Details

sample51.0ms

Algorithm

intervals

Results

19.0ms	45×	body	2560	valid
11.0ms	46×	body	1280	valid
7.0ms	48×	body	640	valid
4.0ms	38×	body	320	valid
2.0ms	65×	body	80	valid
1.0ms	14×	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: 32.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
13.6b	(/ (- 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))

series65.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify59.0ms

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

prune95.0ms

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:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
12.2b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite18.0ms

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)))

series104.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 1/720 (pow x 4))
26.0ms	(* 1/24 (pow x 2))
42.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify38.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (32.0ms)

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

prune121.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 0.1b

Counts

84 → 9

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))

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:

8.0ms	(/ (/ (- 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:

44.0ms	(/ (/ (- 1.0 (cos x)) x) x)
42.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify52.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (39.0ms)

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

prune227.0ms

Filtered

156 candidates to 103 candidates (66.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	151	5	156
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	154	11	165

Merged error: 0.1b

Counts

165 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (log (exp (- 1.0 (cos x)))) x)
0.2b	(exp (- 1.0 (cos x)))
1.8b	(- 1.0 (cos x))
1.9b	(log (exp (- 1.0 (cos x))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

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

series123.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
44.0ms	(exp (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))
18.0ms	(log (exp (- 1.0 (cos x))))

simplify121.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	304	679
1	935	604
2	3744	589
3	5001	587

prune164.0ms

Filtered

115 candidates to 78 candidates (67.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	115	11	126

Merged error: 0.1b

Counts

126 → 11

regimes98.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.5b

bsearch78.0ms

Steps

Iters	Range		Point
10	8.416769919470913e-17	1.2368608357549227	0.03505810655614032
11	-55383.34621353126	-7.66540900750845e-16	-0.029675694574374373

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	16
1	30	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

754.0ms	1563×	body	2560	valid
286.0ms	1204×	body	1280	valid
226.0ms	1457×	body	640	valid
104.0ms	942×	body	320	valid
83.0ms	2315×	body	80	valid
45.0ms	519×	body	160	valid