Details

sample56.0ms

Algorithm

intervals

Results

24.0ms	52×	body	1280	valid
9.0ms	145×	body	80	valid
8.0ms	27×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	12×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	43	9
2	93	9
3	174	9
4	269	9
5	288	9
6	288	9

prune3.0ms

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: 16.9b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
16.7b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
13×	`times-frac`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r`
5×	`associate-*l/`
4×	`pow-prod-down`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 85

Calls

3 calls:

16.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series193.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
45.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
85.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify69.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	412	862
1	2127	656
2	5001	637

prune268.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	11	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 0.1b

Counts

95 → 11

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
28×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
14×	`associate-l`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `associate-*l/`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 104

Calls

3 calls:

5.0ms	(/ (sin (* 0.5 x)) (sin x))
11.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
8.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (sin (* 0.5 x)) (sin x))
86.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify79.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	474	1006
1	2505	814
2	5001	799

prune347.0ms

Filtered

113 candidates to 80 candidates (70.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	7	3	10
Picked	0	1	1
Done	0	0	0
Total	114	10	124

Merged error: 0b

Counts

124 → 10

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 8.0 (sin (* x 0.5))) 3.0)
0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `unswap-sqr`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 100

Calls

3 calls:

6.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
5.0ms	(/ (sin (* 0.5 x)) (sin x))
12.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

series174.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
48.0ms	(/ (sin (* 0.5 x)) (sin x))
88.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	469	1030
1	2437	847
2	5001	823

prune349.0ms

Filtered

109 candidates to 81 candidates (74.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	4	4	8
Picked	0	1	1
Done	1	0	1
Total	110	9	119

Merged error: 0b

Counts

119 → 9

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
0.2b	(/ (sin (* 0.5 x)) (sin x))
0.3b	(* (* 8.0 (sin (* x 0.5))) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-exp-log`
58×	`add-cbrt-cube`
51×	`prod-exp`
42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`*-un-lft-identity` `cbrt-unprod`
25×	`add-cube-cbrt` `div-exp`
17×	`pow1`
14×	`associate-r` `associate-l`
13×	`cbrt-undiv`
9×	`pow-prod-down`
6×	`rec-exp` `1-exp` `unswap-sqr`
5×	`associate-*r/`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`frac-times` `associate-l/` `-commutative`
1×	`frac-2neg` `clear-num`

Counts

3 → 134

Calls

3 calls:

16.0ms	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
5.0ms	(/ (sin (* 0.5 x)) (sin x))
14.0ms	(* (* 8.0 (sin (* x 0.5))) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

series204.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
42.0ms	(/ (sin (* 0.5 x)) (sin x))
92.0ms	(* (* 8.0 (sin (* x 0.5))) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

simplify93.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	647	1480
1	2981	1153
2	5001	1097

prune340.0ms

Filtered

143 candidates to 85 candidates (59.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	145	7	152

Merged error: 0b

Counts

152 → 7

regimes35.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	17	9
2	17	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

745.0ms	1537×	body	1280	valid
378.0ms	1235×	body	640	valid
274.0ms	4306×	body	80	valid
130.0ms	612×	body	320	valid
44.0ms	310×	body	160	valid