Details

Time bar (total: 20.9s)

sample49.0ms

Algorithm
intervals
Results
11.0ms278×body80nan
10.0ms46×body1280valid
8.0ms42×body640valid
6.0ms139×body80valid
3.0ms21×body320valid
1.0ms8×body160valid

simplify37.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
36.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize21.0ms

Local error

Found 2 expressions with local error:

2.2b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite49.0ms

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
44.0ms
(- (sqrt (+ x 1)) (sqrt x))
4.0ms
(sqrt (+ x 1))

series106.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
66.0ms
(- (sqrt (+ x 1)) (sqrt x))
39.0ms
(sqrt (+ x 1))

simplify521.0ms

Counts
28 → 43
Calls
28 calls:
Slowest
96.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
66.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
57.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
54.0ms
(sqrt (- (* x x) (* 1 1)))
23.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune375.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.0b

localize43.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (* (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)))

rewrite207.0ms

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
117.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
39.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
33.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
13.0ms
(* (sqrt x) (sqrt x))

series177.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
27.0ms
(* (sqrt x) (sqrt x))
25.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
22.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))

simplify6.4s

Counts
211 → 191
Calls
211 calls:
Slowest
393.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
381.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
284.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
236.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (+ (pow x 3) (pow 1 3))))
212.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite76.0ms

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
53.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms
(+ (sqrt (+ x 1)) (sqrt x))
4.0ms
(sqrt (+ x 1))

series200.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
106.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
52.0ms
(+ (sqrt (+ x 1)) (sqrt x))
43.0ms
(sqrt (+ x 1))

simplify1.4s

Counts
73 → 87
Calls
73 calls:
Slowest
264.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
146.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
120.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
56.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
46.0ms
(- 0 (log (+ (sqrt (+ x 1)) (sqrt x))))

prune806.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ x 1))
0.2b
(cbrt (+ x 1))
0.2b
(cbrt (+ x 1))
0.2b
(* (cbrt (+ x 1)) (cbrt (+ x 1)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 99
Calls
4 calls:
Slowest
48.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
5.0ms
(cbrt (+ x 1))
4.0ms
(cbrt (+ x 1))
3.0ms
(cbrt (+ x 1))

series182.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
49.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
47.0ms
(cbrt (+ x 1))
46.0ms
(cbrt (+ x 1))
40.0ms
(cbrt (+ x 1))

simplify4.6s

Counts
94 → 111
Calls
94 calls:
Slowest
263.0ms
(* (cbrt (- (* x x) (* 1 1))) (cbrt (+ (pow x 3) (pow 1 3))))
257.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
251.0ms
(* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (- (* x x) (* 1 1))))
250.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
240.0ms
(- (+ (* 2/3 (pow (/ 1 x) 1/3)) (pow (/ -1 x) -2/3)) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes42.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
948.0ms8344×body80nan
566.0ms1671×body1280valid
323.0ms4179×body80valid
248.0ms1207×body640valid
99.0ms633×body320valid
35.0ms310×body160valid