Details

sample60.0ms

Algorithm

intervals

Results

20.0ms	42×	body	1280	valid
14.0ms	150×	body	80	valid
10.0ms	33×	body	640	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

localize12.0ms

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))

rewrite33.0ms

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:

10.0ms	(* (* (/ 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))

series210.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
44.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
95.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify66.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (56.0ms)

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

prune282.0ms

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)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
47.0ms	(/ (sin x) (sin (* 0.5 x)))
51.0ms	(* (/ 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

prune370.0ms

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

series240.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 1 (sin (* x 0.5)))
97.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (* (sin x) (/ 1 (sin (* x 0.5)))))
48.0ms	(* (sin x) (/ 1 (sin (* x 0.5))))
50.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify96.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (82.0ms)

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

localize21.0ms

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))

rewrite43.0ms

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)))
17.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
10.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
5.0ms	(/ 8.0 (cbrt 3.0))

series359.0ms

Counts

4 → 10

Calls

4 calls:

56.0ms	(/ (sin x) (sin (* 0.5 x)))
174.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
129.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
0.0ms	(/ 8.0 (cbrt 3.0))

simplify94.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (78.0ms)

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

prune499.0ms

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

regimes92.0ms

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 (0.0ms)

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

end0.0ms

sample1.7s

Algorithm

intervals

Results

709.0ms	1468×	body	1280	valid
390.0ms	1261×	body	640	valid
301.0ms	4314×	body	80	valid
131.0ms	637×	body	320	valid
52.0ms	320×	body	160	valid

Details

sample60.0ms

simplify25.0ms

prune3.0ms

localize12.0ms

rewrite33.0ms

series210.0ms

simplify66.0ms

prune282.0ms

localize15.0ms

rewrite28.0ms

series194.0ms

simplify79.0ms

prune370.0ms

localize13.0ms

rewrite39.0ms

series240.0ms

simplify96.0ms

prune321.0ms

localize21.0ms

rewrite43.0ms

series359.0ms

simplify94.0ms

prune499.0ms

regimes92.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.7s

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