Details

Time bar (total: 20.0s)

sample107.0ms

Algorithm
intervals
Results
36.0ms41×body1280valid
21.0ms56×body640valid
18.0ms257×body80nan
11.0ms125×body80valid
4.0ms20×body320valid
2.0ms14×body160valid

simplify19.0ms

Calls
1 calls:
Slowest
19.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize24.0ms

Local error

Found 3 expressions with local error:

3.8b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×associate-/r*
8×add-sqr-sqrt
6×add-cube-cbrt div-inv
5×pow1 add-exp-log add-log-exp
4×pow-flip distribute-lft-out--
3×add-cbrt-cube sqrt-prod insert-posit16
2×rec-exp clear-num frac-2neg pow1/2 sqrt-div associate-/r/ inv-pow
1×sub-neg flip3-+ flip3-- diff-log frac-sub flip-+ flip-- difference-of-squares
Calls
3 calls:
Slowest
13.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
3.0ms
(/ 1 (sqrt (+ x 1)))
2.0ms
(/ 1 (sqrt x))

series220.0ms

Calls
3 calls:
Slowest
116.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
58.0ms
(/ 1 (sqrt (+ x 1)))
45.0ms
(/ 1 (sqrt x))

simplify556.0ms

Calls
33 calls:
Slowest
93.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
77.0ms
(/ (exp (/ 1 (sqrt x))) (exp (/ 1 (sqrt (+ x 1)))))
58.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))
55.0ms
(- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1))
36.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune605.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.9b

localize15.0ms

Local error

Found 3 expressions with local error:

3.8b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×*-un-lft-identity
10×add-cbrt-cube add-exp-log
8×add-cube-cbrt
6×times-frac associate-*r* sqrt-prod associate-/l* difference-of-squares
5×pow1 add-log-exp
4×sqrt-div associate-*r/
3×associate-*l* insert-posit16 distribute-lft-out--
2×cbrt-undiv flip3-+ flip3-- pow1/2 div-exp pow-prod-down prod-exp associate-/r/ cbrt-unprod flip-+ flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Calls
3 calls:
Slowest
36.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
14.0ms
(- (sqrt (+ x 1)) (sqrt x))
10.0ms
(* (sqrt x) (sqrt (+ x 1)))

series350.0ms

Calls
3 calls:
Slowest
195.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
95.0ms
(* (sqrt x) (sqrt (+ x 1)))
61.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify1.7s

Calls
56 calls:
Slowest
253.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
191.0ms
(/ (* (* (- (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)))))
168.0ms
(/ (* (* (- (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)))))
126.0ms
(- (log (- (sqrt (+ x 1)) (sqrt x))) (+ (log (sqrt x)) (log (sqrt (+ x 1)))))
86.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))

prune675.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize7.0ms

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))

rewrite70.0ms

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
28.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
25.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
10.0ms
(* (sqrt x) (sqrt (+ x 1)))
6.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series737.0ms

Calls
4 calls:
Slowest
323.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
246.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
96.0ms
(+ (sqrt (+ x 1)) (sqrt x))
72.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify5.2s

Calls
66 calls:
Slowest
455.0ms
(* (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3)))) (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
411.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
371.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
336.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
334.0ms
(* (* (* (* (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))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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
23.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
11.0ms
(+ (sqrt (+ x 1)) (sqrt x))
10.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
5.0ms
(* (sqrt x) (sqrt (+ x 1)))

series435.0ms

Calls
4 calls:
Slowest
256.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
66.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
57.0ms
(* (sqrt x) (sqrt (+ x 1)))
55.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify3.9s

Calls
97 calls:
Slowest
209.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
207.0ms
(/ (* (* (/ 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))))
157.0ms
(- (+ (* 3/8 (/ 1 (pow x 3))) (/ 1 x)) (* 1/2 (/ 1 (pow x 2))))
151.0ms
(- (log (/ 1 (* (sqrt x) (sqrt (+ x 1))))) (log (+ (sqrt (+ x 1)) (sqrt x))))
148.0ms
(/ (/ 1 (* (sqrt x) (sqrt (- (* x x) (* 1 1))))) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))

prune985.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

0% (0.4b remaining)

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

bsearch2.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s1822×body640valid
557.0ms8028×body80nan
542.0ms1154×body1280valid
395.0ms4108×body80valid
138.0ms625×body320valid
67.0ms291×body160valid