Details

sample96.0ms

Algorithm

intervals

Results

31.0ms	62×	body	640	valid
19.0ms	13×	body	1280	valid
18.0ms	137×	body	80	valid
12.0ms	29×	body	320	valid
4.0ms	16×	body	160	valid

simplify288.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	475
9	475
8	357
7	164
6	102
5	81
4	65
3	45
2	35
1	21
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
1.2b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite298.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
56×	`times-frac`
25×	`add-cube-cbrt`
18×	`distribute-lft-out--`
17×	`distribute-lft-out`
14×	`difference-of-squares`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube` `div-inv`
6×	`pow1` `associate-/l*`
4×	`difference-of-sqr-1` `div-exp` `associate-/r/` `insert-posit16`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `1-exp` `frac-sub` `flip-+` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 141

Calls

4 calls:

16.0ms	(/ 1 (- x 1))
8.0ms	(/ 1 (+ x 1))
48.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
222.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (- x 1))
19.0ms	(/ 1 (+ x 1))
26.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
156.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.3s

Counts

153 → 153

Iterations

Iter	Nodes
done	2002
2	1619
1	510
0	219

prune514.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1) x)
0.0b	(- (* 1 x) (* (+ x 1) 2))
1.5b	(+ (/ (- (* 1 x) (* (+ x 1) 2)) (* (+ x 1) x)) (/ 1 (- x 1)))
15.0b	(/ (- (* 1 x) (* (+ x 1) 2)) (* (+ x 1) x))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
4×	`associate-l` `associate-*l/` `insert-posit16`
3×	`flip3-+` `times-frac` `associate-r` `flip-+` `distribute-lft-out` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-sub` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `div-inv` `flip--` `associate-/l/`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `frac-add` `-commutative` `associate-+l-` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

15.0ms	(* (+ x 1) x)
7.0ms	(- (* 1 x) (* (+ x 1) 2))
62.0ms	(+ (/ (- (* 1 x) (* (+ x 1) 2)) (* (+ x 1) x)) (/ 1 (- x 1)))
25.0ms	(/ (- (* 1 x) (* (+ x 1) 2)) (* (+ x 1) x))

series288.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (+ x 1) x)
31.0ms	(- (* 1 x) (* (+ x 1) 2))
154.0ms	(+ (/ (- (* 1 x) (* (+ x 1) 2)) (* (+ x 1) x)) (/ 1 (- x 1)))
40.0ms	(/ (- (* 1 x) (* (+ x 1) 2)) (* (+ x 1) x))

simplify653.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	2000
1	469
0	152

prune362.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (/ 2 x) (* 2 (+ x (* (* x x) x))))
0.1b	(* (* x x) x)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
4×	`add-sqr-sqrt` `add-log-exp`
3×	`-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`pow2` `associate-+r+` `flip3-+` `frac-add` `associate-*r/` `pow-sqr` `flip-+` `insert-posit16`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `associate-l` `pow3` `*-commutative` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

2 → 46

Calls

2 calls:

11.0ms	(+ (/ 2 x) (* 2 (+ x (* (* x x) x))))
17.0ms	(* (* x x) x)

series104.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(+ (/ 2 x) (* 2 (+ x (* (* x x) x))))
44.0ms	(* (* x x) x)

simplify873.0ms

Counts

52 → 52

Iterations

Iter	Nodes
done	2001
2	1423
1	282
0	87

prune120.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(/ 2 (pow x 5))
0.1b	(/ 2 (* (* x x) x))
0.2b	(/ 2 (pow x 7))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
40×	`add-sqr-sqrt`
39×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-exp-log`
24×	`unpow-prod-down`
23×	`pow1`
22×	`add-cbrt-cube`
15×	`associate-/r*`
9×	`div-exp` `associate-/l*`
8×	`sqr-pow`
6×	`pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `pow-prod-down` `div-inv`
2×	`pow2` `pow-to-exp` `pow-exp` `pow-sqr`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

23.0ms	(* (* x x) x)
5.0ms	(/ 2 (pow x 5))
13.0ms	(/ 2 (* (* x x) x))
5.0ms	(/ 2 (pow x 7))

series267.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* x x) x)
63.0ms	(/ 2 (pow x 5))
81.0ms	(/ 2 (* (* x x) x))
84.0ms	(/ 2 (pow x 7))

simplify737.0ms

Counts

157 → 157

Iterations

Iter	Nodes
done	2033
2	1560
1	420
0	207

prune628.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 26.4b

bsearch220.0ms

Steps

Iters	Range		Point
11	0.0038666078177206752	9.350013159855062e+31	110.41034748839138
10	-121993772661.31783	-0.22068356154967622	-128.46375794518042

simplify8.0ms

Iterations

Iter	Nodes
done	47
1	47
0	34

end0.0ms

sample2.7s

Algorithm

intervals

Results

918.0ms	1924×	body	640	valid
894.0ms	4140×	body	80	valid
326.0ms	563×	body	1280	valid
321.0ms	897×	body	320	valid
90.0ms	479×	body	160	valid