Details

sample125.0ms

Algorithm

intervals

Results

59.0ms	54×	body	1280	valid
24.0ms	39×	body	640	valid
16.0ms	135×	body	80	valid
8.0ms	20×	body	320	valid
2.0ms	8×	body	160	valid

simplify191.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize13.0ms

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)))
12.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite214.0ms

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:

87.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
30.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
92.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series208.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
88.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify826.0ms

Counts: 88 → 88

prune277.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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

rewrite170.0ms

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:

19.0ms	(/ (sin (* 0.5 x)) (sin x))
102.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
44.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ (sin (* 0.5 x)) (sin x))
111.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify985.0ms

Counts: 107 → 107

prune464.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite811.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
33×	`associate-l`
28×	`sqrt-prod`
20×	`pow1`
17×	`associate-r`
16×	`prod-exp` `cbrt-unprod`
13×	`sqrt-div` `associate-*l/`
10×	`pow-prod-down`
6×	`frac-times`
4×	`cbrt-undiv` `associate-*r/` `div-exp` `div-inv` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*` `unswap-sqr`
1×	`frac-2neg` `clear-num`

Counts

4 → 139

Calls

4 calls:

39.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
13.0ms	(/ (sin (* 0.5 x)) (sin x))
655.0ms	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
98.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
48.0ms	(/ (sin (* 0.5 x)) (sin x))
204.0ms	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
128.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

simplify1.4s

Counts: 151 → 151

prune656.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite474.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
38×	`add-exp-log` `add-cbrt-cube`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
33×	`associate-l`
28×	`sqrt-prod`
20×	`pow1`
18×	`prod-exp` `cbrt-unprod`
17×	`associate-r`
11×	`sqrt-div` `associate-*l/`
10×	`pow-prod-down`
6×	`frac-times` `associate-*r/`
5×	`cbrt-undiv` `div-exp`
4×	`div-inv` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*` `unswap-sqr`
1×	`frac-2neg` `clear-num`

Counts

4 → 141

Calls

4 calls:

54.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
27.0ms	(/ (sin (* 0.5 x)) (sin x))
113.0ms	(* (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
273.0ms	(* (sqrt (/ 8.0 3.0)) (* (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
51.0ms	(/ (sin (* 0.5 x)) (sin x))
170.0ms	(* (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
175.0ms	(* (sqrt (/ 8.0 3.0)) (* (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x))))

simplify1.3s

Counts: 153 → 153

prune639.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes68.0ms

Accuracy

-10% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify302.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	1564×	body	1280	valid
1.0s	1239×	body	640	valid
930.0ms	4304×	body	80	valid
307.0ms	589×	body	320	valid
133.0ms	304×	body	160	valid