Details

Time bar (total: 1.3m)

sample69.0ms

Algorithm
intervals
Results
13.0ms47×body1280valid
10.0ms48×body640valid
8.0ms133×body80valid
3.0ms16×body320valid
1.0ms12×body160valid

simplify67.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
67.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize26.0ms

Local error

Found 3 expressions with local error:

3.0b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite137.0ms

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
88.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
33.0ms
(/ (+ x 1) (- x 1))
14.0ms
(/ x (+ x 1))

series158.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
83.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
44.0ms
(/ (+ x 1) (- x 1))
31.0ms
(/ x (+ x 1))

simplify4.7s

Counts
142 → 126
Calls
142 calls:
Slowest
408.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
312.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
265.0ms
(/ (* (* x x) x) (* (* (+ x 1) (+ x 1)) (+ x 1)))
234.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
220.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

15.3b
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
0.0b
(* (+ x 1) (+ x 1))
0.0b
(* (+ x 1) (- x 1))
0.0b
(/ (- (* x (- x 1)) (* (+ x 1) (+ x 1))) (* (+ x 1) (- x 1)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
46×associate-*r/
36×flip3-+ flip-+
32×frac-sub
31×*-un-lft-identity
28×frac-times
24×flip3-- flip--
20×add-sqr-sqrt
18×associate-/l/
14×associate-*l/
13×pow1 add-cbrt-cube add-exp-log
12×add-cube-cbrt
11×associate-*r*
8×associate-*l* associate-/r/
7×distribute-lft-out
6×distribute-rgt-in distribute-lft-in swap-sqr add-log-exp
5×sub-neg
4×associate--l+ insert-posit16
3×times-frac prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv div-exp pow-prod-down *-commutative associate--r+ difference-of-squares unswap-sqr
1×pow2 clear-num associate-/r* frac-2neg pow-plus diff-log difference-of-sqr-1 div-sub pow-sqr pow-prod-up div-inv distribute-lft-out--
Counts
4 → 161
Calls
4 calls:
Slowest
49.0ms
(/ (- (* x (- x 1)) (* (+ x 1) (+ x 1))) (* (+ x 1) (- x 1)))
24.0ms
(* (+ x 1) (- x 1))
21.0ms
(* (+ x 1) (+ x 1))
14.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(* (+ x 1) (- x 1))
72.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
64.0ms
(/ (- (* x (- x 1)) (* (+ x 1) (+ x 1))) (* (+ x 1) (- x 1)))
20.0ms
(* (+ x 1) (+ x 1))

simplify28.8s

Counts
163 → 173
Calls
163 calls:
Slowest
1.1s
(* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
822.0ms
(- (* (* x (- (* x x) (* 1 1))) (* (- x 1) (- x 1))) (* (+ x 1) (* (- (* x x) (* 1 1)) (- (* x x) (* 1 1)))))
587.0ms
(/ (* x (- x 1)) (* (+ x 1) (- x 1)))
557.0ms
(* (+ (pow x 3) (pow 1 3)) (- (pow x 3) (pow 1 3)))
514.0ms
(* (+ (* x x) (+ (* 1 1) (* x 1))) (* (- x 1) (+ (* x x) (- (* 1 1) (* x 1)))))

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 3 expressions with local error:

11.8b
(/ (+ (* -3 x) -1) (* (+ x 1) (- x 1)))
0.0b
(* (+ x 1) (- x 1))
0.0b
(+ (* -3 x) -1)

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×*-un-lft-identity
10×add-cbrt-cube add-exp-log
8×frac-times flip3-+ associate-/r/ flip-+
7×associate-*r* add-cube-cbrt
6×flip3-- flip--
5×pow1 add-log-exp
4×associate-*l* associate-*l/ associate-*r/
3×times-frac insert-posit16 associate-/l*
2×distribute-rgt-in cbrt-undiv sub-neg distribute-lft-in div-exp prod-exp cbrt-unprod difference-of-squares associate-/l/
1×+-commutative clear-num associate-/r* sum-log frac-2neg difference-of-sqr-1 pow-prod-down *-commutative div-inv distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
3 → 80
Calls
3 calls:
Slowest
53.0ms
(/ (+ (* -3 x) -1) (* (+ x 1) (- x 1)))
44.0ms
(* (+ x 1) (- x 1))
12.0ms
(+ (* -3 x) -1)

series209.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
89.0ms
(* (+ x 1) (- x 1))
64.0ms
(+ (* -3 x) -1)
55.0ms
(/ (+ (* -3 x) -1) (* (+ x 1) (- x 1)))

simplify8.8s

Counts
63 → 89
Calls
63 calls:
Slowest
979.0ms
(* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
658.0ms
(* (+ (pow x 3) (pow 1 3)) (- (pow x 3) (pow 1 3)))
543.0ms
(* (- x 1) (+ (* x x) (+ (* 1 1) (* x 1))))
527.0ms
(* (+ (pow x 3) (pow 1 3)) (- (* x x) (* 1 1)))
515.0ms
(* (- x 1) (+ (* x x) (+ (* 1 1) (* x 1))))

prune630.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (+ (* -3 x) -1) (+ x 1))
0.0b
(/ (/ (+ (* -3 x) -1) (+ x 1)) (- x 1))
0.0b
(+ (* -3 x) -1)

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
234×times-frac
208×*-un-lft-identity
171×add-sqr-sqrt
95×add-cube-cbrt
38×difference-of-squares
28×distribute-lft-out
21×associate-/l*
20×associate-/r/
19×difference-of-sqr-1 distribute-lft-out--
11×associate-/r* flip3-+ flip-+
10×add-cbrt-cube add-exp-log div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 insert-posit16 associate-/l/
2×clear-num frac-2neg
1×+-commutative sum-log flip3-- flip--
Counts
3 → 217
Calls
3 calls:
Slowest
61.0ms
(/ (/ (+ (* -3 x) -1) (+ x 1)) (- x 1))
32.0ms
(/ (+ (* -3 x) -1) (+ x 1))
12.0ms
(+ (* -3 x) -1)

series151.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
59.0ms
(/ (/ (+ (* -3 x) -1) (+ x 1)) (- x 1))
51.0ms
(/ (+ (* -3 x) -1) (+ x 1))
41.0ms
(+ (* -3 x) -1)

simplify28.2s

Counts
329 → 226
Calls
329 calls:
Slowest
479.0ms
(/ (/ 1 (+ x 1)) (- x 1))
395.0ms
(/ (/ (+ (* -3 x) -1) (- (* x x) (* 1 1))) (+ (sqrt x) 1))
377.0ms
(/ (/ (+ (* -3 x) -1) (+ (pow x 3) (pow 1 3))) (sqrt (- x 1)))
375.0ms
(/ (/ (+ (* -3 x) -1) (- (* x x) (* 1 1))) (* (cbrt (- x 1)) (cbrt (- x 1))))
358.0ms
(/ (/ (+ (* -3 x) -1) (- (* x x) (* 1 1))) (+ (sqrt x) 1))

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

regimes33.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch147.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
890.0ms1724×body1280valid
435.0ms4066×body80valid
431.0ms1257×body640valid
212.0ms610×body320valid
58.0ms343×body160valid