Details

sample78.0ms

Algorithm

intervals

Results

27.0ms	60×	body	640	valid
12.0ms	119×	body	80	valid
11.0ms	34×	body	1280	valid
5.0ms	28×	body	320	valid
2.0ms	15×	body	160	valid

simplify461.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	199
9	199
8	170
7	102
6	84
5	73
4	60
3	41
2	31
1	18
0	10

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize122.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
3.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

706×	`*-un-lft-identity`
688×	`times-frac`
505×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
64×	`div-inv`
56×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
13×	`distribute-lft-out--`
10×	`fma-def` `add-log-exp`
8×	`difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `frac-add` `log1p-expm1-u` `associate-/l*`
2×	`sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `flip--`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `clear-num`

Counts

3 → 579

Calls

3 calls:

27.0ms	(/ 1.0 (+ x 1.0))
177.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.2s	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series567.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ 1.0 (+ x 1.0))
83.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
434.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify9.0s

Counts

588 → 588

Iterations

Iter	Nodes
done	5000
2	2824
1	1091
0	453

prune6.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
3.2b	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

709×	`*-un-lft-identity`
695×	`times-frac`
507×	`add-sqr-sqrt`
489×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+r+`
94×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
21×	`fma-def`
18×	`fma-neg`
13×	`distribute-lft-out--`
10×	`add-log-exp`
7×	`difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `flip3--` `frac-add` `flip--` `log1p-expm1-u` `associate-/l*`
2×	`sub-neg` `diff-log` `sum-log` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `div-exp` `clear-num`

Counts

3 → 590

Calls

3 calls:

20.0ms	(/ 1.0 (+ x 1.0))
309.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
553.0ms	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

series767.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ 1.0 (+ x 1.0))
65.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
655.0ms	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

simplify5.2s

Counts

599 → 599

Iterations

Iter	Nodes
done	5000
2	3580
1	1455
0	634

prune4.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
2.2b	(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))
2.7b	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

898×	`*-un-lft-identity`
562×	`times-frac`
326×	`distribute-lft-out`
292×	`add-sqr-sqrt`
281×	`add-cube-cbrt`
234×	`prod-diff`
101×	`distribute-lft-out--`
50×	`div-inv`
34×	`associate-/r/`
21×	`fma-def`
18×	`fma-neg` `flip-+`
17×	`flip--`
10×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `flip3-+` `frac-sub` `log1p-expm1-u` `associate-/l*`
2×	`flip3--` `diff-log` `frac-add` `sum-log`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `div-exp` `associate--l+` `clear-num`

Counts

3 → 364

Calls

3 calls:

26.0ms	(/ 1.0 (+ x 1.0))
1.8s	(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))
276.0ms	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))

series1.4s

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ 1.0 (+ x 1.0))
797.0ms	(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))
526.0ms	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))

simplify9.6s

Counts

373 → 373

Iterations

Iter	Nodes
done	5001
2	2680
1	891
0	351

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (+ (* 1.0 (+ x 1.0)) (* (- x 1.0) 1.0)) x) (* (* (- x 1.0) (+ x 1.0)) 2.0)) (* (* (- x 1.0) (+ x 1.0)) x))
0.1b	(* (* (- x 1.0) (+ x 1.0)) x)
2.7b	(+ (* 1.0 (+ x 1.0)) (* (- x 1.0) 1.0))
15.3b	(- (* (+ (* 1.0 (+ x 1.0)) (* (- x 1.0) 1.0)) x) (* (* (- x 1.0) (+ x 1.0)) 2.0))

rewrite880.0ms

Algorithm

rewrite-expression-head

Rules

304×	`associate-*l/`
96×	`associate-*r/` `frac-sub`
93×	`flip3-+` `flip-+`
78×	`flip3--` `flip--`
68×	`frac-add`
56×	`frac-times`
50×	`associate-/l/`
18×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`associate-/r/` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`associate-+l+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `fma-def` `frac-2neg` `distribute-lft-in` `fma-neg` `diff-log` `div-sub` `associate-l` `prod-diff` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv`

Counts

4 → 196

Calls

4 calls:

276.0ms	(/ (- (* (+ (* 1.0 (+ x 1.0)) (* (- x 1.0) 1.0)) x) (* (* (- x 1.0) (+ x 1.0)) 2.0)) (* (* (- x 1.0) (+ x 1.0)) x))
204.0ms	(* (* (- x 1.0) (+ x 1.0)) x)
33.0ms	(+ (* 1.0 (+ x 1.0)) (* (- x 1.0) 1.0))
319.0ms	(- (* (+ (* 1.0 (+ x 1.0)) (* (- x 1.0) 1.0)) x) (* (* (- x 1.0) (+ x 1.0)) 2.0))

series446.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (- (* (+ (* 1.0 (+ x 1.0)) (* (- x 1.0) 1.0)) x) (* (* (- x 1.0) (+ x 1.0)) 2.0)) (* (* (- x 1.0) (+ x 1.0)) x))
220.0ms	(* (* (- x 1.0) (+ x 1.0)) x)
48.0ms	(+ (* 1.0 (+ x 1.0)) (* (- x 1.0) 1.0))
4.0ms	(- (* (+ (* 1.0 (+ x 1.0)) (* (- x 1.0) 1.0)) x) (* (* (- x 1.0) (+ x 1.0)) 2.0))

simplify3.8s

Counts

208 → 208

Iterations

Iter	Nodes
done	5002
1	2022
0	466

prune3.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

regimes58.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	8

end0.0ms

sample3.0s

Algorithm

intervals

Results

993.0ms	490×	body	160	valid
789.0ms	1866×	body	640	valid
440.0ms	4097×	body	80	valid
302.0ms	572×	body	1280	valid
274.0ms	975×	body	320	valid