Details

Time bar (total: 1.1m)

sample65.0ms

Algorithm
intervals
Results
19.0ms52×body640valid
13.0ms138×body80valid
10.0ms26×body1280valid
8.0ms27×body320valid
2.0ms13×body160valid

simplify93.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
92.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
58×add-sqr-sqrt
56×times-frac
25×add-cube-cbrt
18×distribute-lft-out--
17×distribute-lft-out
14×difference-of-squares
12×add-exp-log
11×associate-/r* add-log-exp
8×add-cbrt-cube div-inv
6×pow1 associate-/l*
4×difference-of-sqr-1 div-exp associate-/r/ insert-posit16
3×flip3-- frac-add flip--
2×cbrt-undiv rec-exp associate-+l+ clear-num sum-log sub-neg frac-2neg flip3-+ diff-log 1-exp frac-sub flip-+ pow-flip inv-pow
1×+-commutative associate-+l-
Counts
4 → 141
Calls
4 calls:
Slowest
164.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
42.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
17.0ms
(/ 1 (+ x 1))
16.0ms
(/ 1 (- x 1))

series171.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
29.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
20.0ms
(/ 1 (+ x 1))
15.0ms
(/ 1 (- x 1))

simplify8.4s

Counts
151 → 153
Calls
151 calls:
Slowest
663.0ms
(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))
435.0ms
(/ (* (* 1 1) 1) (* (* (+ x 1) (+ x 1)) (+ x 1)))
404.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) 1))
301.0ms
(* (* (+ x 1) x) (- x 1))
299.0ms
(* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (- x 1))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

13.8b
(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))
0.2b
(- (* 1 x) (* (+ x 1) 2))
0.0b
(* (* (+ x 1) x) (- x 1))
0.0b
(* (- (* 1 x) (* (+ x 1) 2)) (- x 1))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
46×associate-*l/
22×flip3-- flip--
17×add-sqr-sqrt
16×frac-times frac-add
14×associate-*r*
13×*-un-lft-identity
12×flip3-+ flip-+
11×pow1 add-cbrt-cube add-exp-log
8×associate-*r/ add-log-exp
7×sub-neg add-cube-cbrt
6×distribute-rgt-in distribute-lft-in
4×associate-+l+ associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 difference-of-squares
2×difference-of-sqr-1 *-commutative distribute-lft-out--
1×+-commutative sum-log diff-log unswap-sqr
Counts
4 → 115
Calls
4 calls:
Slowest
60.0ms
(* (- (* 1 x) (* (+ x 1) 2)) (- x 1))
47.0ms
(* (* (+ x 1) x) (- x 1))
24.0ms
(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))
7.0ms
(- (* 1 x) (* (+ x 1) 2))

series168.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(* (* (+ x 1) x) (- x 1))
29.0ms
(- (* 1 x) (* (+ x 1) 2))
23.0ms
(* (- (* 1 x) (* (+ x 1) 2)) (- x 1))
3.0ms
(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

simplify21.5s

Counts
110 → 127
Calls
110 calls:
Slowest
729.0ms
(* (* (+ (* (* 1 x) (* 1 x)) (+ (* (* (+ x 1) 2) (* (+ x 1) 2)) (* (* 1 x) (* (+ x 1) 2)))) (+ (* x x) (+ (* 1 1) (* x 1)))) (+ (* x x) (- (* 1 1) (* x 1))))
713.0ms
(+ (* (* (- (pow (* 1 x) 3) (pow (* (+ x 1) 2) 3)) (- (pow x 3) (pow 1 3))) (- x 1)) (* (* (+ (* (* 1 x) (* 1 x)) (+ (* (* (+ x 1) 2) (* (+ x 1) 2)) (* (* 1 x) (* (+ x 1) 2)))) (+ (* x x) (+ (* 1 1) (* x 1)))) (* (* (- (* x x) (* 1 1)) x) 1)))
671.0ms
(* (+ (* x x) (- (* 1 1) (* x 1))) (+ (* x x) (+ (* 1 1) (* x 1))))
597.0ms
(+ (* (* (- (pow (* 1 x) 3) (pow (* (+ x 1) 2) 3)) (- (* x x) (* 1 1))) (+ (* x x) (- (* 1 1) (* x 1)))) (* (* (+ (* (* 1 x) (* 1 x)) (+ (* (* (+ x 1) 2) (* (+ x 1) 2)) (* (* 1 x) (* (+ x 1) 2)))) (+ x 1)) (* (* (+ (pow x 3) (pow 1 3)) x) 1)))
572.0ms
(* (- (* (* 1 x) (* 1 x)) (* (* (+ x 1) 2) (* (+ x 1) 2))) (- (pow x 3) (pow 1 3)))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ 2 (* (* (+ x 1) x) (- x 1)))
0.0b
(* (* (+ x 1) x) (- x 1))
0.0b
(* (+ x 1) x)

