Details

sample21.0ms

Algorithm

intervals

Results

7.0ms	67×	body	1280	valid
3.0ms	128×	body	80	valid
3.0ms	33×	body	640	valid
1.0ms	19×	body	320	valid
0.0ms	9×	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: 30.3b

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)))

rewrite49.0ms

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:

5.0ms	(/ x (+ x 1.0))
10.0ms	(/ (+ x 1.0) (- x 1.0))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
125.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune210.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.1b	(pow (/ x (+ x 1.0)) 3)
2.8b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

354×	`*-un-lft-identity`
216×	`times-frac`
190×	`add-sqr-sqrt`
104×	`unpow-prod-down` `cube-prod`
78×	`add-cube-cbrt`
66×	`distribute-lft-out`
61×	`distribute-lft-out--`
44×	`difference-of-squares`
24×	`swap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
16×	`associate-/r/`
14×	`sqr-pow`
13×	`pow1`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`cube-div` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub`

Counts

4 → 303

Calls

4 calls:

20.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
10.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
7.0ms	(pow (/ x (+ x 1.0)) 3)
106.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series460.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
63.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
54.0ms	(pow (/ x (+ x 1.0)) 3)
298.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1164	2932
1	5002	2690

prune548.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 2)
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

199×	`*-un-lft-identity`
140×	`times-frac`
121×	`add-sqr-sqrt`
69×	`add-cube-cbrt`
44×	`associate-r`
39×	`distribute-lft-out`
36×	`associate-l`
31×	`add-exp-log`
28×	`add-cbrt-cube`
26×	`unpow-prod-down`
24×	`swap-sqr`
21×	`distribute-lft-out--`
14×	`pow1` `associate-/r/`
12×	`difference-of-squares`
9×	`div-exp`
8×	`cbrt-undiv` `prod-exp` `cbrt-unprod` `unswap-sqr`
7×	`div-inv`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
3×	`pow-unpow` `flip3--` `flip--`
2×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `*-commutative`
1×	`pow2` `pow-to-exp` `sub-neg` `pow-pow` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up` `frac-sub` `unpow2` `sqr-pow`

Counts

4 → 224

Calls

4 calls:

17.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
22.0ms	(* (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
10.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 2)
33.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
37.0ms	(* (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
53.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 2)
131.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1071	1925
1	5001	1759

prune629.0ms

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	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.1b	(/ 3.0 (pow x 3))
0.3b	(/ (- 1.0) (pow x 2))
6.0b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite163.0ms

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:

58.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
5.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
83.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
39.0ms	(/ 3.0 (pow x 3))
24.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify102.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (76.0ms)

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

prune411.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch95.0ms

Steps

Iters	Range		Point
9	19555.519105776155	5849697155433.691	20005.70299342879
9	-1052513.600169936	-0.041603525395973645	-12471.666509296416

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	38
1	47	38

end0.0ms

sample552.0ms

Algorithm

intervals

Results

187.0ms	1700×	body	1280	valid
114.0ms	1238×	body	640	valid
99.0ms	4097×	body	80	valid
45.0ms	648×	body	320	valid
14.0ms	317×	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