Details

sample44.0ms

Algorithm

intervals

Results

14.0ms	63×	body	1280	valid
8.0ms	45×	body	640	valid
6.0ms	117×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify212.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite282.0ms

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:

14.0ms	(/ x (+ x 1.0))
29.0ms	(/ (+ x 1.0) (- x 1.0))
158.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series265.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ x (+ x 1.0))
73.0ms	(/ (+ x 1.0) (- x 1.0))
154.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.4s

Counts

605 → 605

Iterations

Useful iterations: done (3.4s)

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

prune632.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 (* x x)) (/ 3.0 x))
0.2b	(/ 3.0 (pow x 3))
0.3b	(/ 1.0 (* x x))
5.5b	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite321.0ms

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:

43.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
10.0ms	(/ 3.0 (pow x 3))
9.0ms	(/ 1.0 (* x x))
254.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
54.0ms	(/ 3.0 (pow x 3))
32.0ms	(/ 1.0 (* x x))
44.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify1.3s

Counts

148 → 148

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	202	1801
1	455	1547
2	1624	1460
done	5000	1457

prune382.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cbrt (- x 1.0)) 3)
0.4b	(pow (cbrt (- x 1.0)) 3)
0.4b	(pow (cbrt (- x 1.0)) 3)
23.6b	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (pow (cbrt (- x 1.0)) 3)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

3237×	`*-un-lft-identity`
2751×	`times-frac`
1898×	`add-sqr-sqrt`
1692×	`prod-diff`
1553×	`add-cube-cbrt`
754×	`cbrt-prod`
685×	`distribute-lft-out`
604×	`unpow-prod-down` `cube-prod`
226×	`associate-/r/`
164×	`difference-of-squares`
155×	`distribute-lft-out--`
113×	`div-inv`
95×	`flip3-+` `flip-+`
77×	`sqr-pow`
75×	`cube-mult` `unpow3`
42×	`cube-div` `cbrt-div`
22×	`flip3--` `flip--`
18×	`fma-neg`
9×	`pow-unpow`
7×	`pow1` `add-exp-log`
6×	`pow-pow` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow1/3` `pow-exp` `rem-cube-cbrt`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

4 → 1858

Calls

4 calls:

11.0ms	(pow (cbrt (- x 1.0)) 3)
15.0ms	(pow (cbrt (- x 1.0)) 3)
20.0ms	(pow (cbrt (- x 1.0)) 3)
705.0ms	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (pow (cbrt (- x 1.0)) 3)))

series1.4s

Counts

4 → 12

Calls

4 calls:

438.0ms	(pow (cbrt (- x 1.0)) 3)
399.0ms	(pow (cbrt (- x 1.0)) 3)
405.0ms	(pow (cbrt (- x 1.0)) 3)
206.0ms	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (pow (cbrt (- x 1.0)) 3)))

simplify2.1s

Counts

1870 → 1870

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	1095	152700
1	2352	115966
done	5000	63170

prune935.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
33.6b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite77.0ms

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:

17.0ms	(/ 1 (+ x 1.0))
52.0ms	(/ (+ x 1.0) (- x 1.0))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series268.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ 1 (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
205.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify2.5s

Counts

105 → 105

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	162	1294
1	352	1191
2	846	1077
3	2002	1066
done	5000	1058

prune237.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes51.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.4b

bsearch103.0ms

Steps

Iters	Range		Point
9	0.0033303272193615503	311302.39110615524	11917.97074271185
7	-41918.349557210015	-1608.0958488538781	-13754.175701540715

simplify12.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	25	55
1	38	40
2	49	40
3	51	40
done	51	40

end0.0ms

sample1.4s

Algorithm

intervals

Results

601.0ms	4059×	body	80	valid
372.0ms	1770×	body	1280	valid
191.0ms	1220×	body	640	valid
66.0ms	660×	body	320	valid
20.0ms	291×	body	160	valid