Details

Time bar (total: 36.7s)

sample77.0ms

Algorithm
intervals
Results
47.0ms66×body1280valid
11.0ms45×body640valid
7.0ms121×body80valid
3.0ms16×body320valid
1.0ms8×body160valid

simplify49.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
49.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize16.0ms

Local error

Found 3 expressions with local error:

2.9b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
110×*-un-lft-identity
60×times-frac
57×add-sqr-sqrt
25×add-cube-cbrt
20×distribute-lft-out
18×distribute-lft-out--
14×difference-of-squares
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×difference-of-sqr-1 add-log-exp
4×associate-/r/
3×pow1 insert-posit16
2×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp flip-+ div-inv flip-- associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 117
Calls
3 calls:
Slowest
71.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
35.0ms
(/ (+ x 1) (- x 1))
17.0ms
(/ x (+ x 1))

series149.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
90.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
36.0ms
(/ (+ x 1) (- x 1))
23.0ms
(/ x (+ x 1))

simplify5.1s

Counts
142 → 126
Calls
142 calls:
Slowest
430.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
395.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
377.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
265.0ms
(/ (* (* x x) x) (* (* (+ x 1) (+ x 1)) (+ x 1)))
246.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune843.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

5.6b
(+ (* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x))) (/ -1 (* x x)))
0.7b
(/ -1 (* x x))
0.2b
(* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x)))
0.1b
(/ (/ -1 x) (* x x))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
34×times-frac
24×add-sqr-sqrt *-un-lft-identity
23×add-cbrt-cube add-exp-log
22×add-cube-cbrt
16×associate-/l*
8×cbrt-undiv div-exp
6×pow1 associate-*r/ add-log-exp
5×frac-add
4×associate-*r* prod-exp cbrt-unprod insert-posit16 div-inv
3×flip3-+ associate-*l* flip-+
2×distribute-rgt-in associate-+l+ clear-num associate-/r* frac-2neg distribute-lft-in
1×+-commutative sum-log pow-prod-down *-commutative distribute-lft-out unswap-sqr associate-/l/
Counts
4 → 111
Calls
4 calls:
Slowest
71.0ms
(* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x)))
28.0ms
(+ (* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x))) (/ -1 (* x x)))
10.0ms
(/ -1 (* x x))
9.0ms
(/ (/ -1 x) (* x x))

series182.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
73.0ms
(* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x)))
55.0ms
(/ (/ -1 x) (* x x))
28.0ms
(/ -1 (* x x))
27.0ms
(+ (* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x))) (/ -1 (* x x)))

simplify8.0s

Counts
94 → 123
Calls
94 calls:
Slowest
466.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))
451.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))
443.0ms
(* (+ (* (/ (/ -1 x) (* x x)) (/ (/ -1 x) (* x x))) (- (* (/ -1 x) (/ -1 x)) (* (/ (/ -1 x) (* x x)) (/ -1 x)))) (* x x))
440.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))
420.0ms
(* (- (/ (/ -1 x) (* x x)) (/ -1 x)) (* x x))

prune931.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

5.6b
(+ (+ (/ -3 x) (/ -3 (* x (* x x)))) (/ -1 (* x x)))
0.7b
(/ -1 (* x x))
0.1b
(/ -3 (* x (* x x)))
0.1b
(* x (* x x))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
23×add-cbrt-cube add-exp-log
18×pow1
14×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt add-log-exp
7×prod-exp cbrt-unprod
6×times-frac associate-/l*
5×cbrt-undiv div-exp pow-prod-up
4×frac-add insert-posit16
3×sum-log associate-*l* pow-prod-down distribute-lft-out
2×clear-num associate-/r* frac-2neg flip3-+ flip-+ div-inv
1×pow2 +-commutative associate-+l+ pow-plus cube-unmult associate-*r* pow-sqr *-commutative unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
173.0ms
(+ (+ (/ -3 x) (/ -3 (* x (* x x)))) (/ -1 (* x x)))
24.0ms
(/ -3 (* x (* x x)))
13.0ms
(* x (* x x))
12.0ms
(/ -1 (* x x))

series182.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
61.0ms
(/ -3 (* x (* x x)))
61.0ms
(* x (* x x))
31.0ms
(+ (+ (/ -3 x) (/ -3 (* x (* x x)))) (/ -1 (* x x)))
30.0ms
(/ -1 (* x x))

simplify6.1s

Counts
64 → 102
Calls
64 calls:
Slowest
569.0ms
(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
532.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))
511.0ms
(* (+ (* (/ -3 x) (/ -3 x)) (- (* (/ -3 (* x (* x x))) (/ -3 (* x (* x x)))) (* (/ -3 x) (/ -3 (* x (* x x)))))) (* x x))
458.0ms
(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
436.0ms
(* (* x (* x (* x x))) (* x x))

prune700.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

6.7b
(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))
0.1b
(* (+ x 1) (/ 1 (- x 1)))
0.0b
(/ 1 (- x 1))
0.0b
(/ x (+ x 1))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
69×*-un-lft-identity
56×times-frac
37×add-cube-cbrt
27×associate-*r*
19×add-exp-log
14×difference-of-squares
13×add-cbrt-cube
11×associate-/r*
7×pow1 difference-of-sqr-1 distribute-lft-out--
6×associate-/r/ frac-sub associate-/l* add-log-exp
5×flip3-+ div-exp flip-+ distribute-lft-out
4×frac-times associate-*l* associate-*l/ prod-exp insert-posit16
3×cbrt-undiv flip3-- div-inv flip-- unswap-sqr
2×rec-exp clear-num frac-2neg 1-exp associate-*r/ un-div-inv cbrt-unprod
1×sub-neg diff-log pow-prod-down *-commutative pow-flip inv-pow
Counts
4 → 159
Calls
4 calls:
Slowest
40.0ms
(* (+ x 1) (/ 1 (- x 1)))
34.0ms
(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))
18.0ms
(/ 1 (- x 1))
15.0ms
(/ x (+ x 1))

series183.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))
27.0ms
(* (+ x 1) (/ 1 (- x 1)))
26.0ms
(/ x (+ x 1))
24.0ms
(/ 1 (- x 1))

simplify9.7s

Counts
166 → 171
Calls
166 calls:
Slowest
665.0ms
(* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (/ 1 (- x 1)) (/ 1 (- x 1))) (/ 1 (- x 1))))
565.0ms
(* (+ x 1) (* (+ (* x x) (- (* 1 1) (* x 1))) (- x 1)))
420.0ms
(* (- (* x x) (* 1 1)) (/ 1 (- x 1)))
401.0ms
(* (+ (pow x 3) (pow 1 3)) (/ 1 (- x 1)))
383.0ms
(- (* x (+ (* x x) (- (* 1 1) (* x 1)))) (* (+ x 1) (* (+ (pow x 3) (pow 1 3)) (/ 1 (- x 1)))))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes42.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.4b

bsearch166.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
721.0ms1636×body1280valid
525.0ms4072×body80valid
474.0ms1305×body640valid
472.0ms353×body160valid
159.0ms634×body320valid