Details

sample68.0ms

Algorithm

intervals

Results

25.0ms	48×	body	1280	valid
14.0ms	139×	body	80	valid
13.0ms	36×	body	640	valid
6.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid

simplify21.0ms

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

localize12.0ms

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))

rewrite56.0ms

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))

series189.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
45.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
81.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify61.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (52.0ms)

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

prune272.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))

rewrite29.0ms

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:

11.0ms	(/ (* (/ 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)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
42.0ms	(/ (sin x) (sin (* 0.5 x)))
44.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify72.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (60.0ms)

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

prune381.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize15.0ms

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)))

rewrite30.0ms

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×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `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 → 111

Calls

4 calls:

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

series224.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 8.0 (sin (* x 0.5)))
57.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
81.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
45.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	479	1036
1	2519	840
2	5003	822

prune368.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
0.2b	(/ (sin (* 0.5 x)) 3.0)
0.2b	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

59×	`times-frac`
47×	`add-sqr-sqrt`
42×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r`
7×	`associate-/l*`
6×	`pow1` `prod-exp` `cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num`
2×	`associate-*r/` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

4 → 145

Calls

4 calls:

7.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
3.0ms	(/ (sin (* 0.5 x)) 3.0)
9.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
44.0ms	(/ (sin (* 0.5 x)) 3.0)
79.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
51.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify89.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	592	1396
1	2961	1212
2	5001	1189

prune406.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes45.0ms

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

sample2.0s

Algorithm

intervals

Results

844.0ms	1566×	body	1280	valid
433.0ms	1223×	body	640	valid
354.0ms	4325×	body	80	valid
142.0ms	564×	body	320	valid
56.0ms	322×	body	160	valid