Details

sample56.0ms

Algorithm

intervals

Results

25.0ms	53×	body	2560	valid
8.0ms	36×	body	1280	valid
7.0ms	44×	body	640	valid
5.0ms	36×	body	320	valid
2.0ms	70×	body	80	valid
1.0ms	17×	body	160	valid

simplify7.0ms

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 (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: 31.2b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
17.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

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:

4.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
41.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify63.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

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

prune110.0ms

Filtered

48 candidates to 34 candidates (70.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	35	13	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	13	49

Merged error: 0.2b

Counts

49 → 13

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.8b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

11.0ms	(/ (/ (- 1.0 (cos x)) x) x)
6.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series104.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (/ (- 1.0 (cos x)) x) x)
41.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify54.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	531	1270
1	1899	1197
2	5001	1186

prune246.0ms

Filtered

156 candidates to 103 candidates (66.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	148	8	156
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	156	13	169

Merged error: 0.2b

Counts

169 → 13

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
0.1b	(/ 1 (/ x (- 1.0 (cos x))))
0.1b	(/ x (- 1.0 (cos x)))
1.8b	(- 1.0 (cos x))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

774×	`times-frac`
443×	`add-sqr-sqrt` `*-un-lft-identity`
337×	`add-cube-cbrt`
74×	`associate-/l*`
53×	`distribute-lft-out--` `difference-of-squares`
39×	`associate-/r/`
36×	`add-exp-log`
29×	`associate-/r*`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
18×	`flip3--` `flip--`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`rec-exp` `1-exp`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `associate-/l/` `inv-pow`

Counts

4 → 455

Calls

4 calls:

21.0ms	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
9.0ms	(/ 1 (/ x (- 1.0 (cos x))))
5.0ms	(/ x (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series166.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
51.0ms	(/ 1 (/ x (- 1.0 (cos x))))
44.0ms	(/ x (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify80.0ms

Algorithm

egg-herbie

Counts

467 → 467

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1544	5230
1	5001	4699

prune610.0ms

Filtered

467 candidates to 253 candidates (54.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	464	3	467
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	466	14	480

Merged error: 0.1b

Counts

480 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.4b	(pow (cos x) 3)
0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.6b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
12×	`pow1`
11×	`add-cube-cbrt`
9×	`sqr-pow`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`sqr-cos`
1×	`difference-cubes` `+-commutative` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `associate-+l+` `distribute-rgt-out` `flip3--` `pow-pow` `flip3-+` `pow-plus` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

5.0ms	(* (cos x) (cos x))
3.0ms	(pow (cos x) 3)
5.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
15.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series133.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (cos x) (cos x))
27.0ms	(pow (cos x) 3)
43.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify83.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	380	592
1	1866	548
2	5001	523

prune211.0ms

Filtered

109 candidates to 63 candidates (57.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	5	7	12
Picked	1	0	1
Done	1	0	1
Total	112	11	123

Merged error: 0.1b

Counts

123 → 11

regimes55.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch100.0ms

Steps

Iters	Range		Point
10	0.005370866090842012	4.21737757242384e+15	0.03183279579310355
10	-3.4402871636077537	-5.738045557766166e-18	-0.029450602391327626

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	48
1	64	48

end0.0ms

sample1.7s

Algorithm

intervals

Results

769.0ms	1588×	body	2560	valid
332.0ms	1258×	body	1280	valid
230.0ms	1455×	body	640	valid
112.0ms	961×	body	320	valid
86.0ms	2270×	body	80	valid
38.0ms	468×	body	160	valid