Details

sample55.0ms

Algorithm

intervals

Results

22.0ms	50×	body	2560	valid
13.0ms	43×	body	1280	valid
6.0ms	44×	body	640	valid
3.0ms	33×	body	320	valid
3.0ms	75×	body	80	valid
1.0ms	11×	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: 31.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.7b	(/ (- 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))

series64.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- 1.0 (cos x))
42.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (26.0ms)

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

prune123.0ms

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

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)
2.1b	(- 1.0 (cos x))

rewrite27.0ms

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

series108.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (/ (- 1.0 (cos x)) x) x)
47.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify66.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (46.0ms)

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

prune245.0ms

Filtered

174 candidates to 113 candidates (64.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	168	6	174
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	173	11	184

Merged error: 0.0b

Counts

184 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) x)
0.2b	(log (- 1.0 (cos x)))
0.3b	(exp (log (- 1.0 (cos x))))
2.1b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`log-prod`
25×	`exp-sum`
24×	`times-frac`
9×	`prod-diff`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `flip--` `log1p-expm1-u`
3×	`fma-neg` `associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 118

Calls

4 calls:

8.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
4.0ms	(log (- 1.0 (cos x)))
5.0ms	(exp (log (- 1.0 (cos x))))
8.0ms	(- 1.0 (cos x))

series157.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
73.0ms	(log (- 1.0 (cos x)))
18.0ms	(exp (log (- 1.0 (cos x))))
18.0ms	(- 1.0 (cos x))

simplify39.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	361	939
1	1100	784
2	5002	738

prune221.0ms

Filtered

130 candidates to 86 candidates (66.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	131	10	141

Merged error: 0.0b

Counts

141 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow E (log (- 1.0 (cos x)))) x)
0.2b	(log (- 1.0 (cos x)))
0.3b	(pow E (log (- 1.0 (cos x))))
2.1b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
36×	`times-frac`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
9×	`prod-diff`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `log1p-expm1-u` `pow-sub`
3×	`fma-neg` `associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 144

Calls

4 calls:

8.0ms	(/ (pow E (log (- 1.0 (cos x)))) x)
4.0ms	(log (- 1.0 (cos x)))
5.0ms	(pow E (log (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series598.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(/ (pow E (log (- 1.0 (cos x)))) x)
75.0ms	(log (- 1.0 (cos x)))
193.0ms	(pow E (log (- 1.0 (cos x))))
18.0ms	(- 1.0 (cos x))

simplify53.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	484	1312
1	1789	1102
2	5001	1056

prune278.0ms

Filtered

156 candidates to 110 candidates (70.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	154	12	166

Merged error: 0.0b

Counts

166 → 12

regimes56.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch74.0ms

Steps

Iters	Range		Point
9	0.0002199982819353488	137964.03928948785	0.029919708739934884
9	-0.41295360884021565	-1.1902930357079885e-07	-0.0298241019635357

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	25
1	43	25
2	43	25

end0.0ms

sample1.6s

Algorithm

intervals

Results

748.0ms	1639×	body	2560	valid
283.0ms	1248×	body	1280	valid
200.0ms	1438×	body	640	valid
99.0ms	928×	body	320	valid
73.0ms	2267×	body	80	valid
34.0ms	480×	body	160	valid