Details

sample63.0ms

Algorithm

intervals

Results

26.0ms	54×	body	2560	valid
12.0ms	55×	body	640	valid
9.0ms	32×	body	1280	valid
4.0ms	35×	body	320	valid
2.0ms	64×	body	80	valid
1.0ms	16×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

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

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

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:

3.0ms	(- 1.0 (cos x))
6.0ms	(/ (- 1.0 (cos x)) (* x x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
6.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify57.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (5.0ms)

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

prune86.0ms

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

localize7.0ms

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))

rewrite25.0ms

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:

5.0ms	(/ (- 1.0 (cos x)) x)
13.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms	(- 1.0 (cos x))

series13.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms	(- 1.0 (cos x))

simplify58.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (50.0ms)

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

prune134.0ms

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

localize8.0ms

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))

rewrite40.0ms

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:

3.0ms	(/ (cos x) x)
20.0ms	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
12.0ms	(- (/ 1.0 x) (/ (cos x) x))

series19.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ (cos x) x)
9.0ms	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
7.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify57.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (49.0ms)

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

prune132.0ms

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

localize14.0ms

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)))

rewrite21.0ms

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:

8.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
4.0ms	(* (cos x) (cos x))
3.0ms	(+ 1.0 (cos x))
3.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
3.0ms	(* (cos x) (cos x))
2.0ms	(+ 1.0 (cos x))
5.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (45.0ms)

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

prune101.0ms

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

regimes62.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch28.0ms

Steps

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

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	11
1	34	11

end0.0ms

sample1.7s

Algorithm

intervals

Results

766.0ms	1606×	body	2560	valid
303.0ms	1275×	body	1280	valid
249.0ms	1495×	body	640	valid
96.0ms	868×	body	320	valid
78.0ms	2290×	body	80	valid
37.0ms	466×	body	160	valid

Details

sample63.0ms

simplify6.0ms

prune2.0ms

localize6.0ms

rewrite10.0ms

series9.0ms

simplify57.0ms

prune86.0ms

localize7.0ms

rewrite25.0ms

series13.0ms

simplify58.0ms

prune134.0ms

localize8.0ms

rewrite40.0ms

series19.0ms

simplify57.0ms

prune132.0ms

localize14.0ms

rewrite21.0ms

series25.0ms

simplify52.0ms

prune101.0ms

regimes62.0ms

bsearch28.0ms

simplify1.0ms

end0.0ms

sample1.7s

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