Details

Time bar (total: 1.2m)

sample104.0ms

Algorithm
intervals
Results
57.0ms48×body640valid
23.0ms60×body1280valid
9.0ms114×body80valid
4.0ms22×body320valid
2.0ms12×body160valid

simplify47.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
47.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize40.0ms

Local error

Found 3 expressions with local error:

2.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite110.0ms

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
76.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
18.0ms
(/ (+ x 1) (- x 1))
13.0ms
(/ x (+ x 1))

series172.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
96.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
39.0ms
(/ (+ x 1) (- x 1))
38.0ms
(/ x (+ x 1))

simplify4.4s

Counts
142 → 126
Calls
142 calls:
Slowest
367.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
277.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
228.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
218.0ms
(/ (* (* x x) x) (* (* (+ x 1) (+ x 1)) (+ x 1)))
194.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

5.8b
(+ (* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x))) (/ -1 (* x x)))
0.2b
(* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x)))
0.2b
(/ -1 (* x x))
0.1b
(/ (/ -1 x) (* x x))

rewrite111.0ms

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
61.0ms
(* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x)))
30.0ms
(+ (* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x))) (/ -1 (* x x)))
11.0ms
(/ (/ -1 x) (* x x))
7.0ms
(/ -1 (* x x))

series247.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x)))
48.0ms
(/ (/ -1 x) (* x x))
46.0ms
(/ -1 (* x x))
43.0ms
(+ (* 3 (+ (/ (/ -1 x) (* x x)) (/ -1 x))) (/ -1 (* x x)))

simplify8.0s

Counts
94 → 123
Calls
94 calls:
Slowest
467.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))
464.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))
461.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))
438.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))
425.0ms
(* (- (/ (/ -1 x) (* x x)) (/ -1 x)) (* x x))

prune914.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

5.8b
(+ (+ (/ -3 x) (/ -3 (* x (* x x)))) (/ -1 (* x x)))
0.7b
(/ -3 (* x (* x x)))
0.2b
(/ -1 (* x x))
0.1b
(* x (* x x))

rewrite165.0ms

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
115.0ms
(+ (+ (/ -3 x) (/ -3 (* x (* x x)))) (/ -1 (* x x)))
19.0ms
(/ -3 (* x (* x x)))
18.0ms
(* x (* x x))
12.0ms
(/ -1 (* x x))

series208.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
75.0ms
(/ -3 (* x (* x x)))
70.0ms
(* x (* x x))
31.0ms
(/ -1 (* x x))
31.0ms
(+ (+ (/ -3 x) (/ -3 (* x (* x x)))) (/ -1 (* x x)))

simplify6.5s

Counts
64 → 102
Calls
64 calls:
Slowest
899.0ms
(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
583.0ms
(* (+ (* (/ -3 x) (/ -3 x)) (- (* (/ -3 (* x (* x x))) (/ -3 (* x (* x x)))) (* (/ -3 x) (/ -3 (* x (* x x)))))) (* x x))
494.0ms
(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
492.0ms
(* (* x (* x (* x x))) (* x x))
445.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))

prune669.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (/ x (+ x 1)) (cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))))
0.0b
(cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1))))
0.0b
(* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))
0.0b
(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))

rewrite342.0ms

Algorithm
rewrite-expression-head
Rules
350×*-un-lft-identity
222×times-frac
216×add-sqr-sqrt
76×add-cube-cbrt
72×swap-sqr
68×associate-*r*
65×distribute-lft-out
62×difference-of-squares
57×add-cbrt-cube add-exp-log
37×distribute-lft-out--
36×difference-of-sqr-1
35×associate-*l*
30×pow1
22×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
16×frac-times associate-*l/
14×cbrt-div
10×associate-*r/ associate-/r/
7×pow-plus pow-prod-up frac-sub
6×flip3-- flip-- add-log-exp unswap-sqr
5×div-inv
4×pow-prod-down insert-posit16
3×pow2 pow-sqr
2×pow3 *-commutative
1×cbrt-prod sub-neg pow1/3 diff-log rem-cbrt-cube
Counts
4 → 294
Calls
4 calls:
Slowest
121.0ms
(cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1))))
95.0ms
(* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))
63.0ms
(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
48.0ms
(- (/ x (+ x 1)) (cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(- (/ x (+ x 1)) (cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))))
71.0ms
(cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1))))
52.0ms
(* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))
50.0ms
(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))

simplify44.7s

Counts
362 → 306
Calls
362 calls:
Slowest
604.0ms
(* (* (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1))) (/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))) (/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1))))
579.0ms
(* (/ (+ x 1) (- (pow x 3) (pow 1 3))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))
563.0ms
(- (* x (cbrt (- x 1))) (* (+ x 1) (cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (/ (+ x 1) (- x 1))))))
542.0ms
(* (* (/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1))) (/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))) (/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1))))
540.0ms
(- (* x (cbrt (* (- x 1) (- x 1)))) (* (+ x 1) (cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (+ x 1)))))

prune2.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

100% (0.0b remaining)

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

bsearch124.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
790.0ms4074×body80valid
730.0ms1747×body1280valid
518.0ms1240×body640valid
195.0ms615×body320valid
49.0ms324×body160valid