Details

sample66.0ms

Algorithm

intervals

Results

19.0ms	36×	body	1280	valid
16.0ms	150×	body	80	valid
15.0ms	43×	body	640	valid
5.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 14.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
14.3b	(/ (* (* (/ 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)))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
20.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series186.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
86.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify69.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (56.0ms)

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

prune259.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite38.0ms

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×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 104

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
21.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series161.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (sin (* 0.5 x)) (sin x))
76.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify69.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	474	1006
1	2505	814
2	5001	799

prune294.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-cbrt-cube`
27×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`prod-exp` `cbrt-unprod`
8×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-l` `associate-l/` `-commutative`

Counts

3 → 99

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
3.0ms	(/ (sin (* 0.5 x)) 3.0)
16.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

series170.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (sin (* 0.5 x)) (sin x))
44.0ms	(/ (sin (* 0.5 x)) 3.0)
84.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	437	968
1	2144	808
2	5001	786

prune289.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (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 (* 0.5 x)) (sin x)))
0.5b	(* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5))))
1.0b	(/ (sqrt 8.0) 3.0)

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-exp-log`
97×	`add-cbrt-cube`
67×	`prod-exp`
65×	`times-frac`
61×	`add-sqr-sqrt`
53×	`add-cube-cbrt` `*-un-lft-identity`
46×	`cbrt-unprod`
45×	`associate-l`
39×	`div-exp`
31×	`sqrt-prod`
24×	`cbrt-undiv`
20×	`pow1`
17×	`associate-r`
13×	`associate-*l/`
10×	`pow-prod-down`
9×	`1-exp`
6×	`frac-times` `associate-/l*`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/r` `-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num`

Counts

4 → 206

Calls

4 calls:

14.0ms	(* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))
86.0ms	(* (* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
31.0ms	(* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5))))
3.0ms	(/ (sqrt 8.0) 3.0)

series442.0ms

Counts

4 → 10

Calls

4 calls:

105.0ms	(* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))
198.0ms	(* (* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
139.0ms	(* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5))))
0.0ms	(/ (sqrt 8.0) 3.0)

simplify131.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	909	2334
1	4659	1770
2	5001	1659

prune536.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes73.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	14	9
1	14	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

860.0ms	1526×	body	1280	valid
453.0ms	1246×	body	640	valid
347.0ms	4290×	body	80	valid
151.0ms	608×	body	320	valid
58.0ms	330×	body	160	valid