Details

sample127.0ms

Algorithm

intervals

Results

44.0ms	39×	body	640	valid
36.0ms	45×	body	1280	valid
15.0ms	129×	body	80	valid
11.0ms	27×	body	320	valid
4.0ms	16×	body	160	valid

simplify297.0ms

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: 14.0b

localize42.0ms

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)))
13.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite162.0ms

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:

66.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
23.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
67.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series239.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
54.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
106.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify2.1s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	2504
1	424
0	169

prune611.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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)))

rewrite80.0ms

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:

15.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
11.0ms	(/ (sin (* x 0.5)) (sin x))
51.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
70.0ms	(/ (sin (* x 0.5)) (sin x))
123.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify2.7s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	3384
1	499
0	181

prune774.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize46.0ms

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

rewrite29.0ms

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:

10.0ms	(/ (sin (* x 0.5)) (sin x))
0.0ms	(expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))
0.0ms	(log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0)))
15.0ms	(* (log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))) (/ (sin (* x 0.5)) (sin x)))

series988.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (sin (* x 0.5)) (sin x))
118.0ms	(expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))
266.0ms	(log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0)))
531.0ms	(* (log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))) (/ (sin (* x 0.5)) (sin x)))

simplify1.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1397
1	324
0	154

prune736.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (/ (sin (* x 0.5)) (sin x)) 2.6666666666666665)
0.2b	(* (sin (* x 0.5)) (* (/ (sin (* x 0.5)) (sin x)) 2.6666666666666665))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 86

Calls

3 calls:

17.0ms	(/ (sin (* x 0.5)) (sin x))
16.0ms	(* (/ (sin (* x 0.5)) (sin x)) 2.6666666666666665)
38.0ms	(* (sin (* x 0.5)) (* (/ (sin (* x 0.5)) (sin x)) 2.6666666666666665))

series266.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (sin (* x 0.5)) (sin x))
78.0ms	(* (/ (sin (* x 0.5)) (sin x)) 2.6666666666666665)
129.0ms	(* (sin (* x 0.5)) (* (/ (sin (* x 0.5)) (sin x)) 2.6666666666666665))

simplify1.6s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1774
1	354
0	148

prune536.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes266.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.2s	1517×	body	1280	valid
891.0ms	1213×	body	640	valid
720.0ms	4311×	body	80	valid
314.0ms	633×	body	320	valid
87.0ms	326×	body	160	valid