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
19×add-cbrt-cube add-exp-log
18×associate-*l/
14×add-sqr-sqrt
13×*-un-lft-identity
10×pow1 associate-*r*
8×frac-times associate-/r/ add-cube-cbrt
7×flip3-+ prod-exp cbrt-unprod flip-+
6×flip3-- flip--
5×associate-*l*
4×pow-prod-down associate-*r/
3×cbrt-undiv times-frac div-exp insert-posit16 associate-/l* add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in *-commutative difference-of-squares
1×clear-num associate-/r* frac-2neg difference-of-sqr-1 div-inv distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
3 → 89
Calls
3 calls:
Slowest
49.0ms
(* (* (+ x 1) x) (- x 1))
38.0ms
(/ 2 (* (* (+ x 1) x) (- x 1)))
15.0ms
(* (+ x 1) x)

series275.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
114.0ms
(* (* (+ x 1) x) (- x 1))
98.0ms
(/ 2 (* (* (+ x 1) x) (- x 1)))
63.0ms
(* (+ x 1) x)

simplify8.6s

Counts
73 → 98
Calls
73 calls:
Slowest
532.0ms
(* (- x 1) (+ (* x x) (+ (* 1 1) (* x 1))))
529.0ms
(* (- x 1) (+ (* x x) (+ (* 1 1) (* x 1))))
482.0ms
(/ (* (* 2 2) 2) (* (* (* (* (+ x 1) x) (- x 1)) (* (* (+ x 1) x) (- x 1))) (* (* (+ x 1) x) (- x 1))))
413.0ms
(/ (* (* 2 2) 2) (* (* (* (* (+ x 1) x) (* (+ x 1) x)) (* (+ x 1) x)) (* (* (- x 1) (- x 1)) (- x 1))))
405.0ms
(* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* x x) x))

prune630.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ 2 (* (+ x 1) x))
0.1b
(/ (/ 2 (* (+ x 1) x)) (- x 1))
0.0b
(* (+ x 1) x)

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
75×add-sqr-sqrt
65×*-un-lft-identity
33×add-cube-cbrt
20×associate-*l/ associate-/r/ difference-of-squares
19×add-cbrt-cube add-exp-log
12×associate-/l*
10×flip3-+ difference-of-sqr-1 flip-+ div-inv distribute-lft-out--
8×associate-/r*
7×cbrt-undiv div-exp
5×pow1
4×associate-*l*
3×associate-*r* prod-exp cbrt-unprod insert-posit16 add-log-exp
2×clear-num frac-2neg
1×flip3-- pow-prod-down *-commutative flip-- distribute-lft-out unswap-sqr associate-/l/
Counts
3 → 145
Calls
3 calls:
Slowest
35.0ms
(/ (/ 2 (* (+ x 1) x)) (- x 1))
17.0ms
(/ 2 (* (+ x 1) x))
14.0ms
(* (+ x 1) x)

series150.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
67.0ms
(* (+ x 1) x)
58.0ms
(/ (/ 2 (* (+ x 1) x)) (- x 1))
25.0ms
(/ 2 (* (+ x 1) x))

simplify17.3s

Counts
182 → 154
Calls
182 calls:
Slowest
796.0ms
(/ (/ 2 (* (+ (pow x 3) (pow 1 3)) x)) (* (cbrt (- x 1)) (cbrt (- x 1))))
356.0ms
(/ (/ 2 (* (- (* x x) (* 1 1)) x)) (* (cbrt (- x 1)) (cbrt (- x 1))))
353.0ms
(/ (/ 2 (* (- (* x x) (* 1 1)) x)) (sqrt (- x 1)))
350.0ms
(/ (/ 2 (* (+ (pow x 3) (pow 1 3)) x)) 1)
345.0ms
(/ (/ (* (* 2 2) 2) (* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* x x) x))) (* (* (- x 1) (- x 1)) (- x 1)))

prune979.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
818.0ms4144×body80valid
739.0ms1825×body640valid
275.0ms989×body320valid
274.0ms571×body1280valid
85.0ms471×body160valid