Details

sample56.0ms

Algorithm

intervals

Results

23.0ms	52×	body	1280	valid
10.0ms	35×	body	640	valid
8.0ms	140×	body	80	valid
5.0ms	23×	body	320	valid
1.0ms	6×	body	160	valid

simplify18.0ms

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

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: 15.1b

Counts

2 → 1

localize15.0ms

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))

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))

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)))
80.0ms	(/ (* (* (/ 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

prune212.0ms

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

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)))

rewrite29.0ms

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:

5.0ms	(/ (sin (* 0.5 x)) (sin x))
13.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (sin (* 0.5 x)) (sin x))
79.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify70.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (58.0ms)

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

prune247.0ms

Filtered

107 candidates to 74 candidates (69.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	110	10	120

Merged error: 0b

Counts

120 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

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:

4.0ms	(/ (sin (* 0.5 x)) 3.0)
4.0ms	(/ (sin (* 0.5 x)) (sin x))
14.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

series159.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (sin (* 0.5 x)) 3.0)
38.0ms	(/ (sin (* 0.5 x)) (sin x))
81.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (56.0ms)

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

prune214.0ms

Filtered

102 candidates to 72 candidates (70.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	102	10	112

Merged error: 0b

Counts

112 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
26×	`exp-prod`
20×	`add-exp-log` `associate-r` `add-cbrt-cube`
14×	`associate-l` `log-pow`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`log-prod`
5×	`add-log-exp`
4×	`pow-prod-down` `div-inv`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-l/` `associate-/r` `associate-/l*`
2×	`*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `rem-exp-log`

Counts

4 → 121

Calls

4 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
5.0ms	(exp (/ (sin (* 0.5 x)) (sin x)))
13.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (log (exp (/ (sin (* 0.5 x)) (sin x)))))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (sin (* 0.5 x)) (sin x))
74.0ms	(exp (/ (sin (* 0.5 x)) (sin x)))
80.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (log (exp (/ (sin (* 0.5 x)) (sin x)))))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify72.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	516	1216
1	2553	1026
2	5002	991

prune359.0ms

Filtered

133 candidates to 99 candidates (74.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	133	10	143

Merged error: 0b

Counts

143 → 10

regimes104.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b 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

sample1.6s

Algorithm

intervals

Results

682.0ms	1482×	body	1280	valid
365.0ms	1251×	body	640	valid
265.0ms	4328×	body	80	valid
131.0ms	629×	body	320	valid
42.0ms	310×	body	160	valid