Details

sample89.0ms

Algorithm

intervals

Results

27.0ms	145×	body	80	valid
25.0ms	41×	body	1280	valid
16.0ms	40×	body	640	valid
6.0ms	22×	body	320	valid
1.0ms	8×	body	160	valid

simplify329.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	43	16
3	93	16
4	173	16
5	277	16
6	314	16
done	314	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize19.0ms

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)))
15.7b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite242.0ms

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:

97.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
98.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series213.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
45.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
109.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.5s

Counts

88 → 88

Iterations

Useful iterations: 2 (304.0ms)

Iter	Nodes	Cost
0	163	1474
1	413	1285
2	2715	1064
done	5001	1064

prune334.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite133.0ms

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:

15.0ms	(/ (sin (* x 0.5)) (sin x))
78.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
34.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (sin (* x 0.5)) (sin x))
90.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
52.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify2.5s

Counts

107 → 107

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	183	1718
1	492	1676
2	3232	1342
done	5000	1292

prune372.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
42×	`add-cbrt-cube`
31×	`prod-exp`
21×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`div-exp`
17×	`cbrt-unprod`
13×	`associate-r`
11×	`cbrt-undiv`
8×	`pow1`
6×	`1-exp` `associate-/r*`
4×	`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 → 97

Calls

3 calls:

22.0ms	(/ (sin (* x 0.5)) (sin x))
28.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
94.0ms	(* (* 1 (/ (* 8.0 (sin (* 0.5 x))) 3.0)) (/ (sin (* x 0.5)) (sin x)))

series210.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (sin (* x 0.5)) (sin x))
50.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
105.0ms	(* (* 1 (/ (* 8.0 (sin (* 0.5 x))) 3.0)) (/ (sin (* x 0.5)) (sin x)))

simplify2.2s

Counts

106 → 106

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	199	2000
1	563	1782
2	3821	1469
done	5000	1330

prune393.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (* (/ (sqrt 8.0) 1) (* (sin (* 0.5 x)) (/ (sqrt 8.0) 3.0))) (/ (sin (* x 0.5)) (sin x)))
0.4b	(* (/ (sqrt 8.0) 1) (* (sin (* 0.5 x)) (/ (sqrt 8.0) 3.0)))
1.0b	(/ (sqrt 8.0) 3.0)

rewrite376.0ms

Algorithm

rewrite-expression-head

Rules

130×	`add-exp-log`
94×	`add-cbrt-cube`
65×	`prod-exp`
54×	`times-frac`
47×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
44×	`cbrt-unprod`
39×	`div-exp`
24×	`cbrt-undiv`
23×	`associate-l`
21×	`sqrt-prod`
18×	`pow1`
14×	`associate-r`
10×	`associate-*r/`
9×	`1-exp` `pow-prod-down` `associate-/l*`
6×	`frac-times` `associate-l/` `associate-/r`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`

Counts

4 → 183

Calls

4 calls:

13.0ms	(/ (sin (* x 0.5)) (sin x))
239.0ms	(* (* (/ (sqrt 8.0) 1) (* (sin (* 0.5 x)) (/ (sqrt 8.0) 3.0))) (/ (sin (* x 0.5)) (sin x)))
101.0ms	(* (/ (sqrt 8.0) 1) (* (sin (* 0.5 x)) (/ (sqrt 8.0) 3.0)))
10.0ms	(/ (sqrt 8.0) 3.0)

series441.0ms

Counts

4 → 10

Calls

4 calls:

46.0ms	(/ (sin (* x 0.5)) (sin x))
254.0ms	(* (* (/ (sqrt 8.0) 1) (* (sin (* 0.5 x)) (/ (sqrt 8.0) 3.0))) (/ (sin (* x 0.5)) (sin x)))
141.0ms	(* (/ (sqrt 8.0) 1) (* (sin (* 0.5 x)) (/ (sqrt 8.0) 3.0)))
0.0ms	(/ (sqrt 8.0) 3.0)

simplify466.0ms

Counts

193 → 193

Iterations

Useful iterations: done (460.0ms)

Iter	Nodes	Cost
0	299	4098
1	879	3402
done	5001	2895

prune710.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes62.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	15	18
1	20	16
2	21	16
done	21	16

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	1535×	body	1280	valid
1.2s	1268×	body	640	valid
577.0ms	4280×	body	80	valid
365.0ms	612×	body	320	valid
75.0ms	305×	body	160	valid