Details

Time bar (total: 5.9m)

sample81.0ms

Algorithm
intervals
Results
31.0ms60×body1280valid
19.0ms48×body640valid
12.0ms114×body80valid
7.0ms22×body320valid
2.0ms12×body160valid

simplify84.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
84.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize24.0ms

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))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
1284×*-un-lft-identity
984×times-frac
841×add-sqr-sqrt
612×prod-diff
521×add-cube-cbrt
251×distribute-lft-out
158×difference-of-squares
110×associate-/r/
90×distribute-lft-out--
77×difference-of-sqr-1
55×div-inv
37×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×add-log-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 753
Calls
3 calls:
Slowest
102.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
17.0ms
(/ (+ x 1) (- x 1))
8.0ms
(/ x (+ x 1))

series154.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
90.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
36.0ms
(/ x (+ x 1))
28.0ms
(/ (+ x 1) (- x 1))

simplify5.5m

Counts
1382 → 762
Calls
1382 calls:
Slowest
843.0ms
(fma (sqrt (/ x (+ x 1))) (sqrt (/ x (+ x 1))) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
796.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
795.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
789.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
770.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (sqrt (/ (+ x 1) (- x 1))) (sqrt (/ (+ x 1) (- x 1))))))

prune6.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

6.0b
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))
0.2b
(/ -1 (* x x))
0.1b
(/ (/ -1 x) (* x x))
0.0b
(+ (/ -1 x) (/ (/ -1 x) (* x x)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
43×times-frac
29×*-un-lft-identity
27×add-sqr-sqrt add-cube-cbrt
21×add-cbrt-cube add-exp-log
16×associate-/l*
13×fma-def
8×cbrt-undiv div-exp
6×add-log-exp
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×prod-exp cbrt-unprod
2×clear-num associate-/r* frac-2neg
1×+-commutative sum-log flip3-+ frac-add flip-+ fma-udef distribute-lft-out associate-/l/
Counts
4 → 113
Calls
4 calls:
Slowest
27.0ms
(+ (/ -1 x) (/ (/ -1 x) (* x x)))
10.0ms
(/ (/ -1 x) (* x x))
7.0ms
(/ -1 (* x x))
0.0ms
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))

series191.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
67.0ms
(+ (/ -1 x) (/ (/ -1 x) (* x x)))
60.0ms
(/ (/ -1 x) (* x x))
35.0ms
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))
29.0ms
(/ -1 (* x x))

simplify3.9s

Counts
84 → 125
Calls
84 calls:
Slowest
413.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))
316.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) (* x x)) (* x x)))
234.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
226.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
206.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune810.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

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×expm1-log1p-u associate-*r* prod-exp cbrt-unprod insert-posit16 log1p-expm1-u 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 fma-def pow-prod-down *-commutative distribute-lft-out unswap-sqr associate-/l/
Counts
4 → 120
Calls
4 calls:
Slowest
69.0ms
(* 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))))
28.0ms
(+ (* 3 (+ (/ -1 x) (/ (/ -1 x) (* x x)))) (/ -1 (* x x)))
11.0ms
(/ (/ -1 x) (* x x))
6.0ms
(/ -1 (* x x))

series197.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(* 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))))
42.0ms
(/ (/ -1 x) (* x x))
40.0ms
(+ (* 3 (+ (/ -1 x) (/ (/ -1 x) (* x x)))) (/ -1 (* x x)))
26.0ms
(/ -1 (* x x))

simplify8.4s

Counts
94 → 132
Calls
94 calls:
Slowest
1.1s
(* (- (/ -1 x) (/ (/ -1 x) (* x x))) (* x x))
494.0ms
(/ (/ (* (* -1 -1) -1) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
418.0ms
(* (+ (* (/ -1 x) (/ -1 x)) (- (* (/ (/ -1 x) (* x x)) (/ (/ -1 x) (* x x))) (* (/ -1 x) (/ (/ -1 x) (* x x))))) (* x x))
379.0ms
(+ (* (* 3 (+ (* -1 (* x x)) (* x (/ -1 x)))) (* x x)) (* (* x (* x x)) -1))
377.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))

prune755.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite350.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
23×pow1 add-cbrt-cube add-exp-log
14×times-frac
13×add-sqr-sqrt
12×add-cube-cbrt
10×fma-def
9×add-log-exp
7×prod-exp cbrt-unprod
6×pow-plus pow-prod-up associate-/l*
5×cbrt-undiv div-exp distribute-lft-out
4×expm1-log1p-u distribute-rgt-out frac-add insert-posit16 log1p-expm1-u div-inv
3×sum-log associate-*r* pow-prod-down
2×pow2 clear-num associate-/r* frac-2neg flip3-+ pow-sqr flip-+
1×+-commutative associate-+l+ distribute-lft1-in associate-*l* pow3 *-commutative unswap-sqr
Counts
4 → 112
Calls
4 calls:
Slowest
309.0ms
(+ (+ (/ -3 (* (* x x) x)) (/ -3 x)) (/ -1 (* x x)))
18.0ms
(* (* x x) x)
14.0ms
(/ -3 (* (* x x) x))
7.0ms
(/ -1 (* x x))

series145.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
45.0ms
(/ -3 (* (* x x) x))
38.0ms
(* (* x x) x)
33.0ms
(/ -1 (* x x))
29.0ms
(+ (+ (/ -3 (* (* x x) x)) (/ -3 x)) (/ -1 (* x x)))

simplify5.5s

Counts
70 → 124
Calls
70 calls:
Slowest
560.0ms
(+ (* (- (* (/ -3 (* (* x x) x)) (/ -3 (* (* x x) x))) (* (/ -3 x) (/ -3 x))) (* x x)) (* (- (/ -3 (* (* x x) x)) (/ -3 x)) -1))
524.0ms
(* (- (/ -3 (* (* x x) x)) (/ -3 x)) (* x x))
395.0ms
(* (+ (* (/ -3 (* (* x x) x)) (/ -3 (* (* x x) x))) (- (* (/ -3 x) (/ -3 x)) (* (/ -3 (* (* x x) x)) (/ -3 x)))) (* x x))
378.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))
375.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))

prune758.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

100% (0.0b remaining)

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

bsearch142.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
623.0ms1240×body640valid
580.0ms1747×body1280valid
329.0ms4074×body80valid
132.0ms615×body320valid
36.0ms324×body160valid