Details

sample144.0ms

Algorithm

intervals

Results

78.0ms	64×	body	2560	valid
41.0ms	91×	body	1280	valid
11.0ms	50×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	10×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	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

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

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

series60.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify81.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune153.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	43	15	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	15	59

Merged error: 0.2b

Counts

59 → 15

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b	(* 1/24 (pow x 3))
0.3b	(* 1/240 (pow x 5))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`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×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

8.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
6.0ms	(* 1/24 (pow x 3))
5.0ms	(* 1/240 (pow x 5))

series145.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
35.0ms	(* 1/24 (pow x 3))
51.0ms	(* 1/240 (pow x 5))

simplify47.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	301	375
1	1301	346
2	5001	346

prune186.0ms

Filtered

78 candidates to 49 candidates (62.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	78	15	93

Merged error: 0.2b

Counts

93 → 15

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.1b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
1.5b	(- 1.0 (cos x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`flip3--` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

4.0ms	(/ 1 (sin x))
10.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
4.0ms	(- 1.0 (cos x))

series69.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1 (sin x))
34.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
23.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	320	548
1	1393	482
2	5001	456

prune170.0ms

Filtered

96 candidates to 56 candidates (58.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	5	8	13
Picked	1	0	1
Done	0	1	1
Total	98	13	111

Merged error: 0.2b

Counts

111 → 13

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sin x) -1)
0.1b	(* (- 1.0 (cos x)) (pow (sin x) -1))
1.5b	(- 1.0 (cos x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`add-exp-log`
8×	`add-cube-cbrt`
7×	`unpow-prod-down` `associate-r`
5×	`unpow-1` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`pow-unpow` `flip3--` `prod-exp` `flip--` `unswap-sqr` `sqr-pow`
2×	`frac-times` `pow-to-exp` `associate-*l/` `pow-exp` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-pow` `diff-log` `associate-r/` `un-div-inv` `-commutative` `cbrt-unprod`

Counts

3 → 65

Calls

3 calls:

2.0ms	(pow (sin x) -1)
8.0ms	(* (- 1.0 (cos x)) (pow (sin x) -1))
4.0ms	(- 1.0 (cos x))

series70.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(pow (sin x) -1)
39.0ms	(* (- 1.0 (cos x)) (pow (sin x) -1))
19.0ms	(- 1.0 (cos x))

simplify39.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	259	403
1	1119	373
2	5002	366

prune137.0ms

Filtered

74 candidates to 50 candidates (67.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	75	12	87

Merged error: 0.2b

Counts

87 → 12

regimes110.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 32.0b

bsearch63.0ms

Steps

Iters	Range		Point
6	0.018000635171863108	0.09117784756913819	0.027293184248221757
10	-1421.6155834850151	-1.485944467815708e-07	-0.020610258751472033

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	19
1	34	19

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.2s	1640×	body	2560	valid
1.2s	2761×	body	1280	valid
639.0ms	1824×	body	640	valid
159.0ms	913×	body	320	valid
56.0ms	483×	body	160	valid
25.0ms	376×	body	80	valid
10.0ms	3×	body	5120	valid