Details

sample57.0ms

Algorithm

intervals

Results

21.0ms	45×	body	1280	valid
14.0ms	48×	body	640	valid
9.0ms	137×	body	80	valid
3.0ms	13×	body	320	valid
2.0ms	13×	body	160	valid

simplify24.0ms

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: 14.0b

Counts

2 → 1

localize18.0ms

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)))
13.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite32.0ms

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))

series195.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
89.0ms	(/ (* (* (/ 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

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

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

rewrite27.0ms

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)))

series178.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(/ (* (/ 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)))

simplify76.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (64.0ms)

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 (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

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (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)))

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:

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

series179.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (sin (* 0.5 x)) 3.0)
88.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
50.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	514	1168
1	2579	1010
2	5001	984

prune314.0ms

Filtered

120 candidates to 91 candidates (75.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	120	11	131

Merged error: 0b

Counts

131 → 11

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

7.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
10.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
5.0ms	(/ (sin x) (sin (* 0.5 x)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
89.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
52.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify74.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	433	924
1	2228	739
2	5002	723

prune243.0ms

Filtered

100 candidates to 71 candidates (71.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	100	11	111

Merged error: 0b

Counts

111 → 11

regimes47.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

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

736.0ms	1494×	body	1280	valid
385.0ms	1288×	body	640	valid
276.0ms	4313×	body	80	valid
140.0ms	621×	body	320	valid
46.0ms	284×	body	160	valid