Details

sample45.0ms

Algorithm

intervals

Results

12.0ms	49×	body	1280	valid
9.0ms	49×	body	640	valid
6.0ms	119×	body	80	valid
4.0ms	26×	body	320	valid
1.0ms	13×	body	160	valid

simplify281.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	77	13
9	99	13
10	113	13
11	119	13
12	123	13
done	123	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

23.0ms	(/ x (+ x 1.0))
51.0ms	(/ (+ x 1.0) (- x 1.0))
212.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series294.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ x (+ x 1.0))
47.0ms	(/ (+ x 1.0) (- x 1.0))
193.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.5s

Counts

605 → 605

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	523	34216
1	1199	30851
2	2823	22735
done	5000	16848

prune712.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 (* x x)) (/ 3.0 x))
0.3b	(/ 1.0 (* x x))
0.4b	(/ 3.0 (pow x 3))
7.0b	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`fma-def` `add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp` `frac-add` `distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `sum-log` `log1p-expm1-u` `sqr-pow`
3×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
2×	`+-commutative` `frac-2neg` `clear-num`
1×	`pow-to-exp` `associate-+l+` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

56.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
16.0ms	(/ 1.0 (* x x))
18.0ms	(/ 3.0 (pow x 3))
277.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
49.0ms	(/ 1.0 (* x x))
40.0ms	(/ 3.0 (pow x 3))
46.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify1.2s

Counts

148 → 148

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	202	1801
1	455	1547
2	1633	1460
done	5001	1457

prune451.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b	(fma (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)) (/ x (- x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
3.9b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

4381×	`*-un-lft-identity`
3248×	`times-frac`
2699×	`add-sqr-sqrt`
2436×	`prod-diff`
2258×	`unpow-prod-down` `cube-prod`
1927×	`add-cube-cbrt`
822×	`distribute-lft-out`
412×	`associate-/r/`
397×	`distribute-lft-out--`
380×	`difference-of-squares`
206×	`div-inv`
120×	`flip3-+` `flip-+`
115×	`sqr-pow`
103×	`cube-mult` `unpow3`
87×	`flip3--` `flip--`
42×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `pow-unpow` `add-log-exp`
4×	`cube-div` `expm1-log1p-u` `pow-exp` `log1p-expm1-u` `rem-cube-cbrt`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `div-exp`
1×	`difference-cubes` `sub-neg` `diff-log` `frac-sub` `fma-udef`

Counts

4 → 2709

Calls

4 calls:

44.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
1.0ms	(fma (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)) (/ x (- x 1.0)))
28.0ms	(pow (/ x (+ x 1.0)) 3)
542.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series800.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
199.0ms	(fma (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)) (/ x (- x 1.0)))
101.0ms	(pow (/ x (+ x 1.0)) 3)
406.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify1.8s

Counts

2721 → 2721

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	898	213446
1	2127	176057
done	5000	130726

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ 1 (+ x 1.0))
32.9b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`add-exp-log` `associate-/r*`
7×	`add-cbrt-cube` `associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `associate-/r/`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l/`
1×	`rec-exp` `flip3--` `pow-flip` `1-exp` `flip--` `fma-udef` `inv-pow`

Counts

3 → 96

Calls

3 calls:

39.0ms	(/ (+ x 1.0) (- x 1.0))
19.0ms	(/ 1 (+ x 1.0))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series281.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (+ x 1.0) (- x 1.0))
38.0ms	(/ 1 (+ x 1.0))
190.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify2.7s

Counts

105 → 105

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	162	1294
1	352	1191
2	839	1077
3	1996	1066
done	5001	1058

prune235.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.0b

bsearch207.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	12015.494489501321
9	-115102859795.89769	-7465.585501010854	-10364.722782930596

simplify34.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	47	143
1	63	128
2	70	128
3	73	128
done	73	128

end0.0ms

sample1.3s

Algorithm

intervals

Results

489.0ms	1685×	body	1280	valid
296.0ms	1271×	body	640	valid
216.0ms	4134×	body	80	valid
76.0ms	611×	body	320	valid
24.0ms	299×	body	160	valid