Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	56×	body	1280	valid
3.0ms	44×	body	640	valid
3.0ms	125×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	11×	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: 30.6b

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)))

rewrite124.0ms

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:

10.0ms	(/ x (+ x 1.0))
24.0ms	(/ (+ x 1.0) (- x 1.0))
86.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series187.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ x (+ x 1.0))
33.0ms	(/ (+ x 1.0) (- x 1.0))
123.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5001	716

prune197.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.1b	(/ 3.0 (pow x 3))
0.4b	(/ (- 1.0) (pow x 2))
6.4b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite799.0ms

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:

94.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
8.0ms	(/ 3.0 (pow x 3))
10.0ms	(/ (- 1.0) (pow x 2))
677.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
32.0ms	(/ 3.0 (pow x 3))
29.0ms	(/ (- 1.0) (pow x 2))
29.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify92.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	738	1754
1	3448	1596
2	5001	1578

prune409.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
320×	`times-frac`
170×	`add-sqr-sqrt`
141×	`distribute-lft-out`
106×	`add-cube-cbrt`
72×	`swap-sqr`
52×	`distribute-lft-out--`
44×	`associate-r` `associate-l`
34×	`difference-of-squares`
30×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r/`
18×	`pow1` `frac-sub`
14×	`frac-times` `associate-r/` `associate-l/`
12×	`associate-/r*`
11×	`associate-/l/`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add` `clear-num`

Counts

4 → 329

Calls

4 calls:

50.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
80.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
171.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
24.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
47.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
323.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
188.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify75.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1294	4957
1	5001	4719

prune481.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3.0 (/ 1 (pow x 3)))
0.2b	(* 3.0 (/ 1 x))
0.4b	(/ 1 (pow x 2))
8.0b	(+ (* 1.0 (/ 1 (pow x 2))) (+ (* 3.0 (/ 1 x)) (* 3.0 (/ 1 (pow x 3)))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt` `times-frac`
57×	`*-un-lft-identity`
53×	`associate-r`
52×	`add-cube-cbrt`
42×	`add-exp-log`
23×	`unpow-prod-down`
20×	`frac-add`
16×	`associate-*r/` `un-div-inv` `add-cbrt-cube`
14×	`div-exp` `prod-exp`
12×	`unswap-sqr`
11×	`cube-prod`
9×	`add-log-exp` `sqr-pow`
8×	`pow1` `associate-/r*`
7×	`rec-exp` `1-exp`
6×	`pow-to-exp` `associate-l` `pow-exp`
4×	`cbrt-unprod` `unpow2`
3×	`cbrt-undiv` `cube-mult` `flip3-+` `unpow3` `sum-log` `flip-+` `div-inv` `associate-/l*`
2×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `associate-+r+` `pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 193

Calls

4 calls:

27.0ms	(* 3.0 (/ 1 (pow x 3)))
14.0ms	(* 3.0 (/ 1 x))
8.0ms	(/ 1 (pow x 2))
37.0ms	(+ (* 1.0 (/ 1 (pow x 2))) (+ (* 3.0 (/ 1 x)) (* 3.0 (/ 1 (pow x 3)))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 3.0 (/ 1 (pow x 3)))
15.0ms	(* 3.0 (/ 1 x))
15.0ms	(/ 1 (pow x 2))
25.0ms	(+ (* 1.0 (/ 1 (pow x 2))) (+ (* 3.0 (/ 1 x)) (* 3.0 (/ 1 (pow x 3)))))

simplify108.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	841	1247
1	4404	956
2	5001	924

prune341.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.1b

bsearch64.0ms

Steps

Iters	Range		Point
8	9.114942375872904	154062.39550417996	10731.604757326571
9	-15077057.36594219	-0.2945747773639613	-1.0046554685366835

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	19
1	37	19

end0.0ms

sample532.0ms

Algorithm

intervals

Results

183.0ms	1793×	body	1280	valid
96.0ms	1270×	body	640	valid
92.0ms	4016×	body	80	valid
34.0ms	593×	body	320	valid
13.0ms	328×	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