Details

sample60.0ms

Algorithm

intervals

Results

30.0ms	59×	body	1280	valid
9.0ms	32×	body	640	valid
8.0ms	134×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid

simplify16.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize10.0ms

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)))
13.4b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite51.0ms

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:

20.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
19.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series167.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
76.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (45.0ms)

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

prune202.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite39.0ms

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:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
23.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (sin (* 0.5 x)) (sin x))
76.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify59.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (50.0ms)

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

prune246.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) (sin x))
0.1b	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
0.2b	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
0.3b	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
33×	`associate-l`
28×	`sqrt-prod`
20×	`pow1`
17×	`associate-r`
16×	`prod-exp` `cbrt-unprod`
13×	`sqrt-div` `associate-*l/`
10×	`pow-prod-down`
6×	`frac-times`
4×	`cbrt-undiv` `associate-*r/` `div-exp` `div-inv` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*` `unswap-sqr`
1×	`frac-2neg` `clear-num`

Counts

4 → 139

Calls

4 calls:

3.0ms	(/ (sin (* 0.5 x)) (sin x))
12.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
80.0ms	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
30.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (sin (* 0.5 x)) (sin x))
67.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
156.0ms	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
92.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

simplify78.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	587	1488
1	2990	1184
2	5002	1154

prune434.0ms

Filtered

151 candidates to 108 candidates (71.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
0.3b	(* (/ 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))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

313×	`add-exp-log`
178×	`prod-exp`
122×	`add-cbrt-cube`
81×	`div-exp`
76×	`cbrt-unprod`
50×	`add-sqr-sqrt` `times-frac`
42×	`add-cube-cbrt` `*-un-lft-identity`
39×	`cbrt-undiv`
30×	`associate-l`
22×	`cbrt-prod`
20×	`pow1`
18×	`rec-exp` `1-exp`
17×	`associate-r`
13×	`associate-*l/`
10×	`pow-prod-down`
6×	`frac-times` `associate-/r*`
4×	`associate-*r/` `div-inv` `add-log-exp`
3×	`-commutative` `associate-/l` `unswap-sqr`
1×	`frac-2neg` `clear-num`

Counts

4 → 228

Calls

4 calls:

144.0ms	(* (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
42.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
13.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
3.0ms	(/ 8.0 (cbrt 3.0))

series409.0ms

Counts

4 → 10

Calls

4 calls:

170.0ms	(* (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
132.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
107.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
0.0ms	(/ 8.0 (cbrt 3.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1037	3268
1	5001	2460

prune489.0ms

Filtered

238 candidates to 129 candidates (54.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	13
1	20	13
2	20	13

end0.0ms

sample1.8s

Algorithm

intervals

Results

817.0ms	1579×	body	1280	valid
397.0ms	1210×	body	640	valid
288.0ms	4328×	body	80	valid
143.0ms	602×	body	320	valid
43.0ms	281×	body	160	valid