Details

sample57.0ms

Algorithm

intervals

Results

30.0ms	64×	body	2560	valid
8.0ms	39×	body	1280	valid
6.0ms	41×	body	640	valid
3.0ms	26×	body	320	valid
2.0ms	71×	body	80	valid
1.0ms	15×	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: 33.5b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
17.7b	(/ (- 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:

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))

simplify67.0ms

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

prune107.0ms

Filtered

48 candidates to 34 candidates (70.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	39	9	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	10	49

Merged error: 0.1b

Counts

49 → 10

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.1b	(* 1/24 (pow x 2))
12.8b	(- (+ (* 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)))

series107.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 1/720 (pow x 4))
29.0ms	(* 1/24 (pow x 2))
42.0ms	(- (+ (* 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

prune157.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	74	11	85

Merged error: 0.1b

Counts

85 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

12.0b	(cbrt (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))
12.8b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
12.8b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
12.8b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
6×	`diff-log`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`cbrt-prod` `sub-neg` `associate--l+` `sum-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 55

Calls

4 calls:

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

series274.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))
46.0ms	(- (+ (* 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)))

simplify109.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	216	713
1	740	653
2	3508	623
3	5001	623

prune201.0ms

Filtered

67 candidates to 48 candidates (71.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	67	11	78

Merged error: 0.1b

Counts

78 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

12.0b	(cbrt (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))
12.8b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
12.8b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
12.8b	(- (+ (pow 1/2 1/3) (* 1/6480 (* (pow 1/2 1/3) (pow x 4)))) (* 1/36 (* (pow 1/2 1/3) (pow x 2))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
6×	`diff-log`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`cbrt-prod` `sub-neg` `associate--l+` `sum-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 55

Calls

4 calls:

10.0ms	(cbrt (- (+ (* 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)))
8.0ms	(- (+ (pow 1/2 1/3) (* 1/6480 (* (pow 1/2 1/3) (pow x 4)))) (* 1/36 (* (pow 1/2 1/3) (pow x 2))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))
43.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
48.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
204.0ms	(- (+ (pow 1/2 1/3) (* 1/6480 (* (pow 1/2 1/3) (pow x 4)))) (* 1/36 (* (pow 1/2 1/3) (pow x 2))))

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	293	831
1	1117	761
2	5002	744

prune252.0ms

Filtered

67 candidates to 48 candidates (71.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	67	11	78

Merged error: 0.1b

Counts

78 → 11

regimes99.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.9b

bsearch57.0ms

Steps

Iters	Range		Point
6	0.018000635171863108	0.09117784756913819	0.03010910821075468
10	-1421.6155834850151	-1.485944467815708e-07	-0.03323288645356819

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	10
1	29	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

762.0ms	1643×	body	2560	valid
290.0ms	1221×	body	1280	valid
215.0ms	1450×	body	640	valid
97.0ms	914×	body	320	valid
79.0ms	2291×	body	80	valid
41.0ms	481×	body	160	valid