Details

sample21.0ms

Algorithm

intervals

Results

7.0ms	67×	body	1280	valid
3.0ms	128×	body	80	valid
3.0ms	33×	body	640	valid
1.0ms	19×	body	320	valid
0.0ms	9×	body	160	valid

simplify21.0ms

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

rewrite115.0ms

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))
7.0ms	(/ (+ x 1.0) (- x 1.0))
45.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series207.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
135.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify204.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (74.0ms)

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

prune746.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.8b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

329×	`*-un-lft-identity`
212×	`times-frac`
173×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
72×	`swap-sqr`
62×	`distribute-lft-out`
44×	`associate-r` `associate-l`
37×	`distribute-lft-out--`
30×	`add-exp-log` `add-cbrt-cube`
26×	`difference-of-squares`
18×	`pow1` `associate-/r/`
9×	`cbrt-undiv` `div-exp` `frac-sub` `div-inv`
8×	`frac-times` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `associate-/r*` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `associate-/l/`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num`

Counts

4 → 293

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
21.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
27.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
12.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series363.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (+ x 1.0) (- x 1.0))
49.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
55.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
220.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1168	2966
1	5001	2739

prune495.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3.0 (/ 1 (pow x 3)))
0.2b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.3b	(/ (- 1.0) (pow x 2))
6.0b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite300.0ms

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))
42.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 3.0 (/ 1 (pow x 3)))
82.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
33.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify181.0ms

Algorithm

egg-herbie

Counts

573 → 573

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1314	12850
1	4714	6734
2	5001	6734

prune903.0ms

Pruning

5 alts after pruning (3 fresh and 2 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))
6.0b	(- (- (+ (/ 1.0 (pow x 2)) (/ 3.0 x))) (* 3.0 (/ 1 (pow x 3))))

rewrite66.0ms

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))
17.0ms	(* 3.0 (/ 1 (pow x 3)))
5.0ms	(/ 1.0 (pow x 2))
28.0ms	(- (- (+ (/ 1.0 (pow x 2)) (/ 3.0 x))) (* 3.0 (/ 1 (pow x 3))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (pow x 3))
37.0ms	(* 3.0 (/ 1 (pow x 3)))
30.0ms	(/ 1.0 (pow x 2))
33.0ms	(- (- (+ (/ 1.0 (pow x 2)) (/ 3.0 x))) (* 3.0 (/ 1 (pow x 3))))

simplify118.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 2 (99.0ms)

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

prune424.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch80.0ms

Steps

Iters	Range		Point
8	0.8818080259852756	19555.519105776155	10812.5003292367
9	-1052513.600169936	-0.041603525395973645	-11287.389275273414

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	29
1	47	29
2	47	29

end0.0ms

sample550.0ms

Algorithm

intervals

Results

180.0ms	1700×	body	1280	valid
123.0ms	1238×	body	640	valid
95.0ms	4097×	body	80	valid
41.0ms	648×	body	320	valid
14.0ms	317×	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