Details

sample56.0ms

Algorithm

intervals

Results

19.0ms	35×	body	1280	valid
12.0ms	41×	body	640	valid
9.0ms	144×	body	80	valid
3.0ms	18×	body	320	valid
2.0ms	18×	body	160	valid

simplify25.0ms

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: 14.5b

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)))
14.3b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite31.0ms

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:

9.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
11.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series175.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
81.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify70.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (60.0ms)

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

prune251.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	80	14	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	14	95

Merged error: 0.1b

Counts

95 → 14

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 116

Calls

3 calls:

10.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series165.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
40.0ms	(/ (sin x) (sin (* 0.5 x)))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify79.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	550	1204
1	2727	1016
2	5001	992

prune318.0ms

Filtered

125 candidates to 94 candidates (75.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	128	11	139

Merged error: 0b

Counts

139 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
0.1b	(/ (sin (* 0.5 x)) 3.0)
0.2b	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 145

Calls

4 calls:

7.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
4.0ms	(/ (sin (* 0.5 x)) 3.0)
10.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
35.0ms	(/ (sin (* 0.5 x)) 3.0)
78.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
46.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify86.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	592	1396
1	2961	1212
2	5001	1189

prune336.0ms

Filtered

157 candidates to 117 candidates (74.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	157	11	168

Merged error: 0b

Counts

168 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) 3.0)
0.1b	(/ 1 (sin (* 0.5 x)))
0.2b	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (* (sin x) (/ 1 (sin (* 0.5 x)))))
0.3b	(* (sin x) (/ 1 (sin (* 0.5 x))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
49×	`add-cbrt-cube`
35×	`add-sqr-sqrt`
31×	`div-exp`
30×	`times-frac`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt`
26×	`prod-exp`
18×	`cbrt-undiv`
14×	`cbrt-unprod`
13×	`associate-r`
7×	`pow1` `associate-/r` `associate-/l`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r/` `associate-l*` `clear-num` `unswap-sqr`
2×	`associate-/r/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 142

Calls

4 calls:

4.0ms	(/ (sin (* 0.5 x)) 3.0)
4.0ms	(/ 1 (sin (* 0.5 x)))
11.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (* (sin x) (/ 1 (sin (* 0.5 x)))))
9.0ms	(* (sin x) (/ 1 (sin (* 0.5 x))))

series198.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (sin (* 0.5 x)) 3.0)
35.0ms	(/ 1 (sin (* 0.5 x)))
77.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (* (sin x) (/ 1 (sin (* 0.5 x)))))
47.0ms	(* (sin x) (/ 1 (sin (* 0.5 x))))

simplify91.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	596	1321
1	3094	1049
2	5002	990

prune250.0ms

Filtered

154 candidates to 89 candidates (57.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	156	9	165

Merged error: 0b

Counts

165 → 9

regimes96.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

718.0ms	1519×	body	1280	valid
364.0ms	1243×	body	640	valid
275.0ms	4304×	body	80	valid
124.0ms	628×	body	320	valid
42.0ms	306×	body	160	valid