Details

sample54.0ms

Algorithm

intervals

Results

24.0ms	51×	body	2560	valid
11.0ms	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

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: 32.1b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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:

3.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series61.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
43.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify66.0ms

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

prune104.0ms

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: 0.1b

Counts

49 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 1/24 (pow x 2))
0.3b	(* 1/720 (pow x 4))
10.8b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite21.0ms

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:

7.0ms	(* 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)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 1/24 (pow x 2))
42.0ms	(* 1/720 (pow x 4))
43.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify40.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	268	361
1	1205	316
2	5001	310

prune134.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	76	10	86

Merged error: 0.1b

Counts

86 → 10

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 1/24 (pow x 2))
0.3b	(* 1/720 (pow x 4))
10.8b	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

rewrite17.0ms

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` `associate-+r+` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

3 → 67

Calls

3 calls:

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

series113.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* 1/24 (pow x 2))
36.0ms	(* 1/720 (pow x 4))
47.0ms	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

simplify39.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	274	345
1	1103	314
2	5001	314

prune133.0ms

Filtered

76 candidates to 47 candidates (61.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	76	10	86

Merged error: 0.1b

Counts

86 → 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))

rewrite24.0ms

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:

8.0ms	(/ (/ (- 1.0 (cos x)) x) x)
6.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series109.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (/ (- 1.0 (cos x)) x) x)
48.0ms	(/ (- 1.0 (cos x)) x)
19.0ms	(- 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

prune212.0ms

Filtered

156 candidates to 103 candidates (66.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	154	12	166

Merged error: 0.1b

Counts

166 → 12

regimes51.0ms

Accuracy

99.1% (0.3b remaining)

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

bsearch69.0ms

Steps

Iters	Range		Point
9	2.1846438371975785e-05	719.5386143167987	0.03036072037910726
10	-43540924890.08803	-0.0051836583041924315	-0.03355247327065949

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample1.5s

Algorithm

intervals

Results

713.0ms	1545×	body	2560	valid
306.0ms	1353×	body	1280	valid
209.0ms	1461×	body	640	valid
96.0ms	913×	body	320	valid
72.0ms	2252×	body	80	valid
34.0ms	476×	body	160	valid