Details

sample35.0ms

Algorithm

intervals

Results

12.0ms	53×	body	1280	valid
6.0ms	37×	body	640	valid
6.0ms	134×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	8×	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: 28.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite152.0ms

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:

7.0ms	(/ x (+ x 1.0))
12.0ms	(/ (+ x 1.0) (- x 1.0))
81.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (+ x 1.0))
43.0ms	(/ (+ x 1.0) (- x 1.0))
141.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify198.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (73.0ms)

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

prune907.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
2.0b	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

rewrite355.0ms

Algorithm

rewrite-expression-head

Rules

2065×	`*-un-lft-identity`
1575×	`times-frac`
1316×	`add-sqr-sqrt`
1114×	`cbrt-prod`
1098×	`prod-diff`
949×	`add-cube-cbrt`
524×	`unpow-prod-down` `cube-prod`
392×	`distribute-lft-out`
206×	`associate-/r/`
179×	`difference-of-squares`
166×	`distribute-lft-out--`
103×	`div-inv`
63×	`flip3-+` `flip-+`
42×	`flip3--` `flip--`
22×	`sqr-pow`
20×	`cube-mult` `unpow3`
18×	`fma-neg`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cube-div` `pow-unpow`
2×	`cbrt-undiv` `cbrt-div` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `frac-sub` `rem-cbrt-cube`

Counts

4 → 1337

Calls

4 calls:

14.0ms	(/ (+ x 1.0) (- x 1.0))
13.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
14.0ms	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
154.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (+ x 1.0) (- x 1.0))
64.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
50.0ms	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
147.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

simplify380.0ms

Algorithm

egg-herbie

Counts

1349 → 1349

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1830	50865
1	5001	32280

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
0.0b	(cbrt (pow (- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))) 3))
0.0b	(pow (- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))) 3)
2.0b	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

rewrite716.0ms

Algorithm

rewrite-expression-head

Rules

1989×	`*-un-lft-identity`
1559×	`times-frac`
1412×	`add-sqr-sqrt`
1204×	`cbrt-prod`
1098×	`prod-diff`
923×	`add-cube-cbrt`
550×	`unpow-prod-down` `cube-prod`
376×	`distribute-lft-out`
222×	`difference-of-squares`
200×	`associate-/r/`
157×	`distribute-lft-out--`
100×	`div-inv`
62×	`flip3-+` `flip-+`
41×	`flip3--` `flip--`
31×	`sqr-pow`
21×	`cube-mult` `unpow3`
18×	`fma-neg`
10×	`cube-div`
7×	`cbrt-div`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `frac-sub`
2×	`pow1/3` `rem-cbrt-cube`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `pow-exp` `rem-cube-cbrt`

Counts

4 → 1330

Calls

4 calls:

14.0ms	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
185.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))) 3))
191.0ms	(pow (- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))) 3)
155.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
148.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))) 3))
246.0ms	(pow (- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))) 3)
155.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

simplify421.0ms

Algorithm

egg-herbie

Counts

1342 → 1342

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	2091	52020
1	5001	34758

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
29.3b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite21.0ms

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:

6.0ms	(/ 1 (+ x 1.0))
12.0ms	(/ (+ x 1.0) (- x 1.0))
0.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series213.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ 1 (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
150.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	352	622
1	1229	566
2	5001	540

prune179.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes35.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 29.1b

bsearch96.0ms

Steps

Iters	Range		Point
9	0.8894813891870064	5702493.407928515	14233.510593067505
8	-1043668.381521804	-286.0085757029236	-13596.226620285603

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	18
1	59	18
2	72	18
3	74	18
4	74	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

397.0ms	1766×	body	1280	valid
219.0ms	1207×	body	640	valid
199.0ms	4123×	body	80	valid
80.0ms	607×	body	320	valid
27.0ms	297×	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