Details

sample116.0ms

Algorithm

intervals

Results

43.0ms	52×	body	1280	valid
36.0ms	42×	body	640	valid
15.0ms	136×	body	80	valid
5.0ms	14×	body	320	valid
3.0ms	12×	body	160	valid

simplify11.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize17.0ms

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)))
15.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite229.0ms

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:

88.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
102.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series206.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
50.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
87.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify51.0ms

Counts: 88 → 88

prune291.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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)))

rewrite151.0ms

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:

18.0ms	(/ (sin (* 0.5 x)) (sin x))
86.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (sin (* 0.5 x)) (sin x))
99.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
50.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify56.0ms

Counts: 107 → 107

prune355.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite84.0ms

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

Counts

3 → 93

Calls

3 calls:

19.0ms	(/ (sin (* 0.5 x)) 3.0)
15.0ms	(/ (sin (* 0.5 x)) (sin x))
44.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (sin (* 0.5 x)) 3.0)
58.0ms	(/ (sin (* 0.5 x)) (sin x))
102.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

simplify49.0ms

Counts: 102 → 102

prune267.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* 8.0 (/ (/ (sin (* 0.5 x)) (sqrt 3.0)) (sqrt 3.0))) (/ (sin (* 0.5 x)) (sin x)))
0.3b	(/ (sin (* 0.5 x)) (sqrt 3.0))
0.4b	(/ (/ (sin (* 0.5 x)) (sqrt 3.0)) (sqrt 3.0))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

294×	`times-frac`
171×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
144×	`sqrt-prod`
45×	`add-exp-log` `add-cbrt-cube`
28×	`associate-/l*`
15×	`cbrt-undiv` `div-exp` `associate-/r*`
14×	`prod-exp` `cbrt-unprod`
13×	`associate-r`
11×	`div-inv`
9×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num`
1×	`frac-times` `associate-l` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 284

Calls

4 calls:

20.0ms	(/ (sin (* 0.5 x)) (sin x))
141.0ms	(* (* 8.0 (/ (/ (sin (* 0.5 x)) (sqrt 3.0)) (sqrt 3.0))) (/ (sin (* 0.5 x)) (sin x)))
14.0ms	(/ (sin (* 0.5 x)) (sqrt 3.0))
23.0ms	(/ (/ (sin (* 0.5 x)) (sqrt 3.0)) (sqrt 3.0))

series562.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (sin (* 0.5 x)) (sin x))
266.0ms	(* (* 8.0 (/ (/ (sin (* 0.5 x)) (sqrt 3.0)) (sqrt 3.0))) (/ (sin (* 0.5 x)) (sin x)))
86.0ms	(/ (sin (* 0.5 x)) (sqrt 3.0))
147.0ms	(/ (/ (sin (* 0.5 x)) (sqrt 3.0)) (sqrt 3.0))

simplify111.0ms

Counts: 296 → 296

prune820.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify14.0ms

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.7s	1535×	body	1280	valid
769.0ms	1288×	body	640	valid
605.0ms	578×	body	320	valid
543.0ms	4286×	body	80	valid
70.0ms	313×	body	160	valid