Details

Time bar (total: 20.4s)

sample67.0ms

Algorithm
intervals
Results
16.0ms65×body640valid
14.0ms126×body80valid
13.0ms246×body80nan
9.0ms29×body1280valid
4.0ms24×body320valid
1.0ms12×body160valid

simplify28.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize15.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.2b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×add-sqr-sqrt
9×associate-/r*
8×add-cube-cbrt
6×pow1 add-exp-log sqrt-prod div-inv add-log-exp
4×add-cbrt-cube sqrt-div insert-posit16 pow-flip distribute-lft-out--
3×pow1/2
2×rec-exp clear-num frac-2neg flip3-+ associate-/r/ flip-+ inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip-- difference-of-squares
Calls
4 calls:
Slowest
18.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
4.0ms
(/ 1 (sqrt (+ x 1)))
2.0ms
(/ 1 (sqrt x))
1.0ms
(sqrt (+ x 1))

series76.0ms

Calls
4 calls:
Slowest
39.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
14.0ms
(sqrt (+ x 1))
12.0ms
(/ 1 (sqrt (+ x 1)))
11.0ms
(/ 1 (sqrt x))

simplify658.0ms

Calls
42 calls:
Slowest
82.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
73.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
61.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))
54.0ms
(/ (exp (/ 1 (sqrt x))) (exp (/ 1 (sqrt (+ x 1)))))
49.0ms
(- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1))

prune778.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.1b

localize16.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (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))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
16×*-un-lft-identity
11×add-cbrt-cube add-exp-log
10×add-cube-cbrt
9×sqrt-prod
6×pow1 times-frac sqrt-div associate-*r* associate-/l* add-log-exp difference-of-squares
4×associate-*r/ insert-posit16
3×flip3-+ pow1/2 associate-*l* flip-+ distribute-lft-out--
2×cbrt-undiv flip3-- div-exp pow-prod-down 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
Calls
4 calls:
Slowest
34.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
13.0ms
(- (sqrt (+ x 1)) (sqrt x))
10.0ms
(* (sqrt x) (sqrt (+ x 1)))
1.0ms
(sqrt (+ x 1))

series129.0ms

Calls
4 calls:
Slowest
66.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
31.0ms
(* (sqrt x) (sqrt (+ x 1)))
23.0ms
(- (sqrt (+ x 1)) (sqrt x))
10.0ms
(sqrt (+ x 1))

simplify2.0s

Calls
65 calls:
Slowest
243.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
236.0ms
(/ (* (* (- (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)))))
189.0ms
(/ (* (* (- (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)))))
120.0ms
(- (log (- (sqrt (+ x 1)) (sqrt x))) (+ (log (sqrt x)) (log (sqrt (+ x 1)))))
112.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune867.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 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))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
17×pow1 add-exp-log
14×flip3-+ sqrt-div flip-+
12×*-un-lft-identity
11×add-cbrt-cube
10×associate-*r*
8×add-sqr-sqrt frac-times pow-prod-down associate-/r/ add-cube-cbrt
7×prod-exp
6×add-log-exp
4×associate-*l* associate-*l/ cbrt-unprod insert-posit16
3×rec-exp sqrt-prod pow-flip
2×pow1/2 *-commutative distribute-lft-out
1×distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in sqrt-unprod div-inv inv-pow
Calls
4 calls:
Slowest
43.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
38.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
11.0ms
(+ (sqrt (+ x 1)) (sqrt x))
10.0ms
(* (sqrt x) (sqrt (+ x 1)))

series220.0ms

Calls
4 calls:
Slowest
98.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
68.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
33.0ms
(+ (sqrt (+ x 1)) (sqrt x))
21.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify5.5s

Calls
66 calls:
Slowest
784.0ms
(* (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3)))) (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
376.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
360.0ms
(* (* (* (* (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))))
353.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
329.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

prune941.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

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))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
24×times-frac
19×add-sqr-sqrt add-cube-cbrt
16×add-exp-log
14×sqrt-div associate-*r/ associate-/r/
9×pow1 flip3-+ flip-+
8×add-cbrt-cube distribute-lft-out
7×div-inv
6×associate-*r* associate-/l* add-log-exp
5×associate-/r*
4×rec-exp pow1/2 pow-prod-down insert-posit16
3×div-exp associate-*l* prod-exp sqrt-prod pow-flip
2×clear-num frac-2neg
1×cbrt-undiv +-commutative sum-log sqrt-unprod *-commutative cbrt-unprod inv-pow associate-/l/
Calls
4 calls:
Slowest
19.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
6.0ms
(+ (sqrt (+ x 1)) (sqrt x))
5.0ms
(* (sqrt x) (sqrt (+ x 1)))
5.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))

series205.0ms

Calls
4 calls:
Slowest
105.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
36.0ms
(* (sqrt x) (sqrt (+ x 1)))
32.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
31.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify4.2s

Calls
97 calls:
Slowest
231.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
206.0ms
(/ (* (* (/ 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))))
164.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3))))) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
156.0ms
(/ (/ 1 (* (sqrt x) (sqrt (- (* x x) (* 1 1))))) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
149.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s7996×body80nan
811.0ms1850×body640valid
567.0ms1119×body1280valid
410.0ms4092×body80valid
154.0ms600×body320valid
124.0ms339×body160valid