-+ pow-prod-down flip-+ associate-/l/
2×flip3-- frac-2neg sqrt-pow1 pow1/2 diff-log clear-num flip-- div-inv
1×sub-neg sqrt-unprod div-sub associate--l+ sum-log *-commutative
Counts
4 → 143
Calls
4 calls:
138.0ms
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
77.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
35.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
72.0ms
(- (+ x 1.0) x)

series826.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
561.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
78.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
5.0ms
(- (+ x 1.0) x)

simplify468.0ms

Counts
155 → 155
Iterations

Useful iterations: done (460.0ms)

IterNodesCost
02693162
17942943
done50002571

prune663.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
31×sqrt-prod
29×add-exp-log add-cbrt-cube
27×add-sqr-sqrt
21×distribute-lft-out
19×add-cube-cbrt times-frac
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×associate-*r* associate-/r*
6×associate-*l* add-log-exp
5×associate-*r/
4×flip3-+ sqrt-div associate-/r/ flip-+ associate-/l* unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 116
Calls
4 calls:
33.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
74.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
45.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
31.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
91.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
181.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
675.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
64.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.9s

Counts
128 → 128
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02502311
17152098
246781784
done50011773

prune377.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

0% (0.3b 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
01221
11921
done1921

end0.0ms

sample2.0s

Algorithm
intervals
Results
719.0ms1843×body640valid
335.0ms7921×body80nan
303.0ms1097×body1280valid
210.0ms4136×body80valid
73.0ms613×body320valid
25.0ms311×body160valid