Details

sample21.0ms

Algorithm

intervals

Results

7.0ms	61×	body	1280	valid
3.0ms	39×	body	640	valid
3.0ms	121×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	12×	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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite107.0ms

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))
39.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series205.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ x (+ x 1.0))
36.0ms	(/ (+ x 1.0) (- x 1.0))
132.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify240.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (71.0ms)

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

prune741.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.3b	(/ 1 (pow x 3))
0.5b	(/ (- 1.0) (pow x 2))
5.6b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite92.0ms

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:

1.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
5.0ms	(/ 1 (pow x 3))
6.0ms	(/ (- 1.0) (pow x 2))
40.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series176.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
30.0ms	(/ 1 (pow x 3))
31.0ms	(/ (- 1.0) (pow x 2))
34.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify177.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1159	12779
1	4167	7106
2	5001	7094

prune796.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
0.3b	(/ 1 (pow x 3))
0.5b	(/ (- 1.0) (pow x 2))
5.6b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

rewrite89.0ms

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:

1.0ms	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
5.0ms	(/ 1 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
41.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
31.0ms	(/ 1 (pow x 3))
25.0ms	(/ (- 1.0) (pow x 2))
43.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

simplify168.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1162	11394
1	4062	6475
2	5001	6466

prune773.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (pow x 3))
0.5b	(/ 1.0 (pow x 2))
7.2b	(fma 3.0 (+ (/ 1 x) (/ 1 (pow x 3))) (/ 1.0 (pow x 2)))
12.4b	(/ 0 (pow x 2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
63×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`unpow-prod-down`
28×	`associate-/r*`
23×	`add-exp-log`
12×	`cube-prod` `div-exp` `sqr-pow`
10×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`unpow2`
5×	`pow-to-exp` `pow-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `frac-2neg` `1-exp` `clear-num` `div-inv`
1×	`pow-flip` `div0` `fma-udef` `inv-pow`

Counts

4 → 188

Calls

4 calls:

6.0ms	(/ 1 (pow x 3))
5.0ms	(/ 1.0 (pow x 2))
1.0ms	(fma 3.0 (+ (/ 1 x) (/ 1 (pow x 3))) (/ 1.0 (pow x 2)))
5.0ms	(/ 0 (pow x 2))

series91.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (pow x 3))
24.0ms	(/ 1.0 (pow x 2))
30.0ms	(fma 3.0 (+ (/ 1 x) (/ 1 (pow x 3))) (/ 1.0 (pow x 2)))
1.0ms	(/ 0 (pow x 2))

simplify68.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	453	855
1	2471	637
2	5001	554

prune317.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes49.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch63.0ms

Steps

Iters	Range		Point
8	4050.4462513149238	24048332.968690775	11974.485141399613
7	-225931.74046194248	-3253.153967321615	-12923.888472784707

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	16
1	35	16

end0.0ms

sample571.0ms

Algorithm

intervals

Results

198.0ms	1666×	body	1280	valid
112.0ms	1273×	body	640	valid
101.0ms	4075×	body	80	valid
47.0ms	663×	body	320	valid
15.0ms	323×	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