Details

Time bar (total: 59.6s)

sample81.0ms

Algorithm
intervals
Results
27.0ms251×body80nan
15.0ms56×body640valid
13.0ms38×body1280valid
10.0ms135×body80valid
3.0ms17×body320valid
1.0ms10×body160valid

simplify23.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
23.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize18.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
97×*-un-lft-identity times-frac
64×sqrt-prod
42×add-cube-cbrt
25×difference-of-squares
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube distribute-lft-out
6×div-inv pow-flip associate-/l* add-log-exp
4×sqrt-div div-exp insert-posit16
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg flip3-+ 1-exp associate-/r/ flip-+ inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 167
Calls
4 calls:
Slowest
43.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
15.0ms
(/ 1 (sqrt (+ x 1)))
6.0ms
(sqrt (+ x 1))
5.0ms
(/ 1 (sqrt x))

series532.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
428.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
42.0ms
(/ 1 (sqrt (+ x 1)))
33.0ms
(sqrt (+ x 1))
29.0ms
(/ 1 (sqrt x))

simplify4.0s

Counts
204 → 179
Calls
204 calls:
Slowest
156.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
113.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
100.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
83.0ms
(/ (* (* 1 1) 1) (* (* (sqrt x) (sqrt x)) (sqrt x)))
75.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.6b

localize17.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.0b
(sqrt (+ x 1))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
39×sqrt-prod
36×*-un-lft-identity
12×difference-of-squares
11×add-cbrt-cube add-exp-log add-cube-cbrt
10×times-frac associate-/l*
9×pow1 distribute-lft-out--
7×associate-*r*
6×sqrt-div associate-*l* add-log-exp
5×distribute-lft-out
4×associate-*r/ insert-posit16 unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Counts
4 → 112
Calls
4 calls:
Slowest
57.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
28.0ms
(- (sqrt (+ x 1)) (sqrt x))
16.0ms
(* (sqrt x) (sqrt (+ x 1)))
4.0ms
(sqrt (+ x 1))

series385.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
222.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
81.0ms
(* (sqrt x) (sqrt (+ x 1)))
60.0ms
(- (sqrt (+ x 1)) (sqrt x))
23.0ms
(sqrt (+ x 1))

simplify2.9s

Counts
101 → 124
Calls
101 calls:
Slowest
378.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
246.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
208.0ms
(/ (* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x))) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))))
189.0ms
(/ (* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x))) (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))))
126.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
27×*-un-lft-identity
20×add-cbrt-cube
19×add-sqr-sqrt pow1 sqrt-prod
18×associate-*r/
14×flip3-+ sqrt-div flip-+
13×associate-*r* prod-exp
11×add-cube-cbrt
9×pow-prod-down distribute-lft-out
8×frac-times associate-/r/
7×associate-*l* cbrt-unprod
6×div-exp add-log-exp
4×associate-*l/ insert-posit16 unswap-sqr
3×cbrt-undiv rec-exp times-frac 1-exp pow-flip associate-/l*
2×sqrt-pow1 pow1/2 *-commutative
1×distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in sqrt-unprod div-inv inv-pow
Counts
4 → 123
Calls
4 calls:
Slowest
133.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
102.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
37.0ms
(+ (sqrt (+ x 1)) (sqrt x))
20.0ms
(* (sqrt x) (sqrt (+ x 1)))

series565.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
203.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
80.0ms
(+ (sqrt (+ x 1)) (sqrt x))
68.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify7.1s

Counts
103 → 135
Calls
103 calls:
Slowest
378.0ms
(/ (* (* 1 1) 1) (* (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))
346.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
345.0ms
(/ (* (* 1 1) 1) (* (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))
317.0ms
(/ (* (* 1 1) 1) (* (* (* (* (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 1)) (sqrt x)))))
307.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
795×times-frac
557×*-un-lft-identity
519×add-sqr-sqrt
425×sqrt-prod
353×add-cube-cbrt
166×associate-*l*
95×distribute-lft-out
61×cbrt-prod
54×add-exp-log
44×unswap-sqr
42×associate-*r*
36×associate-/l*
32×associate-/r/
30×add-cbrt-cube
28×sqrt-div
26×div-exp
19×associate-/r*
18×div-inv
16×flip3-+ flip-+
14×cbrt-undiv
10×prod-exp
8×pow1
6×cbrt-unprod
4×rec-exp 1-exp insert-posit16 add-log-exp
3×clear-num frac-2neg pow-flip
1×frac-times sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative inv-pow associate-/l/
Counts
4 → 609
Calls
4 calls:
Slowest
117.0ms
(* (/ (/ 1 (sqrt (+ x 1))) (sqrt x)) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x))))
27.0ms
(/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))
16.0ms
(/ (/ 1 (sqrt (+ x 1))) (sqrt x))
13.0ms
(/ 1 (sqrt (+ x 1)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
210.0ms
(* (/ (/ 1 (sqrt (+ x 1))) (sqrt x)) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x))))
97.0ms
(/ (/ 1 (sqrt (+ x 1))) (sqrt x))
87.0ms
(/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))
42.0ms
(/ 1 (sqrt (+ x 1)))

simplify32.4s

Counts
835 → 621
Calls
835 calls:
Slowest
790.0ms
(* (* (* (/ (/ 1 (sqrt (+ x 1))) (sqrt x)) (/ (/ 1 (sqrt (+ x 1))) (sqrt x))) (/ (/ 1 (sqrt (+ x 1))) (sqrt x))) (* (* (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x))) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))))
402.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (cbrt (sqrt x)) (cbrt (sqrt x))))
296.0ms
(/ 1 (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
270.0ms
(/ (* (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
245.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (cbrt (sqrt x)) (cbrt (sqrt x))))

prune4.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch3.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
708.0ms1872×body640valid
499.0ms7972×body80nan
314.0ms1136×body1280valid
300.0ms4084×body80valid
118.0ms608×body320valid
70.0ms300×body160valid