Details

Time bar (total: 23.4s)

sample72.0ms

Algorithm
intervals
Results
18.0ms53×body1280valid
16.0ms247×body80nan
10.0ms132×body80valid
9.0ms34×body640valid
4.0ms20×body320valid
2.0ms17×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
20.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize20.0ms

Local error

Found 2 expressions with local error:

5.2b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-cbrt-cube sqrt-div add-exp-log insert-posit16 distribute-lft-out
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 37
Calls
2 calls:
Slowest
49.0ms
(- (sqrt (+ x 1)) (sqrt x))
5.0ms
(sqrt (+ x 1))

series110.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
68.0ms
(- (sqrt (+ x 1)) (sqrt x))
42.0ms
(sqrt (+ x 1))

simplify542.0ms

Counts
28 → 43
Calls
28 calls:
Slowest
112.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
62.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
33.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
27.0ms
(sqrt (- (* x x) (* 1 1)))
26.0ms
(+ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune358.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 28.4b

localize26.0ms

Local error

Found 4 expressions with local error:

4.1b
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.0b
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
64×sqrt-prod
56×add-sqr-sqrt
34×pow1
32×add-cube-cbrt
26×distribute-lft-out
24×times-frac
19×swap-sqr
16×sqrt-pow1 pow1/2
13×associate-*r* associate-*l*
12×sqrt-div
10×add-cbrt-cube add-exp-log pow-prod-up
8×difference-of-squares unswap-sqr
7×flip3-+ flip-+
6×associate-/r* pow-prod-down pow-sqr add-log-exp
4×frac-times 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
Counts
4 → 179
Calls
4 calls:
Slowest
71.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
44.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
29.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
17.0ms
(* (sqrt x) (sqrt x))

series173.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
104.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
26.0ms
(* (sqrt x) (sqrt x))
24.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
19.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))

simplify6.4s

Counts
211 → 191
Calls
211 calls:
Slowest
448.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
330.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
330.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
222.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
211.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (+ (pow x 3) (pow 1 3))))

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
16×add-sqr-sqrt
15×add-cube-cbrt
7×add-exp-log
6×associate-/r*
5×pow1 add-cbrt-cube add-log-exp
3×flip3-+ flip-+ insert-posit16 associate-/l*
2×sqrt-div div-exp associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp clear-num sum-log frac-2neg sqrt-pow1 pow1/2 1-exp div-inv pow-flip inv-pow
Counts
3 → 78
Calls
3 calls:
Slowest
27.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms
(+ (sqrt (+ x 1)) (sqrt x))
12.0ms
(sqrt (+ x 1))

series217.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
91.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
87.0ms
(+ (sqrt (+ x 1)) (sqrt x))
39.0ms
(sqrt (+ x 1))

simplify1.4s

Counts
73 → 87
Calls
73 calls:
Slowest
208.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
180.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
106.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
80.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
56.0ms
(sqrt (+ (pow x 3) (pow 1 3)))

prune636.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.2b
(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
0.1b
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

rewrite363.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
74×*-un-lft-identity
37×pow1
32×distribute-lft-out
30×add-sqr-sqrt
28×sqrt-div
18×sqrt-pow1 pow1/2
17×add-exp-log
16×add-cube-cbrt
15×swap-sqr
14×flip3-+ flip-+ pow-flip
11×add-cbrt-cube
10×pow-prod-up
9×associate-*r* associate-*l*
8×frac-times associate-/r/
6×pow-prod-down pow-sqr
4×div-exp associate-*l/ prod-exp associate-*r/ insert-posit16 add-log-exp unswap-sqr
3×times-frac associate-/l*
2×pow2 cbrt-undiv rem-sqrt-square rec-exp pow-plus 1-exp cbrt-unprod
1×clear-num associate-/r* rem-square-sqrt frac-2neg sqrt-unprod *-commutative div-inv inv-pow
Counts
4 → 158
Calls
4 calls:
Slowest
181.0ms
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
105.0ms
(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
45.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
30.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
123.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
93.0ms
(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
68.0ms
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify6.5s

Counts
162 → 170
Calls
162 calls:
Slowest
399.0ms
(* (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))) (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))
389.0ms
(* (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
340.0ms
(sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
327.0ms
(sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
285.0ms
(/ (* (* 1 1) 1) (* (* (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (* (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
595.0ms623×body320valid
577.0ms1764×body1280valid
536.0ms7957×body80nan
370.0ms1209×body640valid
279.0ms4076×body80valid
37.0ms328×body160valid