Details

sample103.0ms

Algorithm

intervals

Results

35.0ms	42×	body	1280	valid
24.0ms	43×	body	640	valid
15.0ms	141×	body	80	valid
10.0ms	25×	body	320	valid
1.0ms	5×	body	160	valid

simplify237.0ms

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: 13.1b

localize11.0ms

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))

rewrite154.0ms

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:

64.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
27.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
60.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series184.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
85.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.0s

Counts

94 → 94

Iterations

Useful iterations: 2 (213.0ms)

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

prune241.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite75.0ms

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:

11.0ms	(/ (sin x) (sin (* 0.5 x)))
34.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
25.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series172.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ (sin x) (sin (* 0.5 x)))
84.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.1s

Counts

125 → 125

Iterations

Useful iterations: 2 (294.0ms)

Iter	Nodes	Cost
0	222	2116
1	527	1956
2	1845	1662
done	5001	1662

prune358.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

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:

11.0ms	(/ (sin (* 0.5 x)) 3.0)
12.0ms	(/ (sin x) (sin (* 0.5 x)))
26.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))

series174.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (sin (* 0.5 x)) 3.0)
44.0ms	(/ (sin x) (sin (* 0.5 x)))
86.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))

simplify999.0ms

Counts

120 → 120

Iterations

Useful iterations: done (995.0ms)

Iter	Nodes	Cost
0	210	2055
1	492	1969
2	1740	1625
done	5000	1623

prune322.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

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:

12.0ms	(/ (sin (* 0.5 x)) 3.0)
13.0ms	(/ (sin (* 0.5 x)) (sin x))
15.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))
28.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ 1 (/ (sin (* 0.5 x)) (sin x))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin (* 0.5 x)) 3.0)
43.0ms	(/ (sin (* 0.5 x)) (sin x))
50.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))
89.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ 1 (/ (sin (* 0.5 x)) (sin x))))

simplify1.1s

Counts

281 → 281

Iterations

Useful iterations: 2 (517.0ms)

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

prune534.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.3b 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	13	18
1	17	18
done	17	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

722.0ms	1463×	body	1280	valid
396.0ms	1240×	body	640	valid
281.0ms	4343×	body	80	valid
139.0ms	636×	body	320	valid
48.0ms	318×	body	160	valid