Details

Time bar (total: 46.1s)

sample72.0ms

Algorithm
intervals
Results
22.0ms131×body80valid
20.0ms59×body640valid
11.0ms23×body1280valid
6.0ms27×body320valid
3.0ms16×body160valid

simplify101.0ms

Calls
1 calls:
Slowest
101.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.9b

localize35.0ms

Local error

Found 4 expressions with local error:

2.1b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
11×add-log-exp
8×add-sqr-sqrt div-inv
6×pow1 associate-/r* add-exp-log add-cube-cbrt distribute-lft-out distribute-lft-out--
4×add-cbrt-cube associate-/r/ insert-posit16
3×flip3-- frac-add flip--
2×rec-exp associate-+l+ clear-num sum-log sub-neg frac-2neg flip3-+ diff-log frac-sub flip-+ pow-flip inv-pow
1×+-commutative associate-+l- difference-of-squares
Calls
4 calls:
Slowest
51.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
12.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
2.0ms
(/ 1 (- x 1))
2.0ms
(/ 1 (+ x 1))

series76.0ms

Calls
4 calls:
Slowest
46.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
18.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
6.0ms
(/ 1 (- x 1))
6.0ms
(/ 1 (+ x 1))

simplify4.6s

Calls
48 calls:
Slowest
606.0ms
(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))
423.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) 1))
352.0ms
(* (* (+ x 1) x) (- x 1))
298.0ms
(* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1))
244.0ms
(- (+ (* 2 x) (+ (* 2 (pow x 3)) (* 2 (/ 1 x)))))

prune645.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

14.8b
(/ (* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (/ 1 (+ x 1)) (/ 2 x))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1)))
7.7b
(+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1)
0.2b
(+ (/ 1 (+ x 1)) (/ 2 x))
0.2b
(+ (/ 1 (+ x 1)) (/ 2 x))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
13×flip3-+ flip-+
12×frac-times
11×associate-/r/ associate-/l/
10×*-un-lft-identity
8×frac-add add-log-exp
5×associate-*l/ associate-*r/
4×add-sqr-sqrt pow1 cbrt-undiv associate-+l+ flip3-- div-exp prod-exp add-cube-cbrt cbrt-unprod insert-posit16 flip-- distribute-lft-out
3×+-commutative div-inv
2×distribute-rgt-in sum-log sub-neg distribute-lft-in
1×clear-num associate-/r* frac-2neg times-frac associate-/l*
Calls
4 calls:
Slowest
34.0ms
(/ (* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (/ 1 (+ x 1)) (/ 2 x))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1)))
19.0ms
(+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1)
6.0ms
(+ (/ 1 (+ x 1)) (/ 2 x))
5.0ms
(+ (/ 1 (+ x 1)) (/ 2 x))

series126.0ms

Calls
4 calls:
Slowest
56.0ms
(/ (* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (/ 1 (+ x 1)) (/ 2 x))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1)))
36.0ms
(+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1)
17.0ms
(+ (/ 1 (+ x 1)) (/ 2 x))
17.0ms
(+ (/ 1 (+ x 1)) (/ 2 x))

simplify10.2s

Calls
60 calls:
Slowest
1.5s
(/ (* (* (* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (/ 1 (+ x 1)) (/ 2 x))) (* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (/ 1 (+ x 1)) (/ 2 x)))) (* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (/ 1 (+ x 1)) (/ 2 x)))) (* (* (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1))))
666.0ms
(* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))))
529.0ms
(* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (- (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (+ x 1))
454.0ms
(* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (* 1 x) (* (+ x 1) 2)))
446.0ms
(- (log (* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (/ 1 (+ x 1)) (/ 2 x)))) (log (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1))))

