Details

sample63.0ms

Algorithm

intervals

Results

24.0ms	51×	body	1280	valid
13.0ms	135×	body	80	valid
10.0ms	35×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	15×	body	160	valid

simplify28.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

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)))
16.4b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite53.0ms

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:

20.0ms	(* (* (/ 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))

series198.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
49.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
89.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify72.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (62.0ms)

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

prune269.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

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

Counts

3 → 116

Calls

3 calls:

4.0ms	(/ (sin x) (sin (* 0.5 x)))
11.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
14.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series181.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (sin x) (sin (* 0.5 x)))
89.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify80.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	550	1204
1	2727	1016
2	5001	992

prune383.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (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)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
24×	`add-sqr-sqrt`
20×	`times-frac`
19×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-l`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
5×	`pow1`
4×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative`

Counts

3 → 91

Calls

3 calls:

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

series204.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
90.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
45.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	433	924
1	2228	739
2	5002	723

prune308.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-exp-log`
97×	`add-cbrt-cube`
87×	`times-frac`
68×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
59×	`div-exp`
47×	`prod-exp`
44×	`associate-l`
38×	`cbrt-undiv`
32×	`cbrt-unprod`
31×	`sqrt-prod`
16×	`associate-/r*`
11×	`pow1`
9×	`1-exp`
7×	`associate-l/` `associate-/l`
6×	`div-inv`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-r/` `clear-num` `-commutative`
1×	`associate-/r/`

Counts

4 → 215

Calls

4 calls:

17.0ms	(* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))
29.0ms	(/ (* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))) (/ (sin x) (sin (* 0.5 x))))
30.0ms	(* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5))))
3.0ms	(/ (sqrt 8.0) 3.0)

series482.0ms

Counts

4 → 10

Calls

4 calls:

106.0ms	(* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))
229.0ms	(/ (* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))) (/ (sin x) (sin (* 0.5 x))))
146.0ms	(* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5))))
0.0ms	(/ (sqrt 8.0) 3.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1000	2528
1	5002	1971

prune588.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes39.0ms

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	15	9
1	17	9
2	17	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

785.0ms	1562×	body	1280	valid
402.0ms	1250×	body	640	valid
275.0ms	4291×	body	80	valid
139.0ms	590×	body	320	valid
51.0ms	307×	body	160	valid