Details

Time bar (total: 18.2s)

sample55.0ms

Algorithm
intervals
Results
12.0ms53×body1280valid
12.0ms273×body80nan
8.0ms47×body640valid
7.0ms15×body320valid
6.0ms130×body80valid
1.0ms11×body160valid

simplify10.0ms

Calls
1 calls:
Slowest
10.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize19.0ms

Local error

Found 2 expressions with local error:

2.8b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite15.0ms

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
13.0ms
(- (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series161.0ms

Calls
2 calls:
Slowest
119.0ms
(- (sqrt (+ x 1)) (sqrt x))
41.0ms
(sqrt (+ x 1))

simplify396.0ms

Calls
18 calls:
Slowest
142.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
54.0ms
(sqrt (- (* x x) (* 1 1)))
37.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
26.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
23.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune348.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 29.2b

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)))
0.0b
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite95.0ms

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
51.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
23.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
11.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
8.0ms
(* (sqrt x) (sqrt x))

series170.0ms

Calls
4 calls:
Slowest
109.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
29.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
17.0ms
(* (sqrt x) (sqrt x))
15.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify4.3s

Calls
108 calls:
Slowest
410.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
339.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
324.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
194.0ms
(/ (* (* (- (* (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))))
191.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

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))

rewrite11.0ms

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
5.0ms
(+ (sqrt (+ x 1)) (sqrt x))
4.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
1.0ms
(sqrt (+ x 1))

series177.0ms

Calls
3 calls:
Slowest
88.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
62.0ms
(+ (sqrt (+ x 1)) (sqrt x))
26.0ms
(sqrt (+ x 1))

simplify498.0ms

Calls
24 calls:
Slowest
170.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
104.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
44.0ms
(sqrt (- (* x x) (* 1 1)))
21.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms
(cbrt (+ (sqrt (+ x 1)) (sqrt x)))

prune429.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
42×times-frac
40×sqrt-prod
32×add-sqr-sqrt
30×add-cube-cbrt
24×sqrt-div
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
10×div-inv distribute-lft-out
9×add-exp-log
8×pow1
6×add-cbrt-cube associate-/l*
5×pow1/2
4×insert-posit16 pow-flip add-log-exp
3×pow-div
2×rem-sqrt-square rec-exp clear-num frac-2neg div-exp inv-pow
1×cbrt-undiv associate-/l/
Calls
4 calls:
Slowest
26.0ms
(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
9.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
6.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
6.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series486.0ms

Calls
4 calls:
Slowest
156.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
127.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
125.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
78.0ms
(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify5.8s

Calls
143 calls:
Slowest
513.0ms
(/ (* (* (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (/ 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)))))
234.0ms
(/ (sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))) (cbrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
212.0ms
(/ (sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
208.0ms
(/ (sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
197.0ms
(/ (sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes73.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
757.0ms4061×body80valid
539.0ms8046×body80nan
443.0ms1670×body1280valid
347.0ms1320×body640valid
95.0ms623×body320valid
33.0ms326×body160valid