Details

sample57.0ms

Algorithm

intervals

Results

23.0ms	50×	body	1280	valid
12.0ms	42×	body	640	valid
8.0ms	131×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid

simplify184.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	42	16
3	90	16
4	168	16
5	237	16
6	255	16
done	255	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize12.0ms

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)))
13.1b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite55.0ms

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×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 85

Calls

3 calls:

20.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
12.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
20.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series182.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
82.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.0s

Counts

94 → 94

Iterations

Useful iterations: 2 (213.0ms)

Iter	Nodes	Cost
0	169	1554
1	414	1349
2	1620	1080
done	5000	1080

prune242.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

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` `associate-r*`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`associate-r/` `associate-l*` `pow-prod-down`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`

Counts

3 → 104

Calls

3 calls:

4.0ms	(/ (sin (* x 0.5)) (sin x))
19.0ms	(* (* (sin (* 0.5 x)) (/ 8.0 3.0)) (/ (sin (* x 0.5)) (sin x)))
9.0ms	(* (sin (* 0.5 x)) (/ 8.0 3.0))

series162.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (sin (* x 0.5)) (sin x))
81.0ms	(* (* (sin (* 0.5 x)) (/ 8.0 3.0)) (/ (sin (* x 0.5)) (sin x)))
42.0ms	(* (sin (* 0.5 x)) (/ 8.0 3.0))

simplify1.0s

Counts

113 → 113

Iterations

Useful iterations: 2 (376.0ms)

Iter	Nodes	Cost
0	196	1801
1	495	1699
2	1959	1357
done	5000	1357

prune305.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `unswap-sqr`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 100

Calls

3 calls:

5.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
4.0ms	(/ (sin (* x 0.5)) (sin x))
15.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

series162.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
44.0ms	(/ (sin (* x 0.5)) (sin x))
81.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify959.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (269.0ms)

Iter	Nodes	Cost
0	184	1811
1	471	1731
2	1823	1375
done	5001	1375

prune298.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
107×	`add-sqr-sqrt`
100×	`add-exp-log`
95×	`*-un-lft-identity`
93×	`add-cube-cbrt`
52×	`add-cbrt-cube`
45×	`div-exp`
44×	`associate-r`
29×	`prod-exp`
21×	`cbrt-undiv`
19×	`associate-/r*`
13×	`cbrt-unprod`
12×	`div-inv`
8×	`rec-exp` `1-exp`
7×	`pow1` `associate-l` `associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/r/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `*-commutative` `inv-pow`

Counts

4 → 231

Calls

4 calls:

6.0ms	(/ 1 (/ (sin x) (sin (* x 0.5))))
5.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
4.0ms	(/ (sin x) (sin (* x 0.5)))
31.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ 1 (/ (sin x) (sin (* x 0.5)))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1 (/ (sin x) (sin (* x 0.5))))
233.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
42.0ms	(/ (sin x) (sin (* x 0.5)))
83.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ 1 (/ (sin x) (sin (* x 0.5)))))

simplify1.4s

Counts

243 → 243

Iterations

Useful iterations: 2 (769.0ms)

Iter	Nodes	Cost
0	341	4624
1	949	4134
2	2894	3391
done	5000	3391

prune527.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	20
1	21	20
done	21	20

end0.0ms

sample1.7s

Algorithm

intervals

Results

735.0ms	1511×	body	1280	valid
370.0ms	1252×	body	640	valid
253.0ms	4277×	body	80	valid
129.0ms	639×	body	320	valid
44.0ms	321×	body	160	valid