Details

sample56.0ms

Algorithm

intervals

Results

20.0ms	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

simplify17.0ms

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

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

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

rewrite35.0ms

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:

15.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
10.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series176.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
74.0ms	(/ (* (* (/ 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 (50.0ms)

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

prune230.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	13	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	13	89

Merged error: 0.1b

Counts

89 → 13

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)))

rewrite28.0ms

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:

12.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series161.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
39.0ms	(/ (sin x) (sin (* 0.5 x)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify66.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (54.0ms)

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

prune314.0ms

Filtered

119 candidates to 89 candidates (74.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Merged error: 0b

Counts

132 → 10

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)))

rewrite23.0ms

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

Counts

3 → 85

Calls

3 calls:

7.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
9.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
4.0ms	(/ (sin x) (sin (* 0.5 x)))

series180.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
78.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
46.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify58.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	423	884
1	2206	701
2	5001	685

prune231.0ms

Filtered

94 candidates to 65 candidates (69.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	95	9	104

Merged error: 0b

Counts

104 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 8.0 (sin (* x 0.5))) (* (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)) 3.0))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.3b	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
0.3b	(pow (/ (sin x) (sin (* 0.5 x))) 3)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
21×	`add-exp-log`
19×	`add-cbrt-cube`
6×	`cbrt-undiv` `div-exp` `div-inv`
5×	`pow1`
4×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `add-log-exp`
3×	`cube-div` `pow-unpow`
2×	`cube-mult` `cbrt-div` `frac-2neg` `unpow3` `pow-exp` `clear-num` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `associate-*l/` `associate-/r/` `rem-cbrt-cube`

Counts

4 → 137

Calls

4 calls:

13.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)) 3.0))
5.0ms	(/ (sin x) (sin (* 0.5 x)))
6.0ms	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
6.0ms	(pow (/ (sin x) (sin (* 0.5 x))) 3)

series251.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)) 3.0))
39.0ms	(/ (sin x) (sin (* 0.5 x)))
48.0ms	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
83.0ms	(pow (/ (sin x) (sin (* 0.5 x))) 3)

simplify95.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	547	1413
1	3109	1238
2	5001	1201

prune280.0ms

Filtered

149 candidates to 79 candidates (53.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	149	9	158

Merged error: 0b

Counts

158 → 9

regimes40.0ms

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

701.0ms	1494×	body	1280	valid
372.0ms	1288×	body	640	valid
268.0ms	4313×	body	80	valid
123.0ms	621×	body	320	valid
44.0ms	284×	body	160	valid