Details

sample114.0ms

Algorithm

intervals

Results

39.0ms	140×	body	80	valid
32.0ms	46×	body	1280	valid
15.0ms	34×	body	640	valid
11.0ms	21×	body	320	valid
4.0ms	15×	body	160	valid

simplify373.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
13.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite197.0ms

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:

82.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
78.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series345.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
79.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
140.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.5s

Counts

94 → 94

Iterations

Useful iterations: 2 (302.0ms)

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

prune384.0ms

Pruning

15 alts after pruning (15 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)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite116.0ms

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:

19.0ms	(/ (sin (* x 0.5)) (sin x))
66.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
27.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series216.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (sin (* x 0.5)) (sin x))
119.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.8s

Counts

113 → 113

Iterations

Useful iterations: 2 (363.0ms)

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

prune367.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 99

Calls

3 calls:

16.0ms	(/ (sin (* 0.5 x)) 3.0)
21.0ms	(/ (sin (* x 0.5)) (sin x))
57.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (sin (* 0.5 x)) 3.0)
60.0ms	(/ (sin (* x 0.5)) (sin x))
103.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

simplify1.7s

Counts

108 → 108

Iterations

Useful iterations: 2 (328.0ms)

Iter	Nodes	Cost
0	193	1725
1	435	1646
2	1549	1310
done	5000	1310

prune472.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

14.0ms	(/ (sin (* x 0.5)) (sin x))
0.0ms	(expm1 (log1p (/ (sin (* 0.5 x)) 3.0)))
1.0ms	(log1p (/ (sin (* 0.5 x)) 3.0))
54.0ms	(* (* 8.0 (expm1 (log1p (/ (sin (* 0.5 x)) 3.0)))) (/ (sin (* x 0.5)) (sin x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (sin (* x 0.5)) (sin x))
354.0ms	(expm1 (log1p (/ (sin (* 0.5 x)) 3.0)))
154.0ms	(log1p (/ (sin (* 0.5 x)) 3.0))
635.0ms	(* (* 8.0 (expm1 (log1p (/ (sin (* 0.5 x)) 3.0)))) (/ (sin (* x 0.5)) (sin x)))

simplify1.8s

Counts

98 → 98

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	165	1577
1	364	1413
2	1291	1137
done	5000	1136

prune433.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes52.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	20
1	21	20
done	21	20

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.8s	1542×	body	1280	valid
796.0ms	1200×	body	640	valid
638.0ms	4318×	body	80	valid
407.0ms	644×	body	320	valid
72.0ms	296×	body	160	valid