Details

Time bar (total: 18.7s)

sample78.0ms

Algorithm
intervals
Results
19.0ms57×body1280valid
16.0ms257×body80nan
13.0ms125×body80valid
11.0ms40×body640valid
4.0ms19×body320valid
2.0ms15×body160valid

simplify20.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize20.0ms

Local error

Found 1 expressions with local error:

3.8b
(- (sqrt (+ x 1)) (sqrt x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
3×*-un-lft-identity add-log-exp
2×difference-of-squares
1×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt sqrt-prod insert-posit16 flip-- distribute-lft-out--
Calls
1 calls:
Slowest
14.0ms
(- (sqrt (+ x 1)) (sqrt x))

series98.0ms

Calls
1 calls:
Slowest
98.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify141.0ms

Calls
9 calls:
Slowest
59.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
21.0ms
(+ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
18.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
17.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
14.0ms
(+ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune169.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 31.3b

localize22.0ms

Local error

Found 4 expressions with local error:

3.2b
(- (* (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)))

rewrite83.0ms

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
31.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
25.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
17.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
8.0ms
(* (sqrt x) (sqrt x))

series175.0ms

Calls
4 calls:
Slowest
104.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
28.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
27.0ms
(* (sqrt x) (sqrt x))
15.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify4.9s

Calls
108 calls:
Slowest
804.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
453.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
432.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
193.0ms
(/ (* (* (- (* (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))))
148.0ms
(+ (* (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

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
4×associate-/r* add-log-exp
3×add-sqr-sqrt pow1 add-exp-log add-cube-cbrt
2×flip3-+ add-cbrt-cube associate-/r/ flip-+ insert-posit16 distribute-lft-out
1×+-commutative rec-exp clear-num sum-log frac-2neg div-inv pow-flip inv-pow
Calls
2 calls:
Slowest
11.0ms
(+ (sqrt (+ x 1)) (sqrt x))
9.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series165.0ms

Calls
2 calls:
Slowest
83.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
82.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify280.0ms

Calls
15 calls:
Slowest
167.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
26.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms
(cbrt (+ (sqrt (+ x 1)) (sqrt x)))
14.0ms
(- (sqrt (+ x 1)) (sqrt x))
13.0ms
(* (exp (sqrt (+ x 1))) (exp (sqrt x)))

prune394.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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)))

rewrite45.0ms

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
15.0ms
(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
12.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
9.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
7.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series526.0ms

Calls
4 calls:
Slowest
166.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
150.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
126.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
84.0ms
(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify6.1s

Calls
143 calls:
Slowest
510.0ms
(/ (* (* (/ 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)))))
224.0ms
(/ (sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
216.0ms
(sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
213.0ms
(/ (sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
211.0ms
(/ (sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes75.0ms

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
663.0ms4113×body80valid
621.0ms1730×body1280valid
552.0ms8028×body80nan
368.0ms1239×body640valid
184.0ms628×body320valid
33.0ms290×body160valid