Details

sample58.0ms

Algorithm

intervals

Results

20.0ms	42×	body	1280	valid
15.0ms	52×	body	640	valid
9.0ms	140×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid

simplify132.0ms

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	246	16
6	264	16
done	264	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

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)))
16.6b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite58.0ms

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:

24.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
20.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series190.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
89.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify812.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (152.0ms)

Iter	Nodes	Cost
0	169	1554
1	423	1349
2	1913	1080
done	5000	1080

prune282.0ms

Pruning

13 alts after pruning (13 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)))

rewrite30.0ms

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	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
49.0ms	(/ (sin x) (sin (* 0.5 x)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.0s

Counts

125 → 125

Iterations

Useful iterations: 2 (200.0ms)

Iter	Nodes	Cost
0	222	2116
1	560	1956
2	2634	1662
done	5000	1662

prune387.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

10.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
4.0ms	(/ (sin x) (sin (* 0.5 x)))
12.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

series196.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
44.0ms	(/ (sin x) (sin (* 0.5 x)))
86.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

simplify1.0s

Counts

100 → 100

Iterations

Useful iterations: 2 (165.0ms)

Iter	Nodes	Cost
0	173	1602
1	446	1539
2	2119	1186
done	5001	1186

prune291.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
137×	`add-sqr-sqrt`
132×	`add-cube-cbrt` `*-un-lft-identity`
100×	`add-exp-log`
60×	`associate-/r*`
58×	`div-exp`
52×	`add-cbrt-cube`
26×	`cbrt-undiv`
16×	`prod-exp` `div-inv`
13×	`associate-l`
8×	`rec-exp` `1-exp` `cbrt-unprod`
7×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num`
2×	`associate-*l/` `unswap-sqr`
1×	`pow-flip` `pow-prod-down` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 274

Calls

4 calls:

18.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ 1 (/ (sin (* x 0.5)) (sin x))))
4.0ms	(/ (sin (* x 0.5)) (sin x))
6.0ms	(/ 1 (/ (sin (* x 0.5)) (sin x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ 1 (/ (sin (* x 0.5)) (sin x))))
49.0ms	(/ (sin (* x 0.5)) (sin x))
44.0ms	(/ 1 (/ (sin (* x 0.5)) (sin x)))
48.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify3.1s

Counts

286 → 286

Iterations

Useful iterations: 2 (534.0ms)

Iter	Nodes	Cost
0	425	5852
1	1156	5184
2	4961	4205
done	5000	4205

prune621.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes44.0ms

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	16
1	15	16
done	15	16

end0.0ms

sample1.8s

Algorithm

intervals

Results

741.0ms	1513×	body	1280	valid
398.0ms	1231×	body	640	valid
280.0ms	4339×	body	80	valid
144.0ms	622×	body	320	valid
43.0ms	295×	body	160	valid