Details

sample59.0ms

Algorithm

intervals

Results

21.0ms	42×	body	1280	valid
11.0ms	33×	body	640	valid
11.0ms	150×	body	80	valid
4.0ms	18×	body	320	valid
2.0ms	13×	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: 16.8b

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)))
16.6b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite37.0ms

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:

15.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
8.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series192.0ms

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)))
84.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify66.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (57.0ms)

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

prune269.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	13	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 0.1b

Counts

95 → 13

localize15.0ms

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)))

rewrite32.0ms

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:

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

series176.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
49.0ms	(/ (sin x) (sin (* 0.5 x)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify80.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (67.0ms)

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

prune350.0ms

Filtered

125 candidates to 96 candidates (76.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	7	5	12
Picked	0	1	1
Done	0	0	0
Total	127	11	138

Merged error: 0b

Counts

138 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin (* x 0.5)))
0.2b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (* (sin x) (/ 1 (sin (* x 0.5)))))
0.3b	(* (sin x) (/ 1 (sin (* x 0.5))))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-exp-log`
52×	`add-cbrt-cube`
40×	`add-sqr-sqrt`
31×	`times-frac` `div-exp`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt` `prod-exp`
18×	`cbrt-undiv`
16×	`associate-r` `associate-l` `cbrt-unprod`
9×	`pow1`
5×	`rec-exp` `1-exp` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r/` `un-div-inv` `*-commutative`
1×	`pow-flip` `associate-/l/` `inv-pow`

Counts

4 → 147

Calls

4 calls:

4.0ms	(/ 1 (sin (* x 0.5)))
13.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (* (sin x) (/ 1 (sin (* x 0.5)))))
9.0ms	(* (sin x) (/ 1 (sin (* x 0.5))))
12.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (sin (* x 0.5)))
88.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (* (sin x) (/ 1 (sin (* x 0.5)))))
50.0ms	(* (sin x) (/ 1 (sin (* x 0.5))))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify94.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	618	1367
1	3234	1034
2	5002	973

prune333.0ms

Filtered

159 candidates to 95 candidates (59.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	160	10	170

Merged error: 0b

Counts

170 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (sin (* 0.5 x)))
0.3b	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
0.4b	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
1.0b	(/ 8.0 (cbrt 3.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
51×	`add-sqr-sqrt`
50×	`times-frac`
46×	`prod-exp`
43×	`add-cube-cbrt` `*-un-lft-identity`
38×	`add-cbrt-cube`
29×	`associate-l`
22×	`cbrt-prod` `div-exp`
20×	`cbrt-unprod`
12×	`cbrt-undiv`
11×	`pow1`
9×	`associate-/r*`
6×	`rec-exp` `1-exp` `associate-/l*`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 167

Calls

4 calls:

5.0ms	(/ (sin x) (sin (* 0.5 x)))
20.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
9.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
5.0ms	(/ 8.0 (cbrt 3.0))

series306.0ms

Counts

4 → 10

Calls

4 calls:

43.0ms	(/ (sin x) (sin (* 0.5 x)))
148.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
115.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
0.0ms	(/ 8.0 (cbrt 3.0))

simplify95.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	656	1522
1	2890	1259
2	5002	1169

prune478.0ms

Filtered

177 candidates to 117 candidates (66.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	177	10	187

Merged error: 0b

Counts

187 → 10

regimes85.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	9
1	16	9
2	16	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

734.0ms	1468×	body	1280	valid
404.0ms	1261×	body	640	valid
329.0ms	4314×	body	80	valid
146.0ms	637×	body	320	valid
49.0ms	320×	body	160	valid