Details

sample34.0ms

Algorithm

intervals

Results

12.0ms	53×	body	1280	valid
6.0ms	37×	body	640	valid
6.0ms	134×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	8×	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: 28.8b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite78.0ms

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))
11.0ms	(/ (+ x 1.0) (- x 1.0))
58.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series205.0ms

Counts

3 → 9

Calls

3 calls:

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

prune204.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

211×	`times-frac`
209×	`*-un-lft-identity`
166×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
34×	`associate-/r*`
31×	`distribute-lft-out` `difference-of-squares`
25×	`distribute-lft-out--`
19×	`add-exp-log`
13×	`associate-/r/` `add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
8×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `cbrt-undiv`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `frac-sub` `inv-pow`

Counts

4 → 234

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
10.0ms	(/ (- x 1.0) (+ x 1.0))
13.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
100.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ x (+ x 1.0))
37.0ms	(/ (- x 1.0) (+ x 1.0))
37.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
128.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify77.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	742	2083
1	3390	1767
2	5001	1758

prune299.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

1022×	`times-frac`
674×	`*-un-lft-identity`
572×	`add-sqr-sqrt`
370×	`add-cube-cbrt`
87×	`associate-/r/`
81×	`difference-of-squares`
74×	`distribute-lft-out`
70×	`distribute-lft-out--`
52×	`div-inv`
50×	`add-exp-log`
35×	`div-exp`
27×	`associate-/r` `associate-/l`
23×	`flip3-+` `flip-+`
21×	`flip3--` `flip--`
20×	`add-cbrt-cube`
10×	`cbrt-undiv`
9×	`rec-exp` `1-exp`
6×	`add-log-exp`
5×	`pow1`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `frac-sub` `associate-/l/` `inv-pow`

Counts

4 → 565

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
6.0ms	(/ 1 (- x 1.0))
25.0ms	(/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0)))
310.0ms	(- (/ x (+ x 1.0)) (/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0))))

series233.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ x (+ x 1.0))
30.0ms	(/ 1 (- x 1.0))
37.0ms	(/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0)))
133.0ms	(- (/ x (+ x 1.0)) (/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0))))

simplify113.0ms

Algorithm

egg-herbie

Counts

577 → 577

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2106	7067
1	5002	6230

prune842.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0))) 3)
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
2.0b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0))) 3))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

2248×	`times-frac`
1436×	`*-un-lft-identity`
1408×	`add-sqr-sqrt`
720×	`add-cube-cbrt`
541×	`unpow-prod-down` `cube-prod`
240×	`difference-of-squares`
170×	`associate-/r/`
166×	`distribute-lft-out`
145×	`distribute-lft-out--`
118×	`div-inv`
60×	`add-exp-log`
48×	`flip3-+` `flip-+`
37×	`flip3--` `div-exp` `flip--`
32×	`add-cbrt-cube`
30×	`sqr-pow`
24×	`swap-sqr`
19×	`pow-exp`
18×	`associate-r` `associate-l`
13×	`pow1` `cbrt-undiv`
8×	`rec-exp` `1-exp`
7×	`rem-cube-cbrt`
6×	`pow-unpow` `add-log-exp`
4×	`cube-div` `prod-exp` `cbrt-unprod` `unswap-sqr`
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 → 1131

Calls

4 calls:

76.0ms	(pow (/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0))) 3)
29.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
8.0ms	(pow (/ x (+ x 1.0)) 3)
1.3s	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0))) 3))

series445.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0))) 3)
43.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
56.0ms	(pow (/ x (+ x 1.0)) 3)
287.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0))) 3))

simplify208.0ms

Algorithm

egg-herbie

Counts

1143 → 1143

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5001	18467

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch104.0ms

Steps

Iters	Range		Point
9	0.8894813891870064	5702493.407928515	11343.191540615622
8	-1043668.381521804	-286.0085757029236	-13216.2772295091

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	54
1	49	54

end0.0ms

sample987.0ms

Algorithm

intervals

Results

393.0ms	1766×	body	1280	valid
209.0ms	1207×	body	640	valid
188.0ms	4123×	body	80	valid
79.0ms	607×	body	320	valid
25.0ms	297×	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