Details

sample126.0ms

Algorithm

intervals

Results

45.0ms	47×	body	1280	valid
33.0ms	44×	body	640	valid
20.0ms	138×	body	80	valid
9.0ms	20×	body	320	valid
2.0ms	7×	body	160	valid

simplify403.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

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)))
16.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite256.0ms

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:

103.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
44.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
102.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series323.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
74.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
144.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify2.0s

Counts

94 → 94

Iterations

Useful iterations: done (2.0s)

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

prune431.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))

rewrite122.0ms

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))
76.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
28.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series249.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (sin (* x 0.5)) (sin x))
137.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
62.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify3.3s

Counts

113 → 113

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	189	1786
1	499	1739
2	3314	1390
done	5001	1349

prune448.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 8.0 (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)))

rewrite136.0ms

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:

39.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
27.0ms	(/ (sin (* x 0.5)) (sin x))
58.0ms	(* (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series216.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
52.0ms	(/ (sin (* x 0.5)) (sin x))
105.0ms	(* (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify3.3s

Counts

109 → 109

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	184	1823
1	502	1744
2	3589	1437
done	5000	1378

prune497.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

27.0ms	(/ (sin (* x 0.5)) (sin x))
45.0ms	(* (log1p (expm1 (/ (* 8.0 (sin (* 0.5 x))) 3.0))) (/ (sin (* x 0.5)) (sin x)))
1.0ms	(expm1 (/ (* 8.0 (sin (* 0.5 x))) 3.0))
0.0ms	(log1p (expm1 (/ (* 8.0 (sin (* 0.5 x))) 3.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (sin (* x 0.5)) (sin x))
553.0ms	(* (log1p (expm1 (/ (* 8.0 (sin (* 0.5 x))) 3.0))) (/ (sin (* x 0.5)) (sin x)))
146.0ms	(expm1 (/ (* 8.0 (sin (* 0.5 x))) 3.0))
287.0ms	(log1p (expm1 (/ (* 8.0 (sin (* 0.5 x))) 3.0)))

simplify1.1s

Counts

97 → 97

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	154	1578
1	324	1425
2	1383	1279
done	5000	1272

prune451.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	18
1	17	18
2	18	18
done	18	18

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.2s	1481×	body	1280	valid
957.0ms	1240×	body	640	valid
536.0ms	4347×	body	80	valid
295.0ms	617×	body	320	valid
192.0ms	315×	body	160	valid