Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	54×	body	2560	valid
0.0hr	55×	body	640	valid
0.0hr	32×	body	1280	valid
0.0hr	35×	body	320	valid
0.0hr	64×	body	80	valid
0.0hr	16×	body	160	valid

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune0.0hr

Filtered

1 candidates to 0 candidates (100.0%)

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: 30.8b

Counts

2 → 1

localize0.0hr

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
15.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

0.0hr	(- 1.0 (cos x))
0.0hr	(/ (- 1.0 (cos x)) (* x x))

series0.0hr

Counts

2 → 6

Calls

2 calls:

0.0hr	(- 1.0 (cos x))
0.0hr	(/ (- 1.0 (cos x)) (* x x))

simplify0.0hr

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune0.0hr

Filtered

48 candidates to 34 candidates (29.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	39	9	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	9	49

Merged error: 0.1b

Counts

49 → 9

localize0.0hr

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
2.0b	(- 1.0 (cos x))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

0.0hr	(/ (- 1.0 (cos x)) x)
0.0hr	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.0hr	(- 1.0 (cos x))

series0.0hr

Counts

3 → 9

Calls

3 calls:

0.0hr	(/ (- 1.0 (cos x)) x)
0.0hr	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.0hr	(- 1.0 (cos x))

simplify0.0hr

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	521	814
1	2334	726
2	5003	690

prune0.0hr

Filtered

123 candidates to 81 candidates (34.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	122	10	132

Merged error: 0.1b

Counts

132 → 10

localize0.0hr

Local error

Found 3 expressions with local error:

0.1b	(/ (cos x) x)
0.1b	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
2.1b	(- (/ 1.0 x) (/ (cos x) x))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `times-frac`
23×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-l`
12×	`associate-r`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`div-inv`
5×	`pow1` `add-log-exp`
4×	`frac-times` `associate-*r/` `prod-exp`
3×	`sub-neg` `flip3--` `div-exp` `associate-/r` `frac-sub` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-rgt-out--` `distribute-lft-in` `cbrt-unprod`
1×	`rec-exp` `frac-2neg` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

3 → 106

Calls

3 calls:

0.0hr	(/ (cos x) x)
0.0hr	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
0.0hr	(- (/ 1.0 x) (/ (cos x) x))

series0.0hr

Counts

3 → 9

Calls

3 calls:

0.0hr	(/ (cos x) x)
0.0hr	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
0.0hr	(- (/ 1.0 x) (/ (cos x) x))

simplify0.0hr

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	478	762
1	2181	681
2	5001	665

prune0.0hr

Filtered

115 candidates to 86 candidates (25.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	114	11	125

Merged error: 0.1b

Counts

125 → 11

localize0.0hr

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
0.3b	(* (cos x) (cos x))
0.5b	(+ 1.0 (cos x))
2.1b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
8×	`add-log-exp`
4×	`times-frac` `associate-/l*`
3×	`swap-sqr` `associate-r` `associate-l` `difference-of-squares`
2×	`cbrt-undiv` `sqr-cos` `flip3--` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `pow-sqr` `cos-mult` `-commutative` `pow-prod-up` `div-inv` `distribute-lft-out` `associate--r+` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

0.0hr	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
0.0hr	(* (cos x) (cos x))
0.0hr	(+ 1.0 (cos x))
0.0hr	(- (* 1.0 1.0) (* (cos x) (cos x)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
0.0hr	(* (cos x) (cos x))
0.0hr	(+ 1.0 (cos x))
0.0hr	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify0.0hr

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	425	655
1	2057	564
2	5001	548

prune0.0hr

Filtered

93 candidates to 68 candidates (26.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	95	9	104

Merged error: 0.1b

Counts

104 → 9

regimes0.0hr

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.8b

bsearch0.0hr

Steps

Iters	Range		Point
9	0.00021166572504141735	1495.4209016812965	0.03236598160168138
10	-249197998.3190651	-3.6532051617239265e-06	-0.028342198228132068

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	34	11
1	34	11

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	1606×	body	2560	valid
0.0hr	1275×	body	1280	valid
0.0hr	1495×	body	640	valid
0.0hr	868×	body	320	valid
0.0hr	2290×	body	80	valid
0.0hr	466×	body	160	valid

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

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