Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	57×	body	640	valid
4.0ms	134×	body	80	valid
2.0ms	31×	body	320	valid
2.0ms	17×	body	1280	valid
1.0ms	17×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7
done	209	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.0b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite343.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

10.0ms	(/ 1.0 (- x 1.0))
12.0ms	(/ 1.0 (+ x 1.0))
56.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
261.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
24.0ms	(/ 1.0 (+ x 1.0))
43.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
204.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify49.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5002	816
done	5002	816

prune245.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 2.0 x) (/ 1.0 (- x 1.0)))
0.0b	(/ 1.0 (+ x 1.0))
2.0b	(- (/ 1.0 (+ x 1.0)) (- (/ 2.0 x) (/ 1.0 (- x 1.0))))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
48×	`add-sqr-sqrt` `times-frac`
23×	`add-cube-cbrt`
21×	`distribute-lft-out--`
11×	`add-log-exp`
10×	`difference-of-squares`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-lft-out` `associate-/l*`
5×	`frac-sub`
4×	`pow1` `flip3--` `diff-log` `associate-/r/` `flip--`
3×	`sub-neg`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `associate--r+`
1×	`flip3-+` `flip-+` `associate--r-`

Counts

4 → 117

Calls

4 calls:

10.0ms	(/ 1.0 (- x 1.0))
36.0ms	(- (/ 2.0 x) (/ 1.0 (- x 1.0)))
10.0ms	(/ 1.0 (+ x 1.0))
140.0ms	(- (/ 1.0 (+ x 1.0)) (- (/ 2.0 x) (/ 1.0 (- x 1.0))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (- x 1.0))
42.0ms	(- (/ 2.0 x) (/ 1.0 (- x 1.0)))
24.0ms	(/ 1.0 (+ x 1.0))
209.0ms	(- (/ 1.0 (+ x 1.0)) (- (/ 2.0 x) (/ 1.0 (- x 1.0))))

simplify48.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	514	909
1	1792	871
2	5002	862
done	5002	862

prune226.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
19.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

88×	`associate-*l/`
32×	`frac-add`
31×	`flip3--` `flip--`
24×	`frac-times` `flip3-+` `flip-+`
18×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
12×	`associate-*r/`
9×	`pow1` `add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-/r/` `add-log-exp`
7×	`add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod`
5×	`sub-neg` `associate-r`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
3×	`cbrt-undiv` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
1×	`+-commutative` `frac-2neg` `diff-log` `associate-l` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 124

Calls

4 calls:

8.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
90.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
43.0ms	(* (* (+ x 1.0) x) (- x 1.0))
27.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series223.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
87.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
95.0ms	(* (* (+ x 1.0) x) (- x 1.0))
2.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify49.0ms

Counts

136 → 136

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	997	2264
1	5001	2129
done	5001	2129

prune424.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3))))
0.2b	(/ 1 (pow x 5))
0.2b	(/ 1 (pow x 7))
0.2b	(/ 1 (pow x 3))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

88×	`*-un-lft-identity`
87×	`times-frac`
64×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
31×	`add-exp-log`
26×	`associate-/r*`
24×	`distribute-lft-out`
18×	`div-exp`
16×	`div-inv`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*` `add-log-exp`
4×	`pow1` `cube-mult` `unpow3` `frac-add`
3×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `sum-log` `inv-pow`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `associate-+r+`

Counts

4 → 208

Calls

4 calls:

208.0ms	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3))))
11.0ms	(/ 1 (pow x 5))
8.0ms	(/ 1 (pow x 7))
9.0ms	(/ 1 (pow x 3))

series184.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3))))
42.0ms	(/ 1 (pow x 5))
59.0ms	(/ 1 (pow x 7))
32.0ms	(/ 1 (pow x 3))

simplify72.0ms

Counts

220 → 220

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	586	1177
1	3298	983
2	5001	983
done	5001	983

prune308.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes24.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 9.4b

bsearch95.0ms

Steps

Iters	Range		Point
9	7.055123656280252	892369.0132880388	109.89750468235896
10	-1.8070707071506563e+17	-0.15939393977811658	-111.02026224228146

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	38	16
done	38	16

end0.0ms

sample613.0ms

Algorithm

intervals

Results

188.0ms	1861×	body	640	valid
113.0ms	4112×	body	80	valid
84.0ms	598×	body	1280	valid
76.0ms	938×	body	320	valid
27.0ms	491×	body	160	valid