Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	50×	body	1280	valid
4.0ms	139×	body	80	valid
4.0ms	35×	body	640	valid
2.0ms	25×	body	320	valid
0.0ms	7×	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

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: 27.4b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite48.0ms

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))
7.0ms	(/ (+ x 1.0) (- x 1.0))
32.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

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

prune183.0ms

Filtered

113 candidates to 76 candidates (67.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Merged error: 0.0b

Counts

114 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
2.1b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite152.0ms

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:

17.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
7.0ms	(pow (/ x (+ x 1.0)) 3)
10.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
98.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series464.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
61.0ms	(pow (/ x (+ x 1.0)) 3)
64.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
296.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify69.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1164	2932
1	5002	2690

prune456.0ms

Filtered

315 candidates to 141 candidates (44.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	315	0	315
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	315	5	320

Merged error: 0.0b

Counts

320 → 5

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ 1 (- x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
7.3b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
5.0ms	(/ 1 (- x 1.0))
12.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
14.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ x (+ x 1.0))
26.0ms	(/ 1 (- x 1.0))
43.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
127.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify76.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	576	950
1	2837	862
2	5001	820

prune190.0ms

Filtered

153 candidates to 100 candidates (65.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	153	5	158

Merged error: 0.0b

Counts

158 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
20.6b	(- (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `associate-*r/` `frac-sub` `flip--`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
18.0ms	(- (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
175.0ms	(cbrt x)
179.0ms	(cbrt x)
147.0ms	(- (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify103.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	186	376
1	637	335
2	3340	317
3	5002	317

prune115.0ms

Filtered

58 candidates to 48 candidates (82.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	58	5	63

Merged error: 0.0b

Counts

63 → 5

regimes33.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch98.0ms

Steps

Iters	Range		Point
11	1.2997713508729505	5.879238312391923e+20	8701.243238823146
9	-83730160.10765809	-5.855776674212404	-7942.168643365506

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	19
1	34	19

end0.0ms

sample638.0ms

Algorithm

intervals

Results

220.0ms	1693×	body	1280	valid
139.0ms	1271×	body	640	valid
115.0ms	4128×	body	80	valid
47.0ms	604×	body	320	valid
17.0ms	304×	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