Details

sample76.0ms

Algorithm

intervals

Results

32.0ms	53×	body	1280	valid
15.0ms	36×	body	640	valid
12.0ms	143×	body	80	valid
4.0ms	15×	body	320	valid
2.0ms	9×	body	160	valid

simplify589.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	43	16
3	89	16
4	168	16
5	257	16
6	273	16
done	273	16

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize14.0ms

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)))
13.7b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite219.0ms

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:

93.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
85.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series227.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
51.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
106.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.4s

Counts

94 → 94

Iterations

Useful iterations: 2 (300.0ms)

Iter	Nodes	Cost
0	169	1554
1	405	1349
2	1480	1080
done	5000	1080

prune294.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 116

Calls

3 calls:

51.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
12.0ms	(/ (sin x) (sin (* 0.5 x)))
32.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series162.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
44.0ms	(/ (sin x) (sin (* 0.5 x)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.3s

Counts

125 → 125

Iterations

Useful iterations: 2 (392.0ms)

Iter	Nodes	Cost
0	222	2116
1	527	1956
2	1843	1662
done	5000	1662

prune459.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
5×	`div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-*r/` `associate-/r/` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

17.0ms	(/ (sin (* 0.5 x)) 3.0)
38.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
17.0ms	(/ (sin x) (sin (* 0.5 x)))

series193.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (sin (* 0.5 x)) 3.0)
86.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
56.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify1.1s

Counts

120 → 120

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	210	2055
1	492	1969
2	1731	1625
done	5000	1623

prune362.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

269×	`times-frac`
132×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
97×	`add-exp-log`
63×	`associate-/r*`
58×	`div-exp`
49×	`add-cbrt-cube`
26×	`cbrt-undiv`
16×	`div-inv`
14×	`prod-exp`
10×	`associate-/l*`
8×	`rec-exp` `1-exp`
6×	`cbrt-unprod`
5×	`pow1`
4×	`expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-*r/` `associate-/l/` `inv-pow`

Counts

4 → 269

Calls

4 calls:

16.0ms	(/ (sin (* 0.5 x)) 3.0)
19.0ms	(/ (sin (* 0.5 x)) (sin x))
49.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ 1 (/ (sin (* 0.5 x)) (sin x))))
19.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (sin (* 0.5 x)) 3.0)
54.0ms	(/ (sin (* 0.5 x)) (sin x))
80.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ 1 (/ (sin (* 0.5 x)) (sin x))))
48.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))

simplify1.5s

Counts

281 → 281

Iterations

Useful iterations: 2 (646.0ms)

Iter	Nodes	Cost
0	415	5791
1	1010	4965
2	2633	4166
done	5000	4166

prune705.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	13	16
done	13	16

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	1466×	body	1280	valid
907.0ms	1254×	body	640	valid
874.0ms	4344×	body	80	valid
574.0ms	617×	body	320	valid
142.0ms	319×	body	160	valid