Details

sample61.0ms

Algorithm

intervals

Results

23.0ms	49×	body	1280	valid
15.0ms	40×	body	640	valid
9.0ms	136×	body	80	valid
4.0ms	19×	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: 13.4b

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

rewrite30.0ms

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))

series170.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
78.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify59.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (50.0ms)

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

prune200.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 0.0b

Counts

89 → 10

localize14.0ms

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)))

rewrite26.0ms

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

Counts

3 → 110

Calls

3 calls:

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

series154.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (sin x) (sin (* 0.5 x)))
75.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify69.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	540	1166
1	2701	980
2	5001	956

prune272.0ms

Filtered

119 candidates to 90 candidates (75.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	122	7	129

Merged error: 0b

Counts

129 → 7

localize10.0ms

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))))

rewrite26.0ms

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` `frac-2neg` `clear-num` `add-log-exp`
1×	`associate-*r/` `associate-/r/` `associate-/l/`

Counts

3 → 105

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) 3.0)
5.0ms	(/ (sin x) (sin (* 0.5 x)))
10.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))

series151.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ (sin (* 0.5 x)) 3.0)
42.0ms	(/ (sin x) (sin (* 0.5 x)))
74.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))

simplify74.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	504	1132
1	2553	976
2	5001	950

prune227.0ms

Filtered

114 candidates to 85 candidates (74.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	114	7	121

Merged error: 0b

Counts

121 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (/ 8.0 3.0) (sin (* x 0.5))))
0.6b	(cbrt (* (/ 8.0 3.0) (sin (* x 0.5))))
0.6b	(cbrt (* (/ 8.0 3.0) (sin (* x 0.5))))
0.6b	(* (cbrt (* (/ 8.0 3.0) (sin (* x 0.5)))) (cbrt (* (/ 8.0 3.0) (sin (* x 0.5)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-l/`
7×	`cbrt-prod` `cbrt-div`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

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

series826.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(cbrt (* (/ 8.0 3.0) (sin (* x 0.5))))
200.0ms	(cbrt (* (/ 8.0 3.0) (sin (* x 0.5))))
193.0ms	(cbrt (* (/ 8.0 3.0) (sin (* x 0.5))))
239.0ms	(* (cbrt (* (/ 8.0 3.0) (sin (* x 0.5)))) (cbrt (* (/ 8.0 3.0) (sin (* x 0.5)))))

simplify149.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (141.0ms)

Iter	Nodes	Cost
0	240	772
1	962	655
2	4792	579
3	5002	572

prune225.0ms

Filtered

76 candidates to 57 candidates (75.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	76	7	83

Merged error: 0b

Counts

83 → 7

regimes31.0ms

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	13	9
1	13	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

760.0ms	1563×	body	1280	valid
396.0ms	1233×	body	640	valid
294.0ms	4221×	body	80	valid
136.0ms	645×	body	320	valid
52.0ms	338×	body	160	valid