Details

sample41.0ms

Algorithm

intervals

Results

14.0ms	53×	body	1280	valid
7.0ms	48×	body	640	valid
5.0ms	118×	body	80	valid
3.0ms	26×	body	320	valid
1.0ms	11×	body	160	valid

simplify237.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	350
14	350
13	346
12	340
11	329
10	222
9	96
8	75
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
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 → 104

Calls

3 calls:

9.0ms	(/ x (+ x 1.0))
30.0ms	(/ (+ x 1.0) (- x 1.0))
145.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series328.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ x (+ x 1.0))
62.0ms	(/ (+ x 1.0) (- x 1.0))
224.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1284
1	408
0	176

prune475.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.2b	(/ (- 3.0) (* x (* x x)))
0.7b	(/ 1.0 (* x x))
5.6b	(- (/ (- 3.0) (* x (* x x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
18×	`pow1` `*-un-lft-identity`
16×	`add-sqr-sqrt`
13×	`times-frac` `add-cube-cbrt` `associate-/l*`
9×	`add-log-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`cbrt-undiv` `div-exp` `pow-prod-up`
3×	`associate-l` `pow-prod-down` `frac-sub`
2×	`neg-sub0` `clear-num` `associate-/r*` `neg-mul-1` `frac-2neg` `diff-log` `div-sub` `frac-add` `div-inv` `distribute-lft-out--`
1×	`associate--l-` `pow2` `sum-log` `sub-neg` `flip3-+` `pow-plus` `flip3--` `cube-unmult` `associate-r` `distribute-frac-neg` `pow-sqr` `*-commutative` `flip-+` `flip--` `distribute-lft-out` `associate--r+` `sub-div` `difference-of-squares` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

15.0ms	(* x (* x x))
31.0ms	(/ (- 3.0) (* x (* x x)))
6.0ms	(/ 1.0 (* x x))
131.0ms	(- (/ (- 3.0) (* x (* x x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* x (* x x))
67.0ms	(/ (- 3.0) (* x (* x x)))
55.0ms	(/ 1.0 (* x x))
49.0ms	(- (/ (- 3.0) (* x (* x x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

simplify1.5s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	2059
1	511
0	192

prune399.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(* x (/ 1 (+ x 1.0)))
7.6b	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
46×	`times-frac`
33×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube` `distribute-lft-out`
9×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3--` `1-exp` `associate-*r/` `un-div-inv` `frac-sub` `cbrt-unprod` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

10.0ms	(/ 1 (+ x 1.0))
21.0ms	(/ (+ x 1.0) (- x 1.0))
38.0ms	(* x (/ 1 (+ x 1.0)))
36.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1 (+ x 1.0))
49.0ms	(/ (+ x 1.0) (- x 1.0))
58.0ms	(* x (/ 1 (+ x 1.0)))
478.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify1.4s

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
2	1643
1	520
0	210

prune572.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(* x (+ (* 1.0 x) 3.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `add-log-exp` `unswap-sqr`

Counts

1 → 22

Calls

1 calls:

22.0ms

(* x (+ (* 1.0 x) 3.0))

series96.0ms

Counts

1 → 3

Calls

1 calls:

96.0ms

(* x (+ (* 1.0 x) 3.0))

simplify2.4s

Counts

25 → 25

Iterations

Iter	Nodes
done	5014
3	2947
2	569
1	158
0	50

prune82.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch133.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	13113.526740685162
10	-17239113253358.373	-4.96108325192681e-05	-11444.735242389535

simplify9.0ms

Iterations

Iter	Nodes
done	35
1	35
0	24

end0.0ms

sample1.1s

Algorithm

intervals

Results

341.0ms	1740×	body	1280	valid
258.0ms	4089×	body	80	valid
193.0ms	1239×	body	640	valid
104.0ms	624×	body	320	valid
21.0ms	308×	body	160	valid