Details

sample59.0ms

Algorithm

intervals

Results

28.0ms	58×	body	2560	valid
11.0ms	46×	body	1280	valid
7.0ms	47×	body	640	valid
3.0ms	28×	body	320	valid
3.0ms	67×	body	80	valid
1.0ms	10×	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: 34.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.4b	(- 1.0 (cos x))
16.8b	(/ (- 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))

simplify64.0ms

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

prune111.0ms

Filtered

48 candidates to 34 candidates (70.8%)

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

localize10.0ms

Local error

Found 3 expressions with local error:

0.4b	(* 1/24 (pow x 2))
0.5b	(* 1/720 (pow x 4))
12.0b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 1/24 (pow x 2))
5.0ms	(* 1/720 (pow x 4))
7.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series103.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* 1/24 (pow x 2))
39.0ms	(* 1/720 (pow x 4))
41.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify41.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	268	347
1	1132	316
2	5001	310

prune145.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	74	10	84

Merged error: 0.1b

Counts

84 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))))
0.4b	(* 1/24 (pow x 2))
0.5b	(* 1/720 (pow x 4))
12.0b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`log-prod` `associate-l` `prod-exp`
5×	`pow1`
4×	`log-pow` `sqr-pow`
3×	`exp-prod` `exp-sum`
2×	`pow-to-exp` `sub-neg` `diff-log` `pow-exp` `associate--l+` `*-commutative` `cbrt-unprod` `unpow2`
1×	`log-div` `flip3--` `exp-diff` `rem-log-exp` `sum-log` `flip--`

Counts

4 → 85

Calls

4 calls:

6.0ms	(log (exp (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))))
5.0ms	(* 1/24 (pow x 2))
9.0ms	(* 1/720 (pow x 4))
7.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(log (exp (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))))
24.0ms	(* 1/24 (pow x 2))
40.0ms	(* 1/720 (pow x 4))
41.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify44.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	303	537
1	1254	484
2	5001	478

prune207.0ms

Filtered

97 candidates to 60 candidates (61.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Merged error: 0.1b

Counts

107 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.4b	(- 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))

series106.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (/ (- 1.0 (cos x)) x) x)
47.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify54.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (41.0ms)

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

prune224.0ms

Filtered

156 candidates to 104 candidates (66.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	3	4	7
Picked	1	0	1
Done	0	2	2
Total	156	10	166

Merged error: 0.1b

Counts

166 → 10

regimes52.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.8b

bsearch86.0ms

Steps

Iters	Range		Point
10	0.0002141056345597589	3206628.0142593775	0.0320878512219627
11	-4.816760182774211e+16	-0.0014803844373699059	-0.034045814957462915

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	14
1	34	14

end0.0ms

sample1.8s

Algorithm

intervals

Results

772.0ms	1566×	body	2560	valid
308.0ms	1274×	body	1280	valid
227.0ms	1439×	body	640	valid
184.0ms	455×	body	160	valid
106.0ms	958×	body	320	valid
81.0ms	2308×	body	80	valid