Details

sample38.0ms

Algorithm

intervals

Results

10.0ms	54×	body	1280	valid
9.0ms	40×	body	640	valid
5.0ms	136×	body	80	valid
2.0ms	21×	body	320	valid
0.0ms	5×	body	160	valid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.5b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite105.0ms

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:

8.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
40.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ x (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify212.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (80.0ms)

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

prune673.0ms

Filtered

605 candidates to 217 candidates (35.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	601	4	605
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	602	4	606

Merged error: 0.1b

Counts

606 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x 1.0) (+ x 1.0))
0.0b	(/ x (+ x 1.0))
0.0b	(/ 1 (/ (- x 1.0) (+ x 1.0)))
2.9b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite354.0ms

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:

8.0ms	(/ (- x 1.0) (+ x 1.0))
5.0ms	(/ x (+ x 1.0))
11.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
108.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (- x 1.0) (+ x 1.0))
35.0ms	(/ x (+ x 1.0))
41.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
129.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify631.0ms

Algorithm

egg-herbie

Counts

1766 → 1766

Iterations

Useful iterations: 1 (67.0ms)

Iter	Nodes	Cost
0	3287	74392
1	5001	61456

prune1.1s

Filtered

1766 candidates to 358 candidates (20.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1765	1	1766
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	1765	5	1770

Merged error: 0.1b

Counts

1770 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
0.1b	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

1139×	`*-un-lft-identity`
796×	`times-frac`
619×	`add-sqr-sqrt`
468×	`prod-diff`
415×	`add-cube-cbrt`
215×	`distribute-lft-out`
137×	`distribute-lft-out--`
92×	`associate-/r/` `difference-of-squares`
46×	`div-inv`
38×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
28×	`flip3-+` `flip-+`
21×	`flip3--` `flip--`
18×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`pow-unpow` `cbrt-div` `frac-sub` `associate-/l*`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 655

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
35.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
31.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
45.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ x (+ x 1.0))
183.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
131.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
137.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify253.0ms

Algorithm

egg-herbie

Counts

667 → 667

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	1372	19256
1	4582	14246
2	5001	14222

prune773.0ms

Filtered

667 candidates to 229 candidates (34.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	665	2	667
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	666	6	672

Merged error: 0.1b

Counts

672 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))
0.0b	(/ x (+ x 1.0))
0.0b	(* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))
2.9b	(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

296×	`*-un-lft-identity`
188×	`cbrt-prod`
187×	`times-frac`
168×	`add-sqr-sqrt`
92×	`add-cube-cbrt`
58×	`associate-r`
53×	`distribute-lft-out`
51×	`swap-sqr`
36×	`distribute-lft-out--`
30×	`pow1` `associate-l`
28×	`cbrt-div`
24×	`difference-of-squares`
18×	`fma-neg` `prod-diff`
16×	`associate-/r/`
15×	`pow1/3`
13×	`add-exp-log`
12×	`unswap-sqr`
11×	`frac-times` `associate-*l/` `pow-prod-up`
8×	`div-inv`
7×	`pow-plus` `associate-*r/` `pow-prod-down` `frac-sub` `add-cbrt-cube`
6×	`flip3--` `flip--` `add-log-exp`
5×	`pow-sqr`
4×	`expm1-log1p-u` `prod-exp` `associate-/r*` `cbrt-unprod` `log1p-expm1-u`
3×	`pow2` `flip3-+` `flip-+` `associate-/l*`
2×	`*-commutative`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow3` `clear-num`

Counts

4 → 301

Calls

4 calls:

35.0ms	(* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))
5.0ms	(/ x (+ x 1.0))
30.0ms	(* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))
12.0ms	(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))
40.0ms	(/ x (+ x 1.0))
185.0ms	(* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))
165.0ms	(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

simplify144.0ms

Algorithm

egg-herbie

Counts

313 → 313

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	868	4792
1	3667	4077
2	5002	3945

prune509.0ms

Filtered

313 candidates to 189 candidates (60.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	313	0	313
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	313	6	319

Merged error: 0.1b

Counts

319 → 6

regimes63.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 29.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	22
1	32	22

end0.0ms

sample532.0ms

Algorithm

intervals

Results

188.0ms	1702×	body	1280	valid
107.0ms	1269×	body	640	valid
94.0ms	4110×	body	80	valid
38.0ms	616×	body	320	valid
13.0ms	303×	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