Details

sample120.0ms

Algorithm

intervals

Results

43.0ms	51×	body	1280	valid
36.0ms	147×	body	80	valid
20.0ms	34×	body	640	valid
4.0ms	11×	body	320	valid
4.0ms	13×	body	160	valid

simplify303.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	275
7	275
6	274
5	226
4	134
3	71
2	35
1	20
0	11

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize28.0ms

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)))
18.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
14×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
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*` `insert-posit16` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 82

Calls

3 calls:

55.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
21.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
58.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series194.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
81.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.8s

Counts

91 → 91

Iterations

Iter	Nodes
done	5003
2	1441
1	414
0	166

prune298.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
0.1b	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
0.2b	(/ (sin x) (sin (* x 0.5)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
98×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
10×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/l*`
5×	`pow1`
3×	`associate-r` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 166

Calls

3 calls:

24.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
36.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
19.0ms	(/ (sin x) (sin (* x 0.5)))

series221.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
96.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
57.0ms	(/ (sin x) (sin (* x 0.5)))

simplify1.9s

Counts

175 → 175

Iterations

Iter	Nodes
done	5002
2	2455
1	677
0	255

prune808.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(* (* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
0.3b	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
111×	`add-sqr-sqrt`
93×	`*-un-lft-identity` `add-cube-cbrt`
45×	`associate-l`
34×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
12×	`associate-r`
11×	`pow1`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
9×	`sqrt-prod`
6×	`associate-/l*` `unswap-sqr`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`associate-*l/`
2×	`clear-num` `frac-2neg` `associate-/r/` `*-commutative`

Counts

4 → 199

Calls

4 calls:

27.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
16.0ms	(/ (sin x) (sin (* x 0.5)))
74.0ms	(* (* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
37.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665))

series398.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
40.0ms	(/ (sin x) (sin (* x 0.5)))
161.0ms	(* (* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
139.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665))

simplify2.0s

Counts

211 → 211

Iterations

Iter	Nodes
done	5000
2	2996
1	811
0	297

prune949.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (* 1 (/ (sin x) (sin (* x 0.5)))))
0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(* (* (/ (sin (* x 0.5)) (* 1 (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
0.3b	(* (/ (sin (* x 0.5)) (* 1 (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-exp-log`
49×	`add-cbrt-cube`
31×	`prod-exp`
24×	`add-sqr-sqrt`
22×	`div-exp`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`cbrt-unprod`
15×	`times-frac`
13×	`cbrt-undiv`
12×	`associate-r`
11×	`pow1`
9×	`associate-l`
7×	`sqrt-prod`
6×	`1-exp` `associate-/l*`
4×	`associate-/r*` `pow-prod-down` `insert-posit16` `add-log-exp`
3×	`associate-*l/` `div-inv`
2×	`clear-num` `frac-2neg` `associate-r/` `associate-/r/` `-commutative` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

28.0ms	(/ (sin (* x 0.5)) (* 1 (/ (sin x) (sin (* x 0.5)))))
18.0ms	(/ (sin x) (sin (* x 0.5)))
170.0ms	(* (* (/ (sin (* x 0.5)) (* 1 (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
59.0ms	(* (/ (sin (* x 0.5)) (* 1 (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665))

series440.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (sin (* x 0.5)) (* 1 (/ (sin x) (sin (* x 0.5)))))
53.0ms	(/ (sin x) (sin (* x 0.5)))
186.0ms	(* (* (/ (sin (* x 0.5)) (* 1 (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
138.0ms	(* (/ (sin (* x 0.5)) (* 1 (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665))

simplify1.9s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	1927
1	549
0	216

prune440.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.3s	1532×	body	1280	valid
1.3s	1302×	body	640	valid
633.0ms	4274×	body	80	valid
381.0ms	314×	body	160	valid
295.0ms	578×	body	320	valid