Details

sample60.0ms

Algorithm

intervals

Results

27.0ms	51×	body	2560	valid
12.0ms	51×	body	1280	valid
6.0ms	41×	body	640	valid
3.0ms	26×	body	320	valid
2.0ms	63×	body	80	valid
2.0ms	24×	body	160	valid

simplify8.0ms

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: 32.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
15.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

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

series65.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify33.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317

prune173.0ms

Filtered

64 candidates to 43 candidates (67.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	54	10	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	10	65

Merged error: 0.1b

Counts

65 → 10

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(* 1/24 (pow x 2))
11.1b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 39

Calls

2 calls:

5.0ms	(* 1/24 (pow x 2))
1.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series71.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* 1/24 (pow x 2))
48.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify106.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	139	194
1	532	171
2	2601	171
3	5001	170

prune93.0ms

Filtered

45 candidates to 30 candidates (66.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	45	10	55

Merged error: 0.1b

Counts

55 → 10

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))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
110×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

9.0ms	(/ (/ (- 1.0 (cos x)) x) x)
10.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series104.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (/ (- 1.0 (cos x)) x) x)
46.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify60.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	592	1453
1	2212	1292
2	5001	1283

prune239.0ms

Filtered

174 candidates to 113 candidates (64.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	170	4	174
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	172	12	184

Merged error: 0.1b

Counts

184 → 12

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

338×	`times-frac`
287×	`add-sqr-sqrt`
267×	`*-un-lft-identity`
227×	`add-cube-cbrt`
169×	`prod-diff`
39×	`div-inv`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/l*`
13×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`distribute-rgt-out--` `add-log-exp`
4×	`associate-/l/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub`

Counts

3 → 306

Calls

3 calls:

29.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
4.0ms	(/ (cos x) x)
18.0ms	(- (/ 1.0 x) (/ (cos x) x))

series188.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
29.0ms	(/ (cos x) x)
62.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify114.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	1009	6352
1	3221	4216
2	5001	3627

prune302.0ms

Filtered

315 candidates to 139 candidates (44.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	313	2	315
Fresh	2	7	9
Picked	0	1	1
Done	1	1	2
Total	316	11	327

Merged error: 0.1b

Counts

327 → 11

regimes51.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.7b

bsearch68.0ms

Steps

Iters	Range		Point
9	2.1846438371975785e-05	719.5386143167987	0.03251997843777283
10	-43540924890.08803	-0.0051836583041924315	-0.03355247327065949

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	32	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

742.0ms	1545×	body	2560	valid
317.0ms	1353×	body	1280	valid
228.0ms	1461×	body	640	valid
99.0ms	913×	body	320	valid
81.0ms	2252×	body	80	valid
36.0ms	476×	body	160	valid