Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	53×	body	640	valid
4.0ms	133×	body	80	valid
3.0ms	36×	body	320	valid
2.0ms	19×	body	1280	valid
1.0ms	16×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 12.2b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
3.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

1261×	`associate-/r*`
1123×	`*-un-lft-identity`
1080×	`frac-sub`
1012×	`frac-add`
966×	`associate-/l*`
867×	`add-sqr-sqrt`
663×	`add-cube-cbrt`
322×	`frac-2neg` `clear-num`
121×	`distribute-lft-out`
106×	`distribute-lft-out--`
100×	`difference-of-squares`
47×	`times-frac`
13×	`flip3--` `flip--`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `associate-/r/`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `flip3-+` `diff-log` `div-exp` `sum-log` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 1212

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
23.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
71.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1.0 (- x 1.0))
31.0ms	(/ 1.0 (+ x 1.0))
42.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
232.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify496.0ms

Algorithm

egg-herbie

Counts

1224 → 1224

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5001	28255

prune1.9s

Filtered

1224 candidates to 538 candidates (44.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1221	3	1224
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1222	3	1225

Merged error: 0.5b

Counts

1225 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) 1.0) (/ x 2.0))
0.0b	(* (- (* 1 (/ x 2.0)) (* (/ (+ x 1.0) 1.0) 1)) (- (- x 1.0)))
0.0b	(* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- (- x 1.0)))
14.1b	(+ (* (- (* 1 (/ x 2.0)) (* (/ (+ x 1.0) 1.0) 1)) (- (- x 1.0))) (* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- 1.0)))

rewrite15.3s

Algorithm

rewrite-expression-head

Rules

127911×	`associate-*l/`
79702×	`frac-times`
69072×	`associate-/l*`
59195×	`*-un-lft-identity`
55476×	`associate-/r*`
52924×	`frac-add`
52272×	`frac-sub`
46706×	`associate-*r/`
37168×	`add-sqr-sqrt`
37026×	`add-cube-cbrt`
35904×	`distribute-neg-frac`
23652×	`clear-num`
18492×	`frac-2neg`
18348×	`flip3--` `flip--`
16872×	`associate-/l/`
10320×	`un-div-inv`
8481×	`distribute-lft-out`
8437×	`flip3-+` `flip-+`
208×	`associate-l`
74×	`times-frac`
58×	`associate-r` `unswap-sqr`
40×	`distribute-lft-out--`
36×	`add-exp-log` `add-cbrt-cube`
29×	`difference-of-squares`
24×	`*-commutative`
14×	`prod-exp` `cbrt-unprod`
13×	`pow1`
12×	`distribute-neg-in`
10×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`cbrt-undiv` `distribute-rgt-out--` `div-exp`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `distribute-rgt-neg-out` `add-log-exp`
5×	`pow-prod-down`
4×	`associate-+l+` `div-inv`
2×	`neg-mul-1`
1×	`+-commutative` `distribute-neg-out` `unsub-neg` `sum-log`

Counts

4 → 54113

Calls

4 calls:

19.0ms	(* (/ (+ x 1.0) 1.0) (/ x 2.0))
87.0ms	(* (- (* 1 (/ x 2.0)) (* (/ (+ x 1.0) 1.0) 1)) (- (- x 1.0)))
55.0ms	(* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- (- x 1.0)))
1.5s	(+ (* (- (* 1 (/ x 2.0)) (* (/ (+ x 1.0) 1.0) 1)) (- (- x 1.0))) (* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- 1.0)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ (+ x 1.0) 1.0) (/ x 2.0))
36.0ms	(* (- (* 1 (/ x 2.0)) (* (/ (+ x 1.0) 1.0) 1)) (- (- x 1.0)))
125.0ms	(* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- (- x 1.0)))
9.0ms	(+ (* (- (* 1 (/ x 2.0)) (* (/ (+ x 1.0) 1.0) 1)) (- (- x 1.0))) (* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- 1.0)))

simplify25.4s

Algorithm

egg-herbie

Counts

54125 → 54125

Iterations

Useful iterations: 0 (1.7s)

Iter	Nodes	Cost
0	86346	2432250

prune2.8m

Filtered

54125 candidates to 25390 candidates (46.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54124	1	54125
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	54125	3	54128

Merged error: 0.3b

Counts

54128 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ (+ x 1.0) 1.0) (/ x 2.0))
0.0b	(* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- (- x 1.0)))
0.3b	(/ (- 1.0) (* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- (- x 1.0))))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

