Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	48×	body	1280	valid
3.0ms	43×	body	640	valid
3.0ms	127×	body	80	valid
2.0ms	28×	body	320	valid
0.0ms	10×	body	160	valid

simplify22.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite120.0ms

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))
8.0ms	(/ (+ x 1.0) (- x 1.0))
45.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series208.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (+ x 1.0))
43.0ms	(/ (+ x 1.0) (- x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify204.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (73.0ms)

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

prune760.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
30.7b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite17.0ms

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:

5.0ms	(/ 1 (+ x 1.0))
8.0ms	(/ (+ x 1.0) (- x 1.0))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series202.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ 1 (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
141.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (33.0ms)

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

prune193.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3.0 (/ 1 (pow x 3)))
0.1b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.3b	(/ (- 1.0) (pow x 2))
6.6b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

448×	`times-frac`
372×	`add-sqr-sqrt`
346×	`*-un-lft-identity`
340×	`add-cube-cbrt`
252×	`prod-diff`
165×	`unpow-prod-down`
123×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`fma-neg`
57×	`sqr-pow`
52×	`unpow2`
41×	`neg-mul-1`
40×	`associate-r`
29×	`add-exp-log`
11×	`cube-prod` `add-cbrt-cube`
10×	`prod-exp` `associate-/l*`
9×	`div-exp` `unswap-sqr`
8×	`associate-/r*`
6×	`pow1` `div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u`
3×	`cube-mult` `rec-exp` `1-exp` `unpow3` `associate-l`
2×	`cbrt-undiv` `neg-sub0` `div-sub` `cbrt-unprod` `fma-udef`
1×	`associate--l-` `sub-neg` `flip3--` `frac-2neg` `diff-log` `associate-r/` `distribute-frac-neg` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `flip--` `associate--r+` `distribute-lft-out--`

Counts

4 → 561

Calls

4 calls:

14.0ms	(* 3.0 (/ 1 (pow x 3)))
1.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
7.0ms	(/ (- 1.0) (pow x 2))
43.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 3.0 (/ 1 (pow x 3)))
81.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
25.0ms	(/ (- 1.0) (pow x 2))
35.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify183.0ms

Algorithm

egg-herbie

Counts

573 → 573

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1317	13029
1	4914	6741
2	5001	6741

prune952.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (pow x 3))
0.1b	(* 3.0 (/ 1 (pow x 3)))
0.3b	(/ 1.0 (pow x 2))
6.6b	(- (- (+ (/ 1.0 (pow x 2)) (/ 3.0 x))) (* 3.0 (/ 1 (pow x 3))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

112×	`times-frac`
103×	`*-un-lft-identity`
95×	`add-sqr-sqrt`
75×	`add-cube-cbrt`
40×	`associate-r`
38×	`add-exp-log`
35×	`unpow-prod-down`
23×	`cube-prod`
20×	`associate-/r*`
15×	`div-exp`
14×	`fma-neg` `prod-diff`
13×	`add-cbrt-cube` `sqr-pow`
11×	`add-log-exp`
10×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `prod-exp`
9×	`unswap-sqr`
8×	`distribute-lft-out`
7×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp`
6×	`pow1` `rec-exp` `1-exp` `frac-sub` `distribute-neg-frac` `associate-/l*`
4×	`expm1-log1p-u` `associate-*r/` `un-div-inv` `log1p-expm1-u` `unpow2`
3×	`cbrt-undiv` `diff-log` `associate-l` `div-inv`
2×	`neg-mul-1` `frac-2neg` `flip3-+` `neg-log` `frac-add` `clear-num` `cbrt-unprod` `flip-+`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-neg-in` `flip3--` `pow-flip` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `inv-pow`

Counts

4 → 255

Calls

4 calls:

6.0ms	(/ 1 (pow x 3))
14.0ms	(* 3.0 (/ 1 (pow x 3)))
5.0ms	(/ 1.0 (pow x 2))
27.0ms	(- (- (+ (/ 1.0 (pow x 2)) (/ 3.0 x))) (* 3.0 (/ 1 (pow x 3))))

series129.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (pow x 3))
42.0ms	(* 3.0 (/ 1 (pow x 3)))
24.0ms	(/ 1.0 (pow x 2))
32.0ms	(- (- (+ (/ 1.0 (pow x 2)) (/ 3.0 x))) (* 3.0 (/ 1 (pow x 3))))

simplify112.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	795	1673
1	4116	1322
2	5002	1298

prune452.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.7b

bsearch87.0ms

Steps

Iters	Range		Point
8	6793.132116615613	39135938.24223837	11598.163947811103
10	-46094758682.62103	-8.718619127186496	-19531.357482678304

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	19
1	47	19
2	47	19

end0.0ms

sample533.0ms

Algorithm

intervals

Results

192.0ms	1734×	body	1280	valid
106.0ms	1220×	body	640	valid
92.0ms	4115×	body	80	valid
38.0ms	618×	body	320	valid
13.0ms	313×	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