Details

sample56.0ms

Algorithm

intervals

Results

26.0ms	52×	body	1280	valid
8.0ms	145×	body	80	valid
8.0ms	27×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	12×	body	160	valid

simplify22.0ms

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

prune2.0ms

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: 16.9b

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)))
16.7b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite29.0ms

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×	`associate-/r*` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 79

Calls

3 calls:

9.0ms	(* (* (/ 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))

series173.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
79.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify58.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	402	818
1	2097	614
2	5002	599

prune210.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 0.1b

Counts

89 → 11

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
28×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
14×	`associate-l`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `associate-*l/`
3×	`associate-/r` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 98

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
10.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (sin (* 0.5 x)) (sin x))
72.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify69.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	463	970
1	2477	779
2	5002	764

prune263.0ms

Filtered

107 candidates to 74 candidates (69.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	109	9	118

Merged error: 0b

Counts

118 → 9

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`add-log-exp`
2×	`frac-2neg` `clear-num` `unswap-sqr`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 94

Calls

3 calls:

6.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
4.0ms	(/ (sin (* 0.5 x)) (sin x))
11.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

series158.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
38.0ms	(/ (sin (* 0.5 x)) (sin x))
80.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	458	994
1	2409	812
2	5001	788

prune259.0ms

Filtered

103 candidates to 75 candidates (72.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	103	9	112

Merged error: 0b

Counts

112 → 9

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-exp-log`
58×	`add-cbrt-cube`
51×	`prod-exp`
42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`*-un-lft-identity` `cbrt-unprod`
25×	`add-cube-cbrt` `div-exp`
17×	`pow1`
14×	`associate-r` `associate-l`
13×	`cbrt-undiv`
9×	`pow-prod-down`
6×	`rec-exp` `1-exp` `unswap-sqr`
5×	`associate-*r/`
3×	`associate-/r` `div-inv` `associate-/l` `add-log-exp`
2×	`frac-times` `associate-l/` `-commutative`
1×	`frac-2neg` `clear-num`

Counts

3 → 128

Calls

3 calls:

10.0ms	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
4.0ms	(/ (sin (* 0.5 x)) (sin x))
11.0ms	(* (* 8.0 (sin (* x 0.5))) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

series174.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
37.0ms	(/ (sin (* 0.5 x)) (sin x))
78.0ms	(* (* 8.0 (sin (* x 0.5))) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

simplify79.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	635	1440
1	2955	1113
2	5001	1057

prune268.0ms

Filtered

137 candidates to 80 candidates (58.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	137	9	146

Merged error: 0b

Counts

146 → 9

regimes36.0ms

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	15	9
1	17	9
2	17	9

end0.0ms

sample1.6s

Algorithm

intervals

Results

699.0ms	1537×	body	1280	valid
381.0ms	1235×	body	640	valid
272.0ms	4306×	body	80	valid
119.0ms	612×	body	320	valid
42.0ms	310×	body	160	valid