Details

sample128.0ms

Algorithm

intervals

Results

52.0ms	52×	body	1280	valid
30.0ms	46×	body	640	valid
17.0ms	128×	body	80	valid
9.0ms	19×	body	320	valid
3.0ms	11×	body	160	valid

simplify198.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize76.0ms

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)))
14.3b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite237.0ms

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:

96.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
28.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
110.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series220.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
48.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
96.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify755.0ms

Counts: 88 → 88

prune322.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite169.0ms

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

Counts

3 → 98

Calls

3 calls:

22.0ms	(/ (sin (* 0.5 x)) (sin x))
100.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ (sin (* 0.5 x)) (sin x))
103.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
54.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify793.0ms

Counts: 107 → 107

prune409.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
0.1b	(/ (sin (* 0.5 x)) 3.0)
0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
37×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
26×	`associate-r`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
8×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
4×	`associate-r/` `associate-l*` `pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative` `unswap-sqr`
1×	`frac-times` `associate-*l/`

Counts

4 → 125

Calls

4 calls:

17.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
12.0ms	(/ (sin (* 0.5 x)) 3.0)
18.0ms	(/ (sin (* 0.5 x)) (sin x))
58.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
38.0ms	(/ (sin (* 0.5 x)) 3.0)
45.0ms	(/ (sin (* 0.5 x)) (sin x))
84.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

simplify773.0ms

Counts: 137 → 137

prune397.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
97×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
49×	`add-cbrt-cube`
44×	`associate-r`
37×	`div-exp`
35×	`prod-exp`
19×	`associate-/r*`
17×	`cbrt-undiv`
15×	`cbrt-unprod`
11×	`div-inv`
10×	`pow1`
9×	`associate-/l*`
8×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num`
2×	`associate-/r/`
1×	`frac-times` `pow-flip` `associate-l` `associate-l/` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 219

Calls

4 calls:

23.0ms	(/ 1 (/ (sin x) (sin (* 0.5 x))))
18.0ms	(/ (sin (* 0.5 x)) 3.0)
83.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ 1 (/ (sin x) (sin (* 0.5 x)))))
24.0ms	(/ (sin x) (sin (* 0.5 x)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 1 (/ (sin x) (sin (* 0.5 x))))
38.0ms	(/ (sin (* 0.5 x)) 3.0)
111.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ 1 (/ (sin x) (sin (* 0.5 x)))))
68.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify1.7s

Counts: 231 → 231

prune682.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes42.0ms

Accuracy

7.6% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.5s

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.2s	1529×	body	1280	valid
1.0s	1197×	body	640	valid
528.0ms	4331×	body	80	valid
282.0ms	619×	body	320	valid
228.0ms	324×	body	160	valid