Details

Time bar (total: 31.7s)

sample111.0ms

Algorithm
intervals
Results
24.0ms60×body640valid
23.0ms267×body80nan
22.0ms132×body80valid
20.0ms36×body1280valid
7.0ms22×body320valid
1.0ms6×body160valid

simplify28.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
28.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize33.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite107.0ms

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
64.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
18.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))
9.0ms
(sqrt (+ x 1))

series191.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
39.0ms
(/ 1 (sqrt x))
32.0ms
(/ 1 (sqrt (+ x 1)))
23.0ms
(sqrt (+ x 1))

simplify4.0s

Counts
204 → 179
Calls
204 calls:
Slowest
163.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
111.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
91.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
68.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))
65.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.3b

localize23.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (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))

rewrite155.0ms

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
81.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
31.0ms
(- (sqrt (+ x 1)) (sqrt x))
31.0ms
(* (sqrt x) (sqrt (+ x 1)))
9.0ms
(sqrt (+ x 1))

series384.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
184.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
92.0ms
(* (sqrt x) (sqrt (+ x 1)))
81.0ms
(- (sqrt (+ x 1)) (sqrt x))
27.0ms
(sqrt (+ x 1))

simplify2.8s

Counts
101 → 124
Calls
101 calls:
Slowest
356.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
251.0ms
(/ (* (* (- (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)))))
201.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
195.0ms
(/ (* (* (- (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)))))
119.0ms
(- (log (- (sqrt (+ x 1)) (sqrt x))) (+ (log (sqrt x)) (log (sqrt (+ x 1)))))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 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))

rewrite225.0ms

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
96.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
88.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms
(* (sqrt x) (sqrt (+ x 1)))
19.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series572.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
231.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
207.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
67.0ms
(* (sqrt x) (sqrt (+ x 1)))
66.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify7.2s

Counts
103 → 135
Calls
103 calls:
Slowest
350.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
339.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
325.0ms
(/ (* (* 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)))))
311.0ms
(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))
306.0ms
(* (* (* (* (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))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
113×*-un-lft-identity
78×times-frac
55×sqrt-prod
45×distribute-lft-out
42×add-sqr-sqrt
36×add-exp-log
34×add-cube-cbrt
20×add-cbrt-cube
18×sqrt-div associate-*r/ associate-/r/
15×div-exp
13×pow1
12×associate-/l*
11×flip3-+ flip-+
9×div-inv
7×cbrt-undiv associate-/r* associate-*r* prod-exp
6×associate-*l* pow-prod-down add-log-exp
4×rec-exp sqrt-pow1 pow1/2 1-exp insert-posit16 pow-flip unswap-sqr
3×cbrt-unprod
2×clear-num frac-2neg
1×+-commutative sum-log sqrt-unprod *-commutative inv-pow associate-/l/
Counts
4 → 175
Calls
4 calls:
Slowest
50.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
25.0ms
(+ (sqrt (+ x 1)) (sqrt x))
18.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
16.0ms
(* (sqrt x) (sqrt (+ x 1)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
212.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
71.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
64.0ms
(+ (sqrt (+ x 1)) (sqrt x))
58.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify8.0s

Counts
201 → 187
Calls
201 calls:
Slowest
294.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
218.0ms
(/ (* (* (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (/ 1 (* (sqrt x) (sqrt (+ x 1))))) (/ 1 (* (sqrt x) (sqrt (+ x 1))))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
199.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3))))) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
196.0ms
(- (- 0 (+ (log (sqrt x)) (log (sqrt (+ x 1))))) (log (+ (sqrt (+ x 1)) (sqrt x))))
184.0ms
(- (- 0 (log (* (sqrt x) (sqrt (+ x 1))))) (log (+ (sqrt (+ x 1)) (sqrt x))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes49.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
559.0ms1829×body640valid
544.0ms4088×body80valid
490.0ms7847×body80nan
399.0ms1147×body1280valid
106.0ms617×body320valid
37.0ms319×body160valid