Details

sample53.0ms

Algorithm

intervals

Results

23.0ms	50×	body	2560	valid
10.0ms	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

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: 31.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

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

series66.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
48.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify62.0ms

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

prune105.0ms

Filtered

48 candidates to 34 candidates (70.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	38	10	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	10	49

Merged error: 0.1b

Counts

49 → 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))

rewrite25.0ms

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:

9.0ms	(/ (/ (- 1.0 (cos x)) x) x)
6.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series105.0ms

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))

simplify56.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (38.0ms)

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

prune223.0ms

Filtered

156 candidates to 102 candidates (65.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	150	6	156
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	155	11	166

Merged error: 0.0b

Counts

166 → 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))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`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 → 98

Calls

4 calls:

8.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
3.0ms	(log (- 1.0 (cos x)))
5.0ms	(exp (log (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series156.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
73.0ms	(log (- 1.0 (cos x)))
18.0ms	(exp (log (- 1.0 (cos x))))
22.0ms	(- 1.0 (cos x))

simplify94.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	297	749
1	840	685
2	3040	643
3	5002	631

prune194.0ms

Filtered

110 candidates to 73 candidates (66.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 0.0b

Counts

121 → 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

47×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `pow-sub`
3×	`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 → 124

Calls

4 calls:

13.0ms	(/ (pow E (log (- 1.0 (cos x)))) x)
3.0ms	(log (- 1.0 (cos x)))
5.0ms	(pow E (log (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series605.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(/ (pow E (log (- 1.0 (cos x)))) x)
75.0ms	(log (- 1.0 (cos x)))
196.0ms	(pow E (log (- 1.0 (cos x))))
18.0ms	(- 1.0 (cos x))

simplify46.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	418	1118
1	1495	999
2	5001	953

prune251.0ms

Filtered

136 candidates to 97 candidates (71.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	134	12	146

Merged error: 0.0b

Counts

146 → 12

regimes192.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch70.0ms

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	47	27
1	49	27
2	49	27

end0.0ms

sample1.6s

Algorithm

intervals

Results

777.0ms	1639×	body	2560	valid
284.0ms	1248×	body	1280	valid
212.0ms	1438×	body	640	valid
101.0ms	928×	body	320	valid
71.0ms	2267×	body	80	valid
35.0ms	480×	body	160	valid