Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	56×	body	1280	valid
3.0ms	41×	body	640	valid
3.0ms	128×	body	80	valid
1.0ms	22×	body	320	valid
0.0ms	9×	body	160	valid

simplify23.0ms

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: 30.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite158.0ms

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:

11.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
81.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series214.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (+ x 1.0) (- x 1.0))
33.0ms	(/ x (+ x 1.0))
137.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify201.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (76.0ms)

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

prune781.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

14.4b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
14.4b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
14.4b	(/ x (- (* x x) (* 1.0 1.0)))
30.6b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
44×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`difference-of-squares`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Counts

4 → 129

Calls

4 calls:

12.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
5.0ms	(/ x (- (* x x) (* 1.0 1.0)))
0.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
37.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
70.0ms	(/ x (- (* x x) (* 1.0 1.0)))
182.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	393	1262
1	1600	1156
2	5001	1097

prune425.0ms

Pruning

4 alts after pruning (3 fresh and 1 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))
30.5b	(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:

23.0ms	(/ 1 (+ x 1.0))
44.0ms	(/ (+ x 1.0) (- x 1.0))
145.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify43.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (34.0ms)

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

prune192.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize13.0ms

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

rewrite133.0ms

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))))
6.0ms	(/ (- 1.0) (pow x 2))
5.0ms	(/ 1 (pow x 3))
84.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
29.0ms	(/ (- 1.0) (pow x 2))
31.0ms	(/ 1 (pow x 3))
43.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify184.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (82.0ms)

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

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch95.0ms

Steps

Iters	Range		Point
10	488.5072251079851	29561296481055.625	13449.22425334713
10	-146662999352.95746	-3.9934486818618	-17519.327964058364

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	15
1	39	15
2	39	15

end0.0ms

sample550.0ms

Algorithm

intervals

Results

186.0ms	1735×	body	1280	valid
110.0ms	1251×	body	640	valid
99.0ms	4040×	body	80	valid
41.0ms	656×	body	320	valid
17.0ms	318×	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