Details

sample56.0ms

Algorithm

intervals

Results

19.0ms	42×	body	1280	valid
13.0ms	33×	body	640	valid
9.0ms	150×	body	80	valid
3.0ms	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))

rewrite41.0ms

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:

17.0ms	(* (* (/ 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))

series250.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
66.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
95.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify71.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (58.0ms)

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

prune274.0ms

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)))

rewrite28.0ms

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

series181.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
45.0ms	(/ (sin x) (sin (* 0.5 x)))
47.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify83.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (69.0ms)

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

prune366.0ms

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)))

rewrite39.0ms

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)))))
8.0ms	(* (sin x) (/ 1 (sin (* x 0.5))))
8.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1 (sin (* x 0.5)))
92.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (* (sin x) (/ 1 (sin (* x 0.5)))))
44.0ms	(* (sin x) (/ 1 (sin (* x 0.5))))
46.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify98.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (84.0ms)

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

prune321.0ms

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))

rewrite42.0ms

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)))
16.0ms	(* (/ 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)))
4.0ms	(/ 8.0 (cbrt 3.0))

series327.0ms

Counts

4 → 10

Calls

4 calls:

51.0ms	(/ (sin x) (sin (* 0.5 x)))
158.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
118.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
0.0ms	(/ 8.0 (cbrt 3.0))

simplify93.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (77.0ms)

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

prune508.0ms

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

regimes93.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.7s

Algorithm

intervals

Results

685.0ms	1468×	body	1280	valid
380.0ms	1261×	body	640	valid
290.0ms	4314×	body	80	valid
139.0ms	637×	body	320	valid
44.0ms	320×	body	160	valid

Details

sample56.0ms

simplify25.0ms

prune3.0ms

localize11.0ms

rewrite41.0ms

series250.0ms

simplify71.0ms

prune274.0ms

localize15.0ms

rewrite28.0ms

series181.0ms

simplify83.0ms

prune366.0ms

localize13.0ms

rewrite39.0ms

series223.0ms

simplify98.0ms

prune321.0ms

localize19.0ms

rewrite42.0ms

series327.0ms

simplify93.0ms

prune508.0ms

regimes93.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.7s

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