Details

sample193.0ms

Algorithm

intervals

Results

95.0ms	51×	body	1280	valid
36.0ms	34×	body	640	valid
32.0ms	147×	body	80	valid
8.0ms	11×	body	320	valid
6.0ms	13×	body	160	valid

simplify290.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	274
6	274
5	256
4	169
3	89
2	43
1	20
0	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

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)))
18.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite170.0ms

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*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 88

Calls

3 calls:

61.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
31.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
76.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series209.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
50.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
86.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify2.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1619
1	423
0	172

prune472.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (sin (* x 0.5)) 8.0) 3.0)
0.1b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (/ (* (sin (* x 0.5)) 8.0) 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` `insert-posit16` `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 → 103

Calls

3 calls:

18.0ms	(/ (* (sin (* x 0.5)) 8.0) 3.0)
16.0ms	(/ (sin (* x 0.5)) (sin x))
45.0ms	(* (/ (* (sin (* x 0.5)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (* (sin (* x 0.5)) 8.0) 3.0)
42.0ms	(/ (sin (* x 0.5)) (sin x))
113.0ms	(* (/ (* (sin (* x 0.5)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify1.8s

Counts

112 → 112

Iterations

Iter	Nodes
done	5003
2	1840
1	484
0	183

prune478.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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` `insert-posit16` `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 → 89

Calls

4 calls:

25.0ms	(/ (sin (* x 0.5)) (sin x))
0.0ms	(log1p (expm1 (/ (* (sin (* x 0.5)) 8.0) 3.0)))
26.0ms	(* (log1p (expm1 (/ (* (sin (* x 0.5)) 8.0) 3.0))) (/ (sin (* x 0.5)) (sin x)))
1.0ms	(expm1 (/ (* (sin (* x 0.5)) 8.0) 3.0))

series930.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (sin (* x 0.5)) (sin x))
290.0ms	(log1p (expm1 (/ (* (sin (* x 0.5)) 8.0) 3.0)))
466.0ms	(* (log1p (expm1 (/ (* (sin (* x 0.5)) 8.0) 3.0))) (/ (sin (* x 0.5)) (sin x)))
104.0ms	(expm1 (/ (* (sin (* x 0.5)) 8.0) 3.0))

simplify2.5s

Counts

101 → 101

Iterations

Iter	Nodes
done	5018
3	4134
2	1165
1	329
0	158

prune553.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
0.1b	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
0.2b	(/ (sin x) (sin (* x 0.5)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
98×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
10×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/l*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 172

Calls

3 calls:

21.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
33.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
23.0ms	(/ (sin x) (sin (* x 0.5)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
117.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
47.0ms	(/ (sin x) (sin (* x 0.5)))

simplify1.9s

Counts

181 → 181

Iterations

Iter	Nodes
done	5002
2	2546
1	684
0	261

prune804.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes49.0ms

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

sample6.7s

Algorithm

intervals

Results

2.8s	1532×	body	1280	valid
2.0s	1302×	body	640	valid
973.0ms	4274×	body	80	valid
489.0ms	578×	body	320	valid
201.0ms	314×	body	160	valid