Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	56×	body	1280	valid
4.0ms	41×	body	640	valid
3.0ms	128×	body	80	valid
1.0ms	22×	body	320	valid
0.0ms	9×	body	160	valid

simplify21.0ms

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: 30.2b

localize9.0ms

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)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

11.0ms	(/ (+ x 1.0) (- x 1.0))
8.0ms	(/ x (+ x 1.0))
56.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series205.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (+ x 1.0) (- x 1.0))
38.0ms	(/ x (+ x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5002	716

prune218.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0))
7.7b	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
14.4b	(/ x (- (* x x) (* 1.0 1.0)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
45×	`times-frac`
33×	`add-cube-cbrt`
18×	`associate-l`
13×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`associate-/r*`
8×	`flip3--` `flip--`
7×	`associate-/l*`
6×	`pow1` `associate-/r/` `distribute-lft-out` `distribute-lft-out--` `add-log-exp`
5×	`sub-neg` `associate-r` `frac-sub`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/` `associate--l+`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 146

Calls

4 calls:

11.0ms	(/ (+ x 1.0) (- x 1.0))
24.0ms	(* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0))
24.0ms	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
5.0ms	(/ x (- (* x x) (* 1.0 1.0)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (+ x 1.0) (- x 1.0))
61.0ms	(* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0))
170.0ms	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
69.0ms	(/ x (- (* x x) (* 1.0 1.0)))

simplify94.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	698	1357
1	3323	1273
2	5001	1271

prune328.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.2b	(/ (- 1.0) (pow x 2))
0.3b	(/ 3.0 (pow x 3))
6.0b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite730.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
120×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
78×	`add-cube-cbrt`
48×	`unpow-prod-down`
29×	`distribute-rgt-neg-in`
27×	`distribute-lft-neg-in`
20×	`associate-/r*`
18×	`sqr-pow`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`cube-prod` `associate-/l*` `unpow2`
11×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`neg-mul-1`
8×	`add-cbrt-cube`
6×	`div-exp`
5×	`frac-sub`
4×	`pow1` `cube-mult` `diff-log` `unpow3`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `associate--l-` `neg-sub0` `pow-to-exp` `frac-2neg` `div-sub` `pow-exp` `associate--l+` `clear-num` `div-inv`
1×	`distribute-frac-neg`

Counts

4 → 234

Calls

4 calls:

85.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
6.0ms	(/ (- 1.0) (pow x 2))
4.0ms	(/ 3.0 (pow x 3))
624.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
25.0ms	(/ (- 1.0) (pow x 2))
40.0ms	(/ 3.0 (pow x 3))
33.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify95.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	738	1754
1	3453	1596
2	5001	1578

prune429.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (- (* (* (/ x (- (* x x) (* 1.0 1.0))) (- (pow x 3) (pow 1.0 3))) (- x 1.0)) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (+ x 1.0))) (* (- x 1.0) (+ (* 1.0 (+ 1.0 x)) (pow x 2))))
5.8b	(* (/ x (- (* x x) (* 1.0 1.0))) (- (pow x 3) (pow 1.0 3)))
14.4b	(/ x (- (* x x) (* 1.0 1.0)))
24.9b	(- (* (* (/ x (- (* x x) (* 1.0 1.0))) (- (pow x 3) (pow 1.0 3))) (- x 1.0)) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (+ x 1.0)))

rewrite470.0ms

Algorithm

rewrite-expression-head

Rules

398×	`frac-times`
272×	`frac-sub`
207×	`flip3-+` `flip-+`
201×	`flip3--` `flip--`
200×	`associate-*r/`
199×	`associate-*l/`
138×	`associate-/l/`
53×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
28×	`times-frac`
25×	`associate-r`
24×	`add-cube-cbrt`
23×	`difference-of-squares`
18×	`associate-l`
16×	`add-exp-log` `add-cbrt-cube`
12×	`unpow-prod-down` `cube-prod` `associate-/r/`
8×	`sqr-pow`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-/r*` `distribute-lft-out--`
4×	`cbrt-undiv` `div-exp` `associate--l+`
3×	`prod-exp` `cbrt-unprod` `div-inv`
2×	`frac-2neg` `clear-num` `associate--r+` `unswap-sqr`
1×	`difference-cubes` `diff-log` `div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 422

Calls

4 calls:

251.0ms	(/ (- (* (* (/ x (- (* x x) (* 1.0 1.0))) (- (pow x 3) (pow 1.0 3))) (- x 1.0)) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (+ x 1.0))) (* (- x 1.0) (+ (* 1.0 (+ 1.0 x)) (pow x 2))))
72.0ms	(* (/ x (- (* x x) (* 1.0 1.0))) (- (pow x 3) (pow 1.0 3)))
6.0ms	(/ x (- (* x x) (* 1.0 1.0)))
91.0ms	(- (* (* (/ x (- (* x x) (* 1.0 1.0))) (- (pow x 3) (pow 1.0 3))) (- x 1.0)) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (+ x 1.0)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(/ (- (* (* (/ x (- (* x x) (* 1.0 1.0))) (- (pow x 3) (pow 1.0 3))) (- x 1.0)) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (+ x 1.0))) (* (- x 1.0) (+ (* 1.0 (+ 1.0 x)) (pow x 2))))
81.0ms	(* (/ x (- (* x x) (* 1.0 1.0))) (- (pow x 3) (pow 1.0 3)))
65.0ms	(/ x (- (* x x) (* 1.0 1.0)))
173.0ms	(- (* (* (/ x (- (* x x) (* 1.0 1.0))) (- (pow x 3) (pow 1.0 3))) (- x 1.0)) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (+ x 1.0)))

simplify222.0ms

Algorithm

egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 1 (88.0ms)

Iter	Nodes	Cost
0	4191	14463
1	5001	14242

prune3.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.3b

bsearch327.0ms

Steps

Iters	Range		Point
10	488.5072251079851	29561296481055.625	8870.391125684653
10	-146662999352.95746	-3.9934486818618	-9937.586096843137

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	39
1	56	39

end0.0ms

sample561.0ms

Algorithm

intervals

Results

191.0ms	1735×	body	1280	valid
115.0ms	1251×	body	640	valid
99.0ms	4040×	body	80	valid
46.0ms	656×	body	320	valid
14.0ms	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