Details

sample69.0ms

Algorithm

intervals

Results

25.0ms	48×	body	1280	valid
13.0ms	36×	body	640	valid
11.0ms	139×	body	80	valid
10.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid

simplify16.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize11.0ms

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)))
13.0b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite52.0ms

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:

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

series194.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
99.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify78.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (65.0ms)

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

prune210.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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)))

rewrite32.0ms

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:

15.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
45.0ms	(/ (sin x) (sin (* 0.5 x)))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify61.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (51.0ms)

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

prune316.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 8.0 (sin (* x 0.5)))
0.2b	(* (/ (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)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

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

series226.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 8.0 (sin (* x 0.5)))
61.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
82.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
47.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	466	988
1	2487	795
2	5002	777

prune283.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (/ 1 (/ (sin (* 0.5 x)) (sin x))) 3.0)
0.2b	(/ (* 8.0 (sin (* x 0.5))) (* (/ 1 (/ (sin (* 0.5 x)) (sin x))) 3.0))
0.2b	(/ 1 (/ (sin (* 0.5 x)) (sin x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

157×	`times-frac`
104×	`add-sqr-sqrt`
100×	`add-exp-log`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
52×	`add-cbrt-cube`
45×	`div-exp`
44×	`associate-l`
29×	`prod-exp`
21×	`cbrt-undiv`
17×	`associate-/r*`
13×	`cbrt-unprod`
11×	`div-inv`
8×	`rec-exp` `1-exp`
7×	`pow1` `associate-/l*`
5×	`unswap-sqr`
4×	`add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/r/`
2×	`associate-*l/`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 213

Calls

4 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
21.0ms	(* (/ 1 (/ (sin (* 0.5 x)) (sin x))) 3.0)
17.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ 1 (/ (sin (* 0.5 x)) (sin x))) 3.0))
5.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (sin (* 0.5 x)) (sin x))
60.0ms	(* (/ 1 (/ (sin (* 0.5 x)) (sin x))) 3.0)
71.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ 1 (/ (sin (* 0.5 x)) (sin x))) 3.0))
61.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	833	2248
1	4363	1881
2	5002	1728

prune697.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes37.0ms

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	19	10
1	21	10
2	21	10

end0.0ms

sample2.0s

Algorithm

intervals

Results

865.0ms	1566×	body	1280	valid
439.0ms	1223×	body	640	valid
343.0ms	4325×	body	80	valid
148.0ms	564×	body	320	valid
61.0ms	322×	body	160	valid