Details

sample105.0ms

Algorithm

intervals

Results

35.0ms	46×	body	1280	valid
28.0ms	137×	body	80	valid
18.0ms	35×	body	640	valid
9.0ms	25×	body	320	valid
3.0ms	13×	body	160	valid

simplify333.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	275
7	275
6	274
5	226
4	134
3	71
2	35
1	20
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize33.0ms

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)))
15.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite233.0ms

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:

109.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
83.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series274.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
63.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
133.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.9s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1537
1	423
0	172

prune380.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (/ 3.0 8.0))
0.2b	(/ (sin (* x 0.5)) (sin x))
0.3b	(* (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ (sin (* x 0.5)) (sin x)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
116×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
31×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`cbrt-undiv` `div-exp` `associate-r`
11×	`div-inv`
6×	`prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
5×	`pow1`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 193

Calls

3 calls:

28.0ms	(/ (sin (* x 0.5)) (/ 3.0 8.0))
22.0ms	(/ (sin (* x 0.5)) (sin x))
59.0ms	(* (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ (sin (* x 0.5)) (sin x)))

series231.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (sin (* x 0.5)) (/ 3.0 8.0))
63.0ms	(/ (sin (* x 0.5)) (sin x))
113.0ms	(* (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ (sin (* x 0.5)) (sin x)))

simplify2.3s

Counts

202 → 202

Iterations

Iter	Nodes
done	5000
2	3547
1	928
0	312

prune951.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (/ 3.0 8.0))
0.1b	(/ 1 (/ (sin x) (sin (* x 0.5))))
0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(* (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ 1 (/ (sin x) (sin (* x 0.5)))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

324×	`times-frac`
223×	`add-sqr-sqrt`
172×	`*-un-lft-identity`
166×	`add-cube-cbrt`
100×	`add-exp-log`
53×	`div-exp`
52×	`add-cbrt-cube`
44×	`associate-r` `associate-l`
29×	`associate-/r*`
25×	`cbrt-undiv`
21×	`prod-exp`
19×	`div-inv`
15×	`unswap-sqr`
9×	`cbrt-unprod` `associate-/l*`
8×	`rec-exp` `1-exp`
7×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 331

Calls

4 calls:

18.0ms	(/ (sin (* x 0.5)) (/ 3.0 8.0))
16.0ms	(/ 1 (/ (sin x) (sin (* x 0.5))))
12.0ms	(/ (sin x) (sin (* x 0.5)))
112.0ms	(* (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ 1 (/ (sin x) (sin (* x 0.5)))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (sin (* x 0.5)) (/ 3.0 8.0))
63.0ms	(/ 1 (/ (sin x) (sin (* x 0.5))))
74.0ms	(/ (sin x) (sin (* x 0.5)))
119.0ms	(* (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ 1 (/ (sin x) (sin (* x 0.5)))))

simplify1.5s

Counts

343 → 343

Iterations

Iter	Nodes
done	5000
1	1468
0	479

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (log1p (expm1 (/ (sin x) (sin (* x 0.5))))))
0.2b	(/ (sin x) (sin (* x 0.5)))
0.2b	(log1p (expm1 (/ (sin x) (sin (* x 0.5)))))
0.3b	(* (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ 1 (log1p (expm1 (/ (sin x) (sin (* x 0.5)))))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
92×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
62×	`add-cube-cbrt`
49×	`add-exp-log`
44×	`associate-l`
29×	`add-cbrt-cube`
21×	`div-exp`
13×	`associate-r`
12×	`prod-exp`
11×	`cbrt-undiv`
9×	`unswap-sqr`
7×	`pow1` `div-inv`
6×	`associate-/r` `cbrt-unprod` `associate-/l`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `log1p-udef` `pow-prod-down` `associate-l/` `log1p-expm1` `associate-r/` `associate-/r/` `un-div-inv` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 176

Calls

4 calls:

5.0ms	(/ 1 (log1p (expm1 (/ (sin x) (sin (* x 0.5))))))
13.0ms	(/ (sin x) (sin (* x 0.5)))
0.0ms	(log1p (expm1 (/ (sin x) (sin (* x 0.5)))))
65.0ms	(* (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ 1 (log1p (expm1 (/ (sin x) (sin (* x 0.5)))))))

series917.0ms

Counts

4 → 12

Calls

4 calls:

285.0ms	(/ 1 (log1p (expm1 (/ (sin x) (sin (* x 0.5))))))
65.0ms	(/ (sin x) (sin (* x 0.5)))
244.0ms	(log1p (expm1 (/ (sin x) (sin (* x 0.5)))))
322.0ms	(* (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ 1 (log1p (expm1 (/ (sin x) (sin (* x 0.5)))))))

simplify2.2s

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
2	3018
1	840
0	316

prune881.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes52.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	1466×	body	1280	valid
1.3s	1207×	body	640	valid
612.0ms	4344×	body	80	valid
299.0ms	636×	body	320	valid
86.0ms	347×	body	160	valid