Details

Time bar (total: 26.6s)

sample53.0ms

Algorithm
intervals
Results
13.0ms298×body80nan
11.0ms46×body1280valid
8.0ms46×body640valid
6.0ms136×body80valid
2.0ms16×body320valid
1.0ms12×body160valid

simplify18.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
18.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize22.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (sqrt (+ x 1)) (sqrt x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out
Counts
1 → 20
Calls
1 calls:
Slowest
38.0ms
(- (sqrt (+ x 1)) (sqrt x))

series91.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
91.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify258.0ms

Counts
17 → 23
Calls
17 calls:
Slowest
36.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
25.0ms
(+ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
22.0ms
(+ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune233.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 28.0b

localize42.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.2b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.0b
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite117.0ms

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
59.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
23.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
23.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
9.0ms
(* (sqrt x) (sqrt x))

series187.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
30.0ms
(* (sqrt x) (sqrt x))
20.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
18.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify6.3s

Counts
211 → 191
Calls
211 calls:
Slowest
380.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
356.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
352.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
241.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
233.0ms
(/ (* (* (- (* (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))))

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r* add-exp-log
4×add-cbrt-cube add-log-exp
3×pow1 associate-/l*
2×flip3-+ div-exp associate-/r/ flip-+ insert-posit16
1×cbrt-undiv +-commutative rec-exp clear-num sum-log frac-2neg 1-exp div-inv pow-flip inv-pow
Counts
2 → 61
Calls
2 calls:
Slowest
33.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
28.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series176.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
116.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
59.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify1.2s

Counts
62 → 67
Calls
62 calls:
Slowest
236.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
150.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
68.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
47.0ms
(/ (sqrt 1) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
45.0ms
(- 0 (log (+ (sqrt (+ x 1)) (sqrt x))))

prune521.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

rewrite293.0ms

Algorithm
rewrite-expression-head
Rules
308×*-un-lft-identity
290×sqrt-prod
168×times-frac
136×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
43×swap-sqr
31×pow1
27×sqrt-pow1 associate-*r* associate-*l*
16×unswap-sqr
14×add-exp-log associate-/r/
12×associate-/r*
11×pow-flip inv-pow
10×add-cbrt-cube
9×pow1/2 pow-prod-up div-inv
7×flip3-+ flip-+
6×associate-/l*
5×sqrt-div pow-prod-down pow-sqr
4×div-exp insert-posit16 add-log-exp
3×rem-sqrt-square
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp
1×pow2 frac-times rem-square-sqrt pow-plus sqrt-unprod associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 282
Calls
4 calls:
Slowest
163.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
51.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
35.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
33.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
91.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
78.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
75.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

simplify9.0s

Counts
359 → 294
Calls
359 calls:
Slowest
427.0ms
(* (* (* (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))))))
395.0ms
(* (sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))) (sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))))
365.0ms
(sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))
305.0ms
(sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))
230.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))

prune3.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch6.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.1s8141×body80nan
609.0ms1722×body1280valid
364.0ms4102×body80valid
332.0ms1216×body640valid
121.0ms647×body320valid
38.0ms313×body160valid