Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	49×	body	1280	valid
5.0ms	48×	body	640	valid
4.0ms	124×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	14×	body	160	valid

simplify7.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite150.0ms

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-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

13.0ms	(/ x (+ x 1.0))
27.0ms	(/ (+ x 1.0) (- x 1.0))
106.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ x (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
135.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify40.0ms

Counts: 113 → 113

prune215.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.4b	(/ 3.0 (pow x 3))
0.7b	(/ (- 1.0) (pow x 2))
5.0b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite888.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
120×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
78×	`add-cube-cbrt`
48×	`unpow-prod-down`
29×	`distribute-rgt-neg-in`
27×	`distribute-lft-neg-in`
20×	`associate-/r*`
18×	`sqr-pow`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`cube-prod` `associate-/l*` `unpow2`
11×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`neg-mul-1`
8×	`add-cbrt-cube`
6×	`div-exp`
5×	`frac-sub`
4×	`pow1` `cube-mult` `diff-log` `unpow3`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `associate--l-` `neg-sub0` `pow-to-exp` `frac-2neg` `div-sub` `pow-exp` `associate--l+` `clear-num` `div-inv`
1×	`distribute-frac-neg`

Counts

4 → 234

Calls

4 calls:

106.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
9.0ms	(/ 3.0 (pow x 3))
12.0ms	(/ (- 1.0) (pow x 2))
751.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
41.0ms	(/ 3.0 (pow x 3))
27.0ms	(/ (- 1.0) (pow x 2))
39.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify96.0ms

Counts: 246 → 246

prune448.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 2.0 (+ (pow x 2) x)) 1.0)
0.0b	(/ x (+ x 1.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `associate-+l+` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 46

Calls

2 calls:

19.0ms	(+ (* 2.0 (+ (pow x 2) x)) 1.0)
12.0ms	(/ x (+ x 1.0))

series63.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(+ (* 2.0 (+ (pow x 2) x)) 1.0)
40.0ms	(/ x (+ x 1.0))

simplify142.0ms

Counts: 52 → 52

prune121.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt x) (sqrt 1.0))
0.0b	(- (sqrt x) (sqrt 1.0))
0.2b	(/ (+ x 1.0) (+ (sqrt x) (sqrt 1.0)))
8.6b	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0))))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
37×	`times-frac`
20×	`distribute-lft-out`
18×	`sqrt-prod`
15×	`add-cube-cbrt`
10×	`add-log-exp` `difference-of-squares`
9×	`distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `associate-/l*`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `flip3--` `diff-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `frac-sub` `div-inv`

Counts

4 → 100

Calls

4 calls:

10.0ms	(+ (sqrt x) (sqrt 1.0))
12.0ms	(- (sqrt x) (sqrt 1.0))
33.0ms	(/ (+ x 1.0) (+ (sqrt x) (sqrt 1.0)))
281.0ms	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0))))

series1.9s

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (sqrt x) (sqrt 1.0))
48.0ms	(- (sqrt x) (sqrt 1.0))
182.0ms	(/ (+ x 1.0) (+ (sqrt x) (sqrt 1.0)))
1.6s	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0))))

simplify65.0ms

Counts: 112 → 112

prune272.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes31.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 31.6b

bsearch102.0ms

Steps

Iters	Range		Point
9	0.21963308938311268	137362616.0762091	1.0149191639264252
11	-2445851338.3862987	-4.2674702477225e-16	-1.327620599565708

simplify2.0ms

end0.0ms

sample885.0ms

Algorithm

intervals

Results

297.0ms	1705×	body	1280	valid
225.0ms	1262×	body	640	valid
153.0ms	4080×	body	80	valid
50.0ms	633×	body	320	valid
20.0ms	320×	body	160	valid