Details

sample68.0ms

Algorithm

intervals

Results

31.0ms	62×	body	1280	valid
12.0ms	37×	body	640	valid
9.0ms	138×	body	80	valid
3.0ms	12×	body	320	valid
1.0ms	7×	body	160	valid

simplify31.0ms

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: 16.7b

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)))
16.5b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite167.0ms

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:

66.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
30.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
68.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series202.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
95.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify73.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (63.0ms)

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

prune292.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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)))

rewrite84.0ms

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:

39.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
12.0ms	(/ (sin x) (sin (* 0.5 x)))
28.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series180.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
52.0ms	(/ (sin x) (sin (* 0.5 x)))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify82.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (70.0ms)

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

prune400.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (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)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
5×	`div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-*r/` `associate-/r/` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

13.0ms	(/ (sin (* 0.5 x)) 3.0)
24.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
17.0ms	(/ (sin x) (sin (* 0.5 x)))

series183.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (sin (* 0.5 x)) 3.0)
91.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
53.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	514	1168
1	2579	1010
2	5001	984

prune365.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

269×	`times-frac`
132×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
97×	`add-exp-log`
63×	`associate-/r*`
58×	`div-exp`
49×	`add-cbrt-cube`
26×	`cbrt-undiv`
16×	`div-inv`
14×	`prod-exp`
10×	`associate-/l*`
8×	`rec-exp` `1-exp`
6×	`cbrt-unprod`
5×	`pow1`
4×	`expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-*r/` `associate-/l/` `inv-pow`

Counts

4 → 269

Calls

4 calls:

12.0ms	(/ (sin (* 0.5 x)) 3.0)
11.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))
13.0ms	(/ (sin (* 0.5 x)) (sin x))
36.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ 1 (/ (sin (* 0.5 x)) (sin x))))

series228.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (sin (* 0.5 x)) 3.0)
45.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))
52.0ms	(/ (sin (* 0.5 x)) (sin x))
84.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ 1 (/ (sin (* 0.5 x)) (sin x))))

simplify65.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1111	3284
1	5001	2865

prune704.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes40.0ms

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	17	10
1	17	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

749.0ms	1477×	body	1280	valid
405.0ms	1283×	body	640	valid
285.0ms	4341×	body	80	valid
127.0ms	586×	body	320	valid
59.0ms	313×	body	160	valid