Details

sample67.0ms

Algorithm

intervals

Results

27.0ms	56×	body	1280	valid
14.0ms	45×	body	640	valid
9.0ms	123×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	13×	body	160	valid

simplify27.0ms

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

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: 14.2b

Counts

2 → 1

localize19.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
14.1b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite31.0ms

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×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 85

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))

series195.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
89.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify66.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	412	862
1	2127	656
2	5001	637

prune293.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	13	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 0.1b

Counts

95 → 13

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
0.2b	(/ (sin (* 0.5 x)) (sin x))
0.3b	(* (/ 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×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 104

Calls

3 calls:

12.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
5.0ms	(/ (sin (* 0.5 x)) (sin x))
8.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series179.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
42.0ms	(/ (sin (* 0.5 x)) (sin x))
48.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify74.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	474	1006
1	2505	814
2	5001	799

prune568.0ms

Filtered

113 candidates to 80 candidates (70.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	113	13	126

Merged error: 0b

Counts

126 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5))))
0.4b	(* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5)))
1.0b	(/ (cbrt 8.0) (cbrt 3.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

86×	`times-frac`
82×	`add-exp-log` `cbrt-prod`
81×	`add-sqr-sqrt`
67×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-l`
44×	`add-cbrt-cube`
39×	`prod-exp` `cbrt-unprod`
20×	`cbrt-undiv` `div-exp`
11×	`pow1`
9×	`associate-/r` `associate-/l`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 206

Calls

4 calls:

5.0ms	(/ (sin (* 0.5 x)) (sin x))
19.0ms	(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5))))
12.0ms	(* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5)))
5.0ms	(/ (cbrt 8.0) (cbrt 3.0))

series437.0ms

Counts

4 → 10

Calls

4 calls:

46.0ms	(/ (sin (* 0.5 x)) (sin x))
234.0ms	(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5))))
156.0ms	(* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5)))
0.0ms	(/ (cbrt 8.0) (cbrt 3.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	746	2316
1	3673	1885
2	5001	1734

prune748.0ms

Filtered

216 candidates to 160 candidates (74.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	216	13	229

Merged error: 0b

Counts

229 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin x)) (cbrt (sin x)))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))

series473.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
116.0ms	(cbrt (sin x))
115.0ms	(cbrt (sin x))
109.0ms	(cbrt (sin x))

simplify120.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	159	483
1	568	431
2	3135	398
3	5001	392

prune280.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	93	13	106

Merged error: 0b

Counts

106 → 13

regimes56.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	9
1	17	9
2	17	9

end0.0ms

sample1.9s

Algorithm

intervals

Results

819.0ms	1584×	body	1280	valid
421.0ms	1220×	body	640	valid
326.0ms	4293×	body	80	valid
148.0ms	601×	body	320	valid
54.0ms	302×	body	160	valid