Details

sample137.0ms

Algorithm

intervals

Results

38.0ms	41×	body	1280	valid
35.0ms	22×	body	320	valid
25.0ms	40×	body	640	valid
19.0ms	145×	body	80	valid
3.0ms	8×	body	160	valid

simplify377.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize14.0ms

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)))
15.7b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite275.0ms

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:

119.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
60.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
92.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series268.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
56.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
122.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify2.1s

Counts

94 → 94

Iterations

Useful iterations: done (2.1s)

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

prune384.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

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

rewrite212.0ms

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:

24.0ms	(/ (sin (* x 0.5)) (sin x))
113.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
68.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ (sin (* x 0.5)) (sin x))
122.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
75.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify3.3s

Counts

113 → 113

Iterations

Useful iterations: done (3.2s)

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

prune490.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite89.0ms

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:

15.0ms	(/ (sin (* x 0.5)) (sin x))
24.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
46.0ms	(* (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series242.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (sin (* x 0.5)) (sin x))
52.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
142.0ms	(* (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify2.9s

Counts

109 → 109

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	184	1823
1	502	1744
2	3618	1429
done	5000	1384

prune482.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
88×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
43×	`associate-r`
31×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
10×	`cbrt-undiv` `div-exp` `div-inv`
9×	`prod-exp` `cbrt-unprod`
8×	`pow1`
6×	`associate-/r*`
3×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`associate-r/` `associate-l` `-commutative` `associate-/l/`

Counts

3 → 170

Calls

3 calls:

15.0ms	(/ (sin (* 0.5 x)) (sin x))
22.0ms	(/ (/ (sin (* 0.5 x)) (sin x)) 3.0)
73.0ms	(* (* 8.0 (sin (* 0.5 x))) (/ (/ (sin (* 0.5 x)) (sin x)) 3.0))

series329.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (sin (* 0.5 x)) (sin x))
114.0ms	(/ (/ (sin (* 0.5 x)) (sin x)) 3.0)
147.0ms	(* (* 8.0 (sin (* 0.5 x))) (/ (/ (sin (* 0.5 x)) (sin x)) 3.0))

simplify950.0ms

Counts

179 → 179

Iterations

Useful iterations: done (940.0ms)

Iter	Nodes	Cost
0	274	3301
1	825	3151
done	5000	2894

prune775.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	15	16
2	16	16
done	16	16

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	1535×	body	1280	valid
1.4s	1268×	body	640	valid
588.0ms	4280×	body	80	valid
286.0ms	612×	body	320	valid
83.0ms	305×	body	160	valid