Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	53×	body	1280	valid
3.0ms	40×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	12×	body	160	valid

simplify116.0ms

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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite202.0ms

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:

11.0ms	(/ x (+ x 1.0))
23.0ms	(/ (+ x 1.0) (- x 1.0))
114.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series212.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
136.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.2s

Counts

605 → 605

Iterations

Useful iterations: done (2.2s)

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

prune446.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1.0 (* x x) (fma 3.0 x 1.0))
0.1b	(fma 3.0 x 1.0)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 1.0 (* x x) (fma 3.0 x 1.0))
0.0ms	(fma 3.0 x 1.0)

series60.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(fma 1.0 (* x x) (fma 3.0 x 1.0))
37.0ms	(fma 3.0 x 1.0)

simplify1.8s

Counts

26 → 26

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	31	236
1	47	227
2	127	201
3	568	175
4	3415	175
done	5000	175

prune59.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 (* x x)) (/ 3.0 x))
0.3b	(/ 3.0 (pow x 3))
0.6b	(/ 1.0 (* x x))
7.8b	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite214.0ms

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:

26.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
8.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ 1.0 (* x x))
168.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
43.0ms	(/ 3.0 (pow x 3))
25.0ms	(/ 1.0 (* x x))
29.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify745.0ms

Counts

148 → 148

Iterations

Useful iterations: done (741.0ms)

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

prune288.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 3) (fma x (fma x 3.0 1.0) 3.0))
0.1b	(fma x (fma x 3.0 1.0) 3.0)
0.1b	(fma x 3.0 1.0)
50.1b	(/ (* (pow x 3) (fma x (fma x 3.0 1.0) 3.0)) (pow x 6))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
19×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `-un-lft-identity` `div-exp` `associate-l*` `prod-exp`
11×	`add-cbrt-cube`
10×	`unpow-prod-down`
8×	`pow-to-exp` `pow-exp`
7×	`times-frac` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `cube-prod` `fma-udef` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`associate-r`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`distribute-rgt-in` `cube-mult` `frac-2neg` `distribute-lft-in` `unpow3` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 96

Calls

4 calls:

16.0ms	(* (pow x 3) (fma x (fma x 3.0 1.0) 3.0))
0.0ms	(fma x (fma x 3.0 1.0) 3.0)
0.0ms	(fma x 3.0 1.0)
14.0ms	(/ (* (pow x 3) (fma x (fma x 3.0 1.0) 3.0)) (pow x 6))

series161.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (pow x 3) (fma x (fma x 3.0 1.0) 3.0))
26.0ms	(fma x (fma x 3.0 1.0) 3.0)
39.0ms	(fma x 3.0 1.0)
47.0ms	(/ (* (pow x 3) (fma x (fma x 3.0 1.0) 3.0)) (pow x 6))

simplify754.0ms

Counts

108 → 108

Iterations

Useful iterations: done (751.0ms)

Iter	Nodes	Cost
0	159	1664
1	348	1556
2	1426	1394
done	5002	1391

prune247.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

100% (0.0b remaining)

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

bsearch78.0ms

Steps

Iters	Range		Point
11	6.1632953816490534e-12	2923699147.8271213	0.9975580681503712
10	-21283307590.397102	-3.152803306627408e-07	-0.9868159492179903

simplify6.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	20	49
1	28	34
2	35	34
3	38	34
done	38	34

end0.0ms

sample701.0ms

Algorithm

intervals

Results

247.0ms	1239×	body	640	valid
183.0ms	1669×	body	1280	valid
95.0ms	4129×	body	80	valid
39.0ms	644×	body	320	valid
13.0ms	319×	body	160	valid