1280×	`frac-times`
1188×	`add-sqr-sqrt`
1041×	`*-un-lft-identity`
993×	`times-frac`
768×	`add-cube-cbrt`
664×	`associate-l`
570×	`associate-/l*`
545×	`associate-/r*`
528×	`distribute-neg-frac`
395×	`associate-/r/`
346×	`associate-*l/`
337×	`associate-r`
264×	`flip3--` `flip--`
249×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
169×	`clear-num`
162×	`frac-2neg`
160×	`unswap-sqr`
140×	`associate-/l/`
109×	`distribute-lft-out`
75×	`neg-mul-1`
70×	`flip3-+` `flip-+`
67×	`associate-*r/`
58×	`add-exp-log` `add-cbrt-cube`
27×	`div-inv`
25×	`*-commutative`
24×	`distribute-lft-out--` `difference-of-squares`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
14×	`un-div-inv`
10×	`pow1`
4×	`distribute-neg-in` `pow-prod-down`
3×	`add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`neg-sub0` `div-sub` `distribute-frac-neg` `distribute-rgt-neg-out`

Counts

3 → 1769

Calls

3 calls:

18.0ms	(* (/ (+ x 1.0) 1.0) (/ x 2.0))
49.0ms	(* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- (- x 1.0)))
86.0ms	(/ (- 1.0) (* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- (- x 1.0))))

series261.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* (/ (+ x 1.0) 1.0) (/ x 2.0))
121.0ms	(* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- (- x 1.0)))
87.0ms	(/ (- 1.0) (* (* (/ (+ x 1.0) 1.0) (/ x 2.0)) (- (- x 1.0))))

simplify224.0ms

Algorithm

egg-herbie

Counts

1778 → 1778

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5001	22743

prune3.7s

Filtered

1778 candidates to 1184 candidates (66.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	1774	4	1778
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	1776	5	1781

Merged error: 0b

Counts

1781 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ (+ x 1.0) 1.0) (/ x 2.0))
0.0b	(/ (- (/ 1.0 (- (* (/ (+ x 1.0) 1.0) (/ x 2.0))))) (- x 1.0))
0.4b	(/ 1.0 (- (* (/ (+ x 1.0) 1.0) (/ x 2.0))))

rewrite877.0ms

Algorithm

rewrite-expression-head

Rules

8965×	`times-frac`
6336×	`add-sqr-sqrt`
6132×	`*-un-lft-identity`
3830×	`add-cube-cbrt`
3808×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
1880×	`associate-/l*`
1789×	`distribute-neg-frac`
1705×	`associate-/r/`
1512×	`frac-times`
1328×	`associate-l`
1131×	`associate-/r*`
1079×	`associate-r`
755×	`distribute-lft-out--` `difference-of-squares`
389×	`distribute-lft-out`
366×	`associate-/l/`
339×	`clear-num`
332×	`unswap-sqr`
325×	`frac-2neg`
180×	`div-inv`
168×	`associate-*l/`
140×	`flip3-+` `flip-+`
126×	`associate-*r/`
83×	`*-commutative`
47×	`neg-mul-1`
28×	`un-div-inv`
19×	`add-exp-log` `add-cbrt-cube`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod`
3×	`add-log-exp`
1×	`neg-sub0` `flip3--` `div-sub` `distribute-frac-neg` `pow-prod-down` `flip--`

Counts

3 → 5278

Calls

3 calls:

18.0ms	(* (/ (+ x 1.0) 1.0) (/ x 2.0))
212.0ms	(/ (- (/ 1.0 (- (* (/ (+ x 1.0) 1.0) (/ x 2.0))))) (- x 1.0))
44.0ms	(/ 1.0 (- (* (/ (+ x 1.0) 1.0) (/ x 2.0))))

series206.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (/ (+ x 1.0) 1.0) (/ x 2.0))
104.0ms	(/ (- (/ 1.0 (- (* (/ (+ x 1.0) 1.0) (/ x 2.0))))) (- x 1.0))
40.0ms	(/ 1.0 (- (* (/ (+ x 1.0) 1.0) (/ x 2.0))))

simplify790.0ms

Algorithm

egg-herbie

Counts

5287 → 5287

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	6962	85186

prune12.0s

Filtered

5287 candidates to 3692 candidates (69.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	5285	2	5287
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	5288	4	5292

Merged error: 0b

Counts

5292 → 4

regimes21.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	9
1	23	9
2	23	9

end0.0ms

sample548.0ms

Algorithm

intervals

Results

195.0ms	1872×	body	640	valid
113.0ms	4196×	body	80	valid
68.0ms	922×	body	320	valid
67.0ms	538×	body	1280	valid
24.0ms	477×	body	160	valid