Details

sample61.0ms

Algorithm

intervals

Results

24.0ms	49×	body	1280	valid
12.0ms	40×	body	640	valid
9.0ms	136×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	12×	body	160	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 13.4b

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)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
13.3b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite39.0ms

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)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
13.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series182.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
79.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify76.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (65.0ms)

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

prune247.0ms

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: 0.0b

Counts

95 → 11

localize15.0ms

Local error

Found 3 expressions with local error:

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

5.0ms	(/ (sin x) (sin (* 0.5 x)))
15.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
8.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (sin x) (sin (* 0.5 x)))
82.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify88.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (72.0ms)

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

prune336.0ms

Filtered

125 candidates to 96 candidates (76.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Merged error: 0b

Counts

136 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
5×	`div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-*r/` `associate-/r/` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) 3.0)
5.0ms	(/ (sin x) (sin (* 0.5 x)))
11.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))

series162.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (sin (* 0.5 x)) 3.0)
44.0ms	(/ (sin x) (sin (* 0.5 x)))
80.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))

simplify84.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	514	1168
1	2579	1010
2	5002	984

prune274.0ms

Filtered

120 candidates to 91 candidates (75.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	120	8	128

Merged error: 0b

Counts

128 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

313×	`add-exp-log`
134×	`prod-exp`
125×	`div-exp`
122×	`add-cbrt-cube`
72×	`times-frac`
59×	`cbrt-undiv`
57×	`add-sqr-sqrt`
56×	`cbrt-unprod`
49×	`add-cube-cbrt` `*-un-lft-identity`
29×	`associate-l`
22×	`cbrt-prod`
19×	`associate-/r*`
18×	`rec-exp` `1-exp`
11×	`pow1`
7×	`associate-*l/`
6×	`div-inv`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-r/` `clear-num` `-commutative`
1×	`associate-/r/`

Counts

4 → 245

Calls

4 calls:

24.0ms	(/ (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin x) (sin (* 0.5 x))))
16.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
13.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
5.0ms	(/ 8.0 (cbrt 3.0))

series422.0ms

Counts

4 → 10

Calls

4 calls:

170.0ms	(/ (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin x) (sin (* 0.5 x))))
139.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
113.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
0.0ms	(/ 8.0 (cbrt 3.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1140	3561
1	5001	2807

prune553.0ms

Filtered

255 candidates to 147 candidates (57.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	255	8	263

Merged error: 0b

Counts

263 → 8

regimes74.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

778.0ms	1563×	body	1280	valid
403.0ms	1233×	body	640	valid
307.0ms	4221×	body	80	valid
140.0ms	645×	body	320	valid
53.0ms	338×	body	160	valid