Details

Time bar (total: 4.9s)

sample33.0ms

Algorithm
intervals
Results
7.0ms71×body640valid
6.0ms278×body80nan
5.0ms41×body1280valid
3.0ms114×body80valid
1.0ms21×body320valid
0.0ms9×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0116
1146
2146
done146

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.5b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite83.0ms

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:
12.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
60.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series247.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
135.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify43.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04101006
11310954
25001912
done5001912

prune286.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite123.0ms

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:
55.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
42.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series390.0ms

Counts
3 → 9
Calls
3 calls:
260.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify62.0ms

Counts
86 → 86
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0492793
12495678
25002667
done5002667

prune203.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
105×*-un-lft-identity
41×distribute-lft-out
35×sqrt-prod
31×times-frac
29×add-exp-log add-sqr-sqrt add-cbrt-cube
21×add-cube-cbrt
9×cbrt-undiv div-exp add-log-exp
8×pow1 prod-exp cbrt-unprod distribute-lft-out--
7×associate-*r* associate-/r*
6×associate-*l* associate-/l*
5×flip3-+ associate-*r/ flip-+
4×sqrt-div associate-/r/ unswap-sqr
3×pow-prod-down associate-/l/
2×associate-+r- associate-+r+ frac-2neg sqrt-pow1 pow1/2 clear-num sum-log div-inv
1×+-commutative sub-neg sqrt-unprod diff-log div-sub *-commutative
Counts
4 → 136
Calls
4 calls:
81.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
56.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
14.0ms
(+ x (- 1.0 x))

series679.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
485.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
55.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(+ x (- 1.0 x))

simplify93.0ms

Counts
148 → 148
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
07101587
138371359
250011323
done50011323

prune297.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite141.0ms

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:
29.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
40.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
40.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
27.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series723.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
139.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
472.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
54.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify87.0ms

Counts
128 → 128
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06711264
135141071
250011043
done50011043

prune255.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01410
11410
done1410

end0.0ms

sample869.0ms

Algorithm
intervals
Results
183.0ms1962×body640valid
162.0ms8018×body80nan
129.0ms1075×body1280valid
103.0ms4041×body80valid
41.0ms610×body320valid
14.0ms312×body160valid