Details

sample58.0ms

Algorithm

intervals

Results

21.0ms	47×	body	1280	valid
15.0ms	51×	body	640	valid
7.0ms	126×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify131.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
15.4b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite56.0ms

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:

23.0ms	(* (* (/ 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))

series172.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
77.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify780.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (143.0ms)

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

prune244.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite29.0ms

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

series159.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
44.0ms	(/ (sin x) (sin (* 0.5 x)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.2s

Counts

125 → 125

Iterations

Useful iterations: 2 (191.0ms)

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

prune330.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

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:

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

series147.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (sin (* x 0.5)) 3.0)
73.0ms	(/ (* 8.0 (/ (sin (* x 0.5)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
38.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify909.0ms

Counts

120 → 120

Iterations

Useful iterations: done (905.0ms)

Iter	Nodes	Cost
0	219	2055
1	538	1969
2	2612	1625
done	5001	1623

prune330.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
65×	`add-exp-log`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`add-cbrt-cube`
33×	`cbrt-undiv` `div-exp`
24×	`cbrt-prod`
23×	`associate-/r*`
14×	`associate-/l*`
13×	`div-inv`
12×	`prod-exp` `cbrt-unprod`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`
1×	`associate-*r/` `associate-/r/`

Counts

4 → 187

Calls

4 calls:

6.0ms	(/ (sin (* x 0.5)) (* (cbrt 3.0) (cbrt 3.0)))
20.0ms	(/ (* 8.0 (/ (/ (sin (* x 0.5)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
9.0ms	(/ (/ (sin (* x 0.5)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))

series432.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (sin (* x 0.5)) (* (cbrt 3.0) (cbrt 3.0)))
163.0ms	(/ (* 8.0 (/ (/ (sin (* x 0.5)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))) (/ (sin x) (sin (* 0.5 x))))
44.0ms	(/ (sin x) (sin (* 0.5 x)))
113.0ms	(/ (/ (sin (* x 0.5)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))

simplify1.4s

Counts

199 → 199

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	336	4524
1	849	3908
2	4080	3089
done	5000	3087

prune558.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes38.0ms

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	14	16
done	14	16

end0.0ms

sample1.7s

Algorithm

intervals

Results

743.0ms	1519×	body	1280	valid
391.0ms	1285×	body	640	valid
256.0ms	4288×	body	80	valid
127.0ms	607×	body	320	valid
42.0ms	301×	body	160	valid