Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	53×	body	1280	valid
5.0ms	127×	body	80	valid
5.0ms	49×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	8×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

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)))

rewrite162.0ms

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))
14.0ms	(/ (+ x 1.0) (- x 1.0))
84.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series202.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ x (+ x 1.0))
41.0ms	(/ (+ x 1.0) (- x 1.0))
128.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify208.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (76.0ms)

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

prune721.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.2b	(/ (- 1.0) (pow x 2))
0.3b	(/ 1 (pow x 3))
5.0b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
354×	`add-sqr-sqrt`
344×	`*-un-lft-identity`
342×	`add-cube-cbrt`
252×	`prod-diff`
166×	`unpow-prod-down`
123×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`fma-neg`
56×	`sqr-pow`
52×	`unpow2`
41×	`neg-mul-1`
20×	`associate-/r*`
18×	`add-exp-log`
13×	`associate-/l*`
12×	`cube-prod`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `clear-num` `fma-udef`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 559

Calls

4 calls:

0.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
7.0ms	(/ (- 1.0) (pow x 2))
5.0ms	(/ 1 (pow x 3))
83.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
30.0ms	(/ (- 1.0) (pow x 2))
30.0ms	(/ 1 (pow x 3))
35.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify185.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	1159	12779
1	4169	7106
2	5001	7094

prune778.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
0.2b	(/ (- 1.0) (pow x 2))
0.3b	(/ 1 (pow x 3))
5.0b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
354×	`add-sqr-sqrt`
344×	`*-un-lft-identity`
342×	`add-cube-cbrt`
252×	`prod-diff`
166×	`unpow-prod-down`
123×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`fma-neg`
56×	`sqr-pow`
52×	`unpow2`
41×	`neg-mul-1`
20×	`associate-/r*`
18×	`add-exp-log`
13×	`associate-/l*`
12×	`cube-prod`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `clear-num` `fma-udef`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 559

Calls

4 calls:

0.0ms	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
7.0ms	(/ (- 1.0) (pow x 2))
5.0ms	(/ 1 (pow x 3))
87.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
30.0ms	(/ (- 1.0) (pow x 2))
31.0ms	(/ 1 (pow x 3))
35.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

simplify172.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1162	11394
1	4064	6475
2	5002	6466

prune757.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite878.0ms

Algorithm

rewrite-expression-head

Rules

2691×	`*-un-lft-identity`
1724×	`times-frac`
1185×	`add-sqr-sqrt`
936×	`prod-diff`
813×	`add-cube-cbrt`
506×	`distribute-lft-out`
392×	`distribute-lft-out--`
186×	`sqrt-prod`
182×	`associate-/r/`
168×	`difference-of-squares`
91×	`div-inv`
79×	`swap-sqr`
55×	`flip3-+` `flip-+`
46×	`flip3--` `flip--`
36×	`fma-neg`
24×	`sqrt-div`
19×	`pow1` `associate-r` `associate-l`
10×	`frac-sub`
9×	`frac-times`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `associate-/l*`
2×	`sub-neg` `diff-log`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 1226

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
368.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
85.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
84.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ x (+ x 1.0))
127.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify372.0ms

Algorithm

egg-herbie

Counts

1238 → 1238

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1276	37668
1	4441	27636
2	5001	27556

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.7b

bsearch118.0ms

Steps

Iters	Range		Point
10	4.8244160186105205e-08	257763.20554958374	0.9988614242893094
9	-3246994039.700852	-772.3369502403921	-11098.444471894443

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	42
1	62	42
2	62	42

end0.0ms

sample735.0ms

Algorithm

intervals

Results

239.0ms	1750×	body	1280	valid
175.0ms	4087×	body	80	valid
146.0ms	1263×	body	640	valid
54.0ms	619×	body	320	valid
19.0ms	281×	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