Details

Time bar (total: 14.0s)

sample57.0ms

Algorithm
intervals
Results
13.0ms54×body1280valid
13.0ms139×body80valid
12.0ms249×body80nan
6.0ms30×body640valid
3.0ms24×body320valid
1.0ms9×body160valid

simplify13.0ms

Calls
1 calls:
Slowest
13.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize12.0ms

Local error

Found 2 expressions with local error:

2.3b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
5×*-un-lft-identity
4×sqrt-prod add-log-exp
3×add-cube-cbrt
2×pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 difference-of-squares
1×rem-sqrt-square sub-neg flip3-+ flip3-- pow1/2 diff-log flip-+ flip-- distribute-lft-out--
Calls
2 calls:
Slowest
7.0ms
(- (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series40.0ms

Calls
2 calls:
Slowest
23.0ms
(- (sqrt (+ x 1)) (sqrt x))
17.0ms
(sqrt (+ x 1))

simplify353.0ms

Calls
18 calls:
Slowest
116.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
55.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
31.0ms
(sqrt (- (* x x) (* 1 1)))
28.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
17.0ms
(+ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune339.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 27.4b

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.1b
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
16×times-frac
14×pow1
12×sqrt-div
10×add-cbrt-cube add-exp-log
9×associate-*r* associate-*l*
8×pow1/2
7×flip3-+ flip-+
6×sqrt-prod add-log-exp difference-of-squares
5×distribute-lft-out
4×frac-times associate-/r* pow-prod-down pow-prod-up insert-posit16 associate-/l*
2×pow2 rem-square-sqrt pow-plus flip3-- sqrt-unprod associate-*l/ prod-exp associate-*r/ associate-/r/ *-commutative cbrt-unprod flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Calls
4 calls:
Slowest
48.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
14.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
7.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
4.0ms
(* (sqrt x) (sqrt x))

series71.0ms

Calls
4 calls:
Slowest
45.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
10.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
9.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
7.0ms
(* (sqrt x) (sqrt x))

simplify4.8s

Calls
108 calls:
Slowest
472.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
458.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
421.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
236.0ms
(/ (* (* (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
206.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(sqrt (+ x 1))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×add-cube-cbrt add-log-exp
4×pow1 associate-/r* add-exp-log
3×flip3-+ add-cbrt-cube sqrt-prod flip-+ insert-posit16
2×sqrt-div associate-/r/ distribute-lft-out
1×+-commutative rem-sqrt-square rec-exp clear-num sum-log frac-2neg pow1/2 div-inv pow-flip inv-pow
Calls
3 calls:
Slowest
9.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
8.0ms
(+ (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series77.0ms

Calls
3 calls:
Slowest
33.0ms
(+ (sqrt (+ x 1)) (sqrt x))
29.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
15.0ms
(sqrt (+ x 1))

simplify523.0ms

Calls
24 calls:
Slowest
160.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
122.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
43.0ms
(sqrt (- (* x x) (* 1 1)))
24.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
21.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune563.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
15×*-un-lft-identity
12×add-sqr-sqrt
11×pow1 add-cube-cbrt
10×associate-/r/
9×associate-*r* associate-*l*
8×associate-/r* add-exp-log
6×add-cbrt-cube
5×flip3-+ pow1/2 sqrt-div flip-+ div-inv
4×insert-posit16 add-log-exp
2×rec-exp clear-num frac-2neg pow-prod-down pow-prod-up pow-flip distribute-lft-out inv-pow
1×pow2 frac-times rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
16.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
9.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
9.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
3.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

series199.0ms

Calls
4 calls:
Slowest
62.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
50.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
44.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
43.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.9s

Calls
66 calls:
Slowest
193.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
175.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
174.0ms
(* (* (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (* (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))
166.0ms
(sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
94.0ms
(sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes84.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
596.0ms1691×body1280valid
547.0ms7956×body80nan
516.0ms591×body320valid
334.0ms1267×body640valid
319.0ms4125×body80valid
38.0ms326×body160valid