Details

sample80.0ms

Algorithm

intervals

Results

36.0ms	49×	body	1280	valid
15.0ms	36×	body	640	valid
11.0ms	136×	body	80	valid
8.0ms	26×	body	320	valid
2.0ms	9×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 15.1b

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)))
14.9b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite27.0ms

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)))
6.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
10.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series20.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify58.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (47.0ms)

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

prune177.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	12	89

Merged error: 0.1b

Counts

89 → 12

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (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)))

rewrite24.0ms

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

series23.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ (sin (* 0.5 x)) (sin x))
13.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
4.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify60.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (51.0ms)

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

prune193.0ms

Filtered

73 candidates to 107 candidates (-46.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	109	10	119

Merged error: 0b

Counts

119 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 93

Calls

3 calls:

6.0ms	(/ (sin (* 0.5 x)) 3.0)
4.0ms	(/ (sin (* 0.5 x)) (sin x))
10.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

series21.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify59.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	426	934
1	2116	775
2	5001	753

prune176.0ms

Filtered

73 candidates to 102 candidates (-39.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	103	9	112

Merged error: 0b

Counts

112 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 3.0 (sin (* 0.5 x)))
0.1b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* 8.0 (/ 1 (/ 3.0 (sin (* 0.5 x))))) (/ (sin (* 0.5 x)) (sin x)))
0.2b	(/ 1 (/ 3.0 (sin (* 0.5 x))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
83×	`add-exp-log`
69×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
45×	`add-cbrt-cube`
31×	`div-exp`
30×	`prod-exp`
19×	`associate-/r*`
15×	`cbrt-undiv`
14×	`cbrt-unprod`
13×	`associate-r`
10×	`pow1`
9×	`associate-/l*`
8×	`div-inv`
6×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num`
2×	`frac-times` `associate-*l/` `un-div-inv`
1×	`pow-flip` `associate-l` `associate-/r/` `*-commutative` `inv-pow`

Counts

4 → 183

Calls

4 calls:

4.0ms	(/ 3.0 (sin (* 0.5 x)))
4.0ms	(/ (sin (* 0.5 x)) (sin x))
16.0ms	(* (* 8.0 (/ 1 (/ 3.0 (sin (* 0.5 x))))) (/ (sin (* 0.5 x)) (sin x)))
6.0ms	(/ 1 (/ 3.0 (sin (* 0.5 x))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 3.0 (sin (* 0.5 x)))
6.0ms	(/ (sin (* 0.5 x)) (sin x))
11.0ms	(* (* 8.0 (/ 1 (/ 3.0 (sin (* 0.5 x))))) (/ (sin (* 0.5 x)) (sin x)))
4.0ms	(/ 1 (/ 3.0 (sin (* 0.5 x))))

simplify93.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	763	1838
1	3872	1546
2	5002	1449

prune252.0ms

Filtered

109 candidates to 195 candidates (-78.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	195	9	204

Merged error: 0b

Counts

204 → 9

regimes51.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	9
1	14	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

994.0ms	1505×	body	1280	valid
548.0ms	1280×	body	640	valid
379.0ms	4308×	body	80	valid
174.0ms	605×	body	320	valid
59.0ms	302×	body	160	valid

Details

sample80.0ms

simplify15.0ms

prune3.0ms

localize11.0ms

rewrite27.0ms

series20.0ms

simplify58.0ms

prune177.0ms

localize13.0ms

rewrite24.0ms

series23.0ms

simplify60.0ms

prune193.0ms

localize11.0ms

rewrite23.0ms

series21.0ms

simplify59.0ms

prune176.0ms

localize12.0ms

rewrite37.0ms

series26.0ms

simplify93.0ms

prune252.0ms

regimes51.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

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