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

8.3b
(- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))
1.2b
(/ (* (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))) (+ (/ 1 (+ x 1)) (/ 2 x))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1)))
0.4b
(/ 2 (* x x))
0.2b
(/ 2 (pow x 4))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
23×associate-/l/
21×frac-times
17×frac-sub
16×add-cbrt-cube add-exp-log
13×flip3-- flip--
11×associate-/r/
9×add-sqr-sqrt flip3-+ frac-add flip-+
8×associate-*l/
7×*-un-lft-identity
6×add-log-exp
5×associate-/r* associate-*r/ add-cube-cbrt
4×pow1 cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16
3×clear-num frac-2neg div-inv
2×times-frac difference-of-squares
1×sub-neg diff-log associate-/l* distribute-lft-out--
Calls
4 calls:
Slowest
53.0ms
(/ (* (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))) (+ (/ 1 (+ x 1)) (/ 2 x))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1)))
11.0ms
(- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))
1.0ms
(/ 2 (pow x 4))
1.0ms
(/ 2 (* x x))

series133.0ms

Calls
4 calls:
Slowest
66.0ms
(- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))
33.0ms
(/ (* (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))) (+ (/ 1 (+ x 1)) (/ 2 x))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1)))
21.0ms
(/ 2 (pow x 4))
14.0ms
(/ 2 (* x x))

simplify13.2s

Calls
69 calls:
Slowest
873.0ms
(* (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))) (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))))
658.0ms
(* (- (* 2 (+ (* (/ (/ 2 x) (* x x)) (/ (/ 2 x) (* x x))) (+ (* (/ 2 (pow x 4)) (/ 2 (pow x 4))) (* (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))))) (* (* x x) (- (pow (/ (/ 2 x) (* x x)) 3) (pow (/ 2 (pow x 4)) 3)))) (+ (pow (/ 1 (+ x 1)) 3) (pow (/ 2 x) 3)))
555.0ms
(- (+ (log (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4))))) (log (+ (/ 1 (+ x 1)) (/ 2 x)))) (+ (log (+ (/ 1 (+ x 1)) (/ 2 x))) (log (- x 1))))
491.0ms
(- (+ (log (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4))))) (log (+ (/ 1 (+ x 1)) (/ 2 x)))) (log (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1))))
484.0ms
(* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (- (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (+ x 1))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

19.4b
(/ (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))) (+ (/ 1 (+ x 1)) (/ 2 x)))
8.3b
(- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))
0.4b
(/ 2 (* x x))
0.2b
(/ 2 (pow x 4))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
34×add-sqr-sqrt
31×times-frac
19×distribute-lft-out--
18×add-cube-cbrt
14×distribute-lft-out
10×div-inv
9×associate-/r*
8×difference-of-squares
6×add-cbrt-cube add-exp-log associate-/l* add-log-exp
5×frac-sub associate-/l/
4×pow1 insert-posit16
3×clear-num frac-2neg flip3-- associate-/r/ flip--
1×cbrt-undiv sub-neg flip3-+ diff-log div-sub div-exp frac-add flip-+
Calls
4 calls:
Slowest
83.0ms
(/ (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))) (+ (/ 1 (+ x 1)) (/ 2 x)))
18.0ms
(- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))
1.0ms
(/ 2 (pow x 4))
1.0ms
(/ 2 (* x x))

series149.0ms

Calls
4 calls:
Slowest
67.0ms
(- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))
44.0ms
(/ (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))) (+ (/ 1 (+ x 1)) (/ 2 x)))
20.0ms
(/ 2 (pow x 4))
18.0ms
(/ 2 (* x x))

simplify10.0s

Calls
102 calls:
Slowest
367.0ms
(- (pow (/ 2 (* x x)) 3) (pow (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4))) 3))
328.0ms
(- (* 2 (+ (* (/ (/ 2 x) (* x x)) (/ (/ 2 x) (* x x))) (+ (* (/ 2 (pow x 4)) (/ 2 (pow x 4))) (* (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))))) (* (* x x) (- (pow (/ (/ 2 x) (* x x)) 3) (pow (/ 2 (pow x 4)) 3))))
290.0ms
(/ (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))) (+ (/ 1 (+ x 1)) (/ 2 x)))
283.0ms
(/ (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))) (+ (/ 1 (+ x 1)) (/ 2 x)))
231.0ms
(/ (- (/ 2 (* x x)) (- (/ (/ 2 x) (* x x)) (/ 2 (pow x 4)))) (+ (/ 1 (+ x 1)) (/ 2 x)))

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes90.0ms

Accuracy

99.6% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.6b

bsearch135.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
763.0ms4218×body80valid
745.0ms1868×body640valid
337.0ms916×body320valid
284.0ms554×body1280valid
140.0ms445×body160valid