Details

sample51.0ms

Algorithm

intervals

Results

21.0ms	48×	body	2560	valid
10.0ms	45×	body	1280	valid
7.0ms	54×	body	640	valid
2.0ms	26×	body	320	valid
2.0ms	65×	body	80	valid
1.0ms	18×	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: 32.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1.0 (cos x))
14.6b	(/ (- 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))

simplify65.0ms

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

prune112.0ms

Filtered

48 candidates to 34 candidates (70.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	37	11	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	11	49

Merged error: 0.0b

Counts

49 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
12.4b	(- (+ (* 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	(* 1/720 (pow x 4))
5.0ms	(* 1/24 (pow x 2))
7.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* 1/720 (pow x 4))
24.0ms	(* 1/24 (pow x 2))
47.0ms	(- (+ (* 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

prune140.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	75	11	86

Merged error: 0.0b

Counts

86 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

7.7b	(sqrt (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))
7.7b	(sqrt (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))
12.4b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
12.4b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `diff-log` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate--l+` `sum-log`

Counts

4 → 58

Calls

4 calls:

6.0ms	(sqrt (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))
6.0ms	(sqrt (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))
7.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
7.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))
104.0ms	(sqrt (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))
41.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
45.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify172.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	202	748
1	828	692
2	4536	678
3	5002	678

prune190.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	70	11	81

Merged error: 0.0b

Counts

81 → 11

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.2b	(- 1.0 (cos x))

rewrite26.0ms

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))

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))

simplify56.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (42.0ms)

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

prune220.0ms

Filtered

156 candidates to 104 candidates (66.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	155	12	167

Merged error: 0.0b

Counts

167 → 12

regimes100.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.7b

bsearch61.0ms

Steps

Iters	Range		Point
7	0.00999808388340962	0.475758948552502	0.030798941289724838
9	-164485.30314980465	-0.009598081335721272	-0.03106715975092916

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	11
1	30	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

738.0ms	1621×	body	2560	valid
268.0ms	1232×	body	1280	valid
224.0ms	1497×	body	640	valid
101.0ms	946×	body	320	valid
68.0ms	2270×	body	80	valid
35.0ms	434×	body	160	valid