Details

sample140.0ms

Algorithm

intervals

Results

48.0ms	46×	body	1280	valid
35.0ms	49×	body	640	valid
18.0ms	126×	body	80	valid
11.0ms	21×	body	320	valid
5.0ms	14×	body	160	valid

simplify736.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	313
6	313
5	275
4	171
3	90
2	43
1	20
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.0b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
14×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
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×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 85

Calls

3 calls:

71.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
21.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
80.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series259.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
50.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
114.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.9s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	2504
1	424
0	169

prune587.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`*-un-lft-identity` `add-cube-cbrt`
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×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 100

Calls

3 calls:

24.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
20.0ms	(/ (sin (* x 0.5)) (sin x))
30.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series226.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
52.0ms	(/ (sin (* x 0.5)) (sin x))
100.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify2.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	3384
1	499
0	181

prune717.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

13.0ms	(/ (sin (* x 0.5)) (sin x))
0.0ms	(expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))
20.0ms	(* (log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))) (/ (sin (* x 0.5)) (sin x)))
1.0ms	(log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0)))

series980.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (sin (* x 0.5)) (sin x))
110.0ms	(expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))
538.0ms	(* (log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))) (/ (sin (* x 0.5)) (sin x)))
275.0ms	(log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0)))

simplify1.5s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1367
1	324
0	154

prune682.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

53.0ms	(/ (* (/ (sin (* 0.5 x)) (sin x)) (* (sin (* 0.5 x)) 8.0)) 3.0)
10.0ms	(/ (sin (* 0.5 x)) (sin x))
87.0ms	(* (/ (sin (* 0.5 x)) (sin x)) (* (sin (* 0.5 x)) 8.0))

series283.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(/ (* (/ (sin (* 0.5 x)) (sin x)) (* (sin (* 0.5 x)) 8.0)) 3.0)
68.0ms	(/ (sin (* 0.5 x)) (sin x))
113.0ms	(* (/ (sin (* 0.5 x)) (sin x)) (* (sin (* 0.5 x)) 8.0))

simplify1.7s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
2	2469
1	462
0	172

prune563.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	20
2	20
1	19
0	13

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.1s	1532×	body	1280	valid
850.0ms	1246×	body	640	valid
771.0ms	607×	body	320	valid
590.0ms	4286×	body	80	valid
139.0ms	329×	body	160	valid