Details

sample136.0ms

Algorithm

intervals

Results

55.0ms	43×	body	1280	valid
27.0ms	38×	body	640	valid
20.0ms	140×	body	80	valid
13.0ms	26×	body	320	valid
3.0ms	9×	body	160	valid

simplify381.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	43	16
3	93	16
4	173	16
5	277	16
6	314	16
done	314	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize23.0ms

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)))
14.7b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite243.0ms

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:

109.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
85.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series253.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
52.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
116.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.7s

Counts

94 → 94

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	169	1554
1	424	1349
2	2490	1130
done	5002	1088

prune399.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite107.0ms

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:

47.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
25.0ms	(/ (sin x) (sin (* x 0.5)))
32.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
56.0ms	(/ (sin x) (sin (* x 0.5)))
62.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify2.8s

Counts

125 → 125

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	217	2116
1	578	1964
2	3999	1712
done	5000	1700

prune427.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite146.0ms

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:

58.0ms	(* (/ (sin x) (sin (* x 0.5))) 3.0)
25.0ms	(/ (sin x) (sin (* x 0.5)))
56.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* x 0.5))) 3.0))

series278.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(* (/ (sin x) (sin (* x 0.5))) 3.0)
62.0ms	(/ (sin x) (sin (* x 0.5)))
125.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* x 0.5))) 3.0))

simplify1.7s

Counts

100 → 100

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	171	1602
1	448	1539
2	2934	1232
done	5000	1231

prune464.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(/ (* 8.0 (sin (* x 0.5))) (* (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)) 3.0))
0.3b	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
0.4b	(pow (/ (sin x) (sin (* 0.5 x))) 3)

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
21×	`add-exp-log`
19×	`add-cbrt-cube`
6×	`cbrt-undiv` `div-exp` `div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`cube-div` `pow-unpow`
2×	`cube-mult` `cbrt-div` `frac-2neg` `unpow3` `pow-exp` `clear-num` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `associate-*l/` `associate-/r/` `rem-cbrt-cube`

Counts

4 → 145

Calls

4 calls:

24.0ms	(/ (sin x) (sin (* 0.5 x)))
67.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)) 3.0))
30.0ms	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
23.0ms	(pow (/ (sin x) (sin (* 0.5 x))) 3)

series348.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (sin x) (sin (* 0.5 x)))
109.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)) 3.0))
59.0ms	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
132.0ms	(pow (/ (sin x) (sin (* 0.5 x))) 3)

simplify429.0ms

Counts

157 → 157

Iterations

Useful iterations: done (424.0ms)

Iter	Nodes	Cost
0	220	2820
1	678	2370
done	5000	2113

prune521.0ms

Pruning

8 alts after pruning (6 fresh and 2 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	13	16
1	14	16
done	14	16

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.2s	1478×	body	1280	valid
800.0ms	1243×	body	640	valid
625.0ms	4364×	body	80	valid
354.0ms	605×	body	320	valid
73.0ms	310×	body	160	valid