Details

sample100.0ms

Algorithm

intervals

Results

33.0ms	37×	body	1280	valid
24.0ms	45×	body	640	valid
16.0ms	146×	body	80	valid
6.0ms	15×	body	320	valid
3.0ms	13×	body	160	valid

simplify475.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize21.0ms

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)))
14.9b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite236.0ms

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:

111.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
32.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
90.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series292.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
58.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
142.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.8s

Counts

94 → 94

Iterations

Useful iterations: 2 (357.0ms)

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

prune438.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
28×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
14×	`associate-l`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `associate-*l/`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 104

Calls

3 calls:

14.0ms	(/ (sin (* x 0.5)) (sin x))
99.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series295.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ (sin (* x 0.5)) (sin x))
157.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
69.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify2.1s

Counts

113 → 113

Iterations

Useful iterations: 2 (442.0ms)

Iter	Nodes	Cost
0	189	1786
1	447	1612
2	1605	1349
done	5001	1349

prune453.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 100

Calls

3 calls:

29.0ms	(/ (sin (* x 0.5)) (sin x))
48.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
48.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

series277.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (sin (* x 0.5)) (sin x))
69.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
134.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify1.7s

Counts

109 → 109

Iterations

Useful iterations: 2 (465.0ms)

Iter	Nodes	Cost
0	184	1811
1	450	1731
2	1654	1375
done	5000	1375

prune565.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
0.1b	(log1p (expm1 (/ (* (sin (* 0.5 x)) 8.0) 3.0)))
0.2b	(expm1 (/ (* (sin (* 0.5 x)) 8.0) 3.0))
0.2b	(* (log1p (expm1 (/ (* (sin (* 0.5 x)) 8.0) 3.0))) (/ (sin (* x 0.5)) (sin x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

19.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
0.0ms	(log1p (expm1 (/ (* (sin (* 0.5 x)) 8.0) 3.0)))
0.0ms	(expm1 (/ (* (sin (* 0.5 x)) 8.0) 3.0))
25.0ms	(* (log1p (expm1 (/ (* (sin (* 0.5 x)) 8.0) 3.0))) (/ (sin (* x 0.5)) (sin x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
306.0ms	(log1p (expm1 (/ (* (sin (* 0.5 x)) 8.0) 3.0)))
149.0ms	(expm1 (/ (* (sin (* 0.5 x)) 8.0) 3.0))
537.0ms	(* (log1p (expm1 (/ (* (sin (* 0.5 x)) 8.0) 3.0))) (/ (sin (* x 0.5)) (sin x)))

simplify1.5s

Counts

91 → 91

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	179	1481
1	394	1328
2	1424	1105
done	5001	1104

prune404.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes62.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	18
1	17	18
done	17	18

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.7s	1456×	body	1280	valid
1.2s	1271×	body	640	valid
1.1s	4346×	body	80	valid
325.0ms	603×	body	320	valid
156.0ms	324×	body	160	valid