Details

Time bar (total: 47.0s)

sample119.0ms

Algorithm
intervals
Results
34.0ms67×body640valid
26.0ms273×body80nan
19.0ms33×body1280valid
15.0ms130×body80valid
5.0ms16×body320valid
2.0ms10×body160valid

simplify37.0ms

Calls
1 calls:
Slowest
37.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize52.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite21.0ms

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
14.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
3.0ms
(/ 1 (sqrt (+ x 1)))
2.0ms
(/ 1 (sqrt x))
1.0ms
(sqrt (+ x 1))

series199.0ms

Calls
4 calls:
Slowest
92.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
41.0ms
(/ 1 (sqrt x))
33.0ms
(/ 1 (sqrt (+ x 1)))
32.0ms
(sqrt (+ x 1))

simplify686.0ms

Calls
42 calls:
Slowest
104.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
99.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
51.0ms
(sqrt (- (* x x) (* 1 1)))
49.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))
46.0ms
(/ (exp (/ 1 (sqrt x))) (exp (/ 1 (sqrt (+ x 1)))))

prune826.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.4b

localize17.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
0.5b
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
0.3b
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(/ 1 (sqrt x))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
32×frac-sub
28×times-frac
24×div-inv
20×add-sqr-sqrt add-cube-cbrt distribute-lft-out
18×associate-/l/
17×frac-times associate-*l/ associate-*r/ un-div-inv
16×pow1
15×add-exp-log
12×pow-flip
10×associate-/r*
9×difference-of-squares
8×add-cbrt-cube
7×inv-pow
6×pow-prod-up add-log-exp
5×rec-exp pow1/2
4×associate-*r* associate-*l* pow-prod-down prod-exp insert-posit16 associate-/l*
3×associate-/r/
2×clear-num frac-2neg flip3-- flip--
1×pow2 cbrt-undiv sub-neg flip3-+ pow-plus diff-log div-sub div-exp frac-add *-commutative cbrt-unprod flip-+
Calls
4 calls:
Slowest
52.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
8.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
5.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
1.0ms
(/ 1 (sqrt x))

series255.0ms

Calls
4 calls:
Slowest
151.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
47.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
35.0ms
(/ 1 (sqrt x))
21.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))

simplify19.4s

Calls
176 calls:
Slowest
588.0ms
(/ (sqrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) (cbrt (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))
432.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
407.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
397.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
396.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
0.5b
(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
108×sqrt-div
98×associate-*r/
84×frac-times
72×flip3-+ flip-+
51×pow1
45×add-exp-log
35×associate-/r/
30×pow-prod-down
28×prod-exp
26×add-cbrt-cube
24×associate-*l/
18×frac-add
16×associate-*l*
15×*-un-lft-identity cbrt-unprod
11×add-sqr-sqrt add-cube-cbrt
10×associate-*r*
8×pow1/2
6×rec-exp sqrt-prod pow-flip
5×div-inv
4×pow-prod-up insert-posit16 distribute-lft-out add-log-exp
3×*-commutative
2×pow2 rem-square-sqrt pow-plus sqrt-unprod
1×clear-num associate-/r* frac-2neg inv-pow
Calls
4 calls:
Slowest
62.0ms
(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
60.0ms
(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
6.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
4.0ms
(* (sqrt x) (sqrt x))

series324.0ms

Calls
4 calls:
Slowest
154.0ms
(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
131.0ms
(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
20.0ms
(* (sqrt x) (sqrt x))
19.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))

simplify18.1s

Calls
178 calls:
Slowest
532.0ms
(* (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (* (* (sqrt x) (sqrt x)) (* (sqrt (- (* x x) (* 1 1))) (sqrt (+ (pow x 3) (pow 1 3))))))
372.0ms
(* (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (+ (pow x 3) (pow 1 3))))))
354.0ms
(* (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (+ x 1)))))
338.0ms
(* (* (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (* (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt x) (sqrt x)) (sqrt x))) (* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
336.0ms
(* (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1))
0.4b
(/ (+ x 1) (sqrt x))
0.3b
(* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x))))
0.0b
(+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt
9×times-frac
8×add-exp-log
7×associate-/r*
6×add-cbrt-cube add-log-exp
5×flip3-+ flip-+
4×pow1 sqrt-div associate-*r* frac-add associate-*r/ insert-posit16
3×rec-exp associate-/l*
2×clear-num frac-2neg div-inv distribute-lft-out associate-/l/
1×distribute-rgt-in pow-to-exp cbrt-undiv +-commutative sum-log unpow-prod-down distribute-lft-in div-exp pow-exp *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
10.0ms
(* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x))))
6.0ms
(+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))
3.0ms
(/ (+ x 1) (sqrt x))
3.0ms
(/ 1 (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1))

series375.0ms

Calls
4 calls:
Slowest
131.0ms
(/ 1 (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1))
112.0ms
(* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x))))
85.0ms
(+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))
46.0ms
(/ (+ x 1) (sqrt x))

simplify1.0s

Calls
60 calls:
Slowest
151.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (sqrt x) (sqrt x)) (sqrt x)))
116.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (/ (+ x 1) (sqrt x)) (/ (+ x 1) (sqrt x))) (* (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))))
76.0ms
(+ (* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt x)) (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ x 1)))
71.0ms
(+ (* (sqrt (- (* x x) (* 1 1))) (sqrt x)) (* (sqrt (- x 1)) (+ x 1)))
46.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (sqrt x))

prune557.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.4b remaining)

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

bsearch1.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
483.0ms1879×body640valid
440.0ms1115×body1280valid
363.0ms8046×body80nan
340.0ms628×body320valid
275.0ms4052×body80valid
34.0ms326×body160valid