Details

sample64.0ms

Algorithm

intervals

Results

29.0ms	56×	body	1280	valid
13.0ms	45×	body	640	valid
8.0ms	123×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	13×	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: 14.2b

Counts

2 → 1

localize11.0ms

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))

rewrite29.0ms

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

series173.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
79.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (46.0ms)

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

prune217.0ms

Filtered

88 candidates to 62 candidates (70.5%)

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

localize14.0ms

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)))

rewrite27.0ms

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:

11.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
5.0ms	(/ (sin (* 0.5 x)) (sin x))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
44.0ms	(/ (sin (* 0.5 x)) (sin x))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify63.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (54.0ms)

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

prune454.0ms

Filtered

107 candidates to 74 candidates (69.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	106	13	119

Merged error: 0b

Counts

119 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
0.4b	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
1.0b	(/ 8.0 (cbrt 3.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
51×	`add-sqr-sqrt`
50×	`times-frac`
46×	`prod-exp`
43×	`add-cube-cbrt` `*-un-lft-identity`
38×	`add-cbrt-cube`
29×	`associate-l`
22×	`cbrt-prod` `div-exp`
20×	`cbrt-unprod`
12×	`cbrt-undiv`
11×	`pow1`
9×	`associate-/r*`
6×	`rec-exp` `1-exp` `associate-/l*`
4×	`associate-r` `pow-prod-down` `associate-*l/` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 159

Calls

4 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
15.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
9.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
4.0ms	(/ 8.0 (cbrt 3.0))

series274.0ms

Counts

4 → 10

Calls

4 calls:

40.0ms	(/ (sin (* 0.5 x)) (sin x))
130.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
104.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
0.0ms	(/ 8.0 (cbrt 3.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	643	1471
1	2936	1211
2	5001	1121

prune412.0ms

Filtered

169 candidates to 109 candidates (64.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	169	13	182

Merged error: 0b

Counts

182 → 13

localize18.0ms

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))

rewrite15.0ms

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×	`add-cbrt-cube` `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 → 73

Calls

4 calls:

9.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))

series400.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
96.0ms	(cbrt (sin x))
95.0ms	(cbrt (sin x))
94.0ms	(cbrt (sin x))

simplify104.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	154	453
1	551	401
2	3082	369
3	5002	363

prune225.0ms

Filtered

85 candidates to 60 candidates (70.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	85	13	98

Merged error: 0b

Counts

98 → 13

regimes104.0ms

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 (0.0ms)

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

end0.0ms

sample1.7s

Algorithm

intervals

Results

752.0ms	1584×	body	1280	valid
370.0ms	1220×	body	640	valid
286.0ms	4293×	body	80	valid
124.0ms	601×	body	320	valid
44.0ms	302×	body	160	valid