Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	57×	body	1280	valid
3.0ms	40×	body	640	valid
3.0ms	131×	body	80	valid
1.0ms	14×	body	320	valid
1.0ms	14×	body	160	valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite146.0ms

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:

5.0ms	(/ x (+ x 1.0))
11.0ms	(/ (+ x 1.0) (- x 1.0))
74.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series207.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
133.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify205.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	1208	18366
1	3687	13388
2	5001	13292

prune749.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (- x 1.0) (+ x 1.0))
0.0b	(/ 1 (/ (- x 1.0) (+ x 1.0)))
3.3b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite390.0ms

Algorithm

rewrite-expression-head

Rules

3703×	`times-frac`
3383×	`*-un-lft-identity`
2296×	`add-sqr-sqrt`
1789×	`add-cube-cbrt`
1494×	`prod-diff`
553×	`distribute-lft-out`
307×	`associate-/r/`
247×	`difference-of-squares`
241×	`distribute-lft-out--`
164×	`div-inv`
144×	`flip3-+` `flip-+`
34×	`associate-/r*`
19×	`add-exp-log`
18×	`fma-neg`
13×	`add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `frac-sub` `inv-pow`

Counts

4 → 1754

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
11.0ms	(/ (- x 1.0) (+ x 1.0))
13.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
140.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ x (+ x 1.0))
36.0ms	(/ (- x 1.0) (+ x 1.0))
38.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
137.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify592.0ms

Algorithm

egg-herbie

Counts

1766 → 1766

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	3287	74392
1	5001	61456

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(fma (/ (+ x 1.0) (- x 1.0)) 1 (/ x (+ x 1.0)))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite729.0ms

Algorithm

rewrite-expression-head

Rules

2822×	`*-un-lft-identity`
2112×	`times-frac`
1644×	`add-sqr-sqrt`
1404×	`prod-diff`
1186×	`add-cube-cbrt`
560×	`distribute-lft-out`
470×	`distribute-rgt-in` `distribute-lft-in`
268×	`associate-/r/`
250×	`distribute-lft-out--`
224×	`difference-of-squares`
134×	`div-inv`
85×	`flip3-+` `flip-+`
59×	`flip3--` `flip--`
18×	`fma-def` `fma-neg`
16×	`associate-r`
12×	`associate-l`
9×	`frac-times`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`frac-add` `frac-sub`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `associate-r/` `associate-l/`
1×	`+-commutative` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 1562

Calls

4 calls:

412.0ms	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
49.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0ms	(fma (/ (+ x 1.0) (- x 1.0)) 1 (/ x (+ x 1.0)))
77.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series604.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
97.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
86.0ms	(fma (/ (+ x 1.0) (- x 1.0)) 1 (/ x (+ x 1.0)))
141.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify579.0ms

Algorithm

egg-herbie

Counts

1574 → 1574

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	3685	67443
1	5002	63475

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(fma (/ (+ x 1.0) (- x 1.0)) 1 (/ x (+ x 1.0)))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

992×	`*-un-lft-identity`
732×	`times-frac`
564×	`add-sqr-sqrt`
468×	`prod-diff`
408×	`add-cube-cbrt`
199×	`distribute-lft-out`
92×	`associate-/r/`
89×	`distribute-lft-out--`
76×	`difference-of-squares`
46×	`div-inv`
29×	`flip3-+` `flip-+`
19×	`flip3--` `flip--`
18×	`fma-def` `fma-neg`
8×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `sub-neg` `expm1-log1p` `diff-log` `frac-add` `sum-log` `frac-sub` `fma-udef` `expm1-udef`

Counts

4 → 576

Calls

4 calls:

0.0ms	(expm1 (log1p (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
51.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0ms	(fma (/ (+ x 1.0) (- x 1.0)) 1 (/ x (+ x 1.0)))
75.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(expm1 (log1p (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
99.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
85.0ms	(fma (/ (+ x 1.0) (- x 1.0)) 1 (/ x (+ x 1.0)))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify218.0ms

Algorithm

egg-herbie

Counts

588 → 588

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1193	18324
1	3339	13359
2	5001	13255

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes40.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 30.0b

bsearch111.0ms

Steps

Iters	Range		Point
10	4.555257425893614e-05	47183757994.54101	10905.852488132816
9	-13600.963204601821	-0.00047371797307045637	-13007.685004338058

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	47
1	72	47
2	90	47
3	96	47
4	98	47
5	98	47

end0.0ms

sample543.0ms

Algorithm

intervals

Results

189.0ms	1725×	body	1280	valid
108.0ms	1317×	body	640	valid
99.0ms	4016×	body	80	valid
41.0ms	656×	body	320	valid
12.0ms	286×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6