Details

sample61.0ms

Algorithm

intervals

Results

23.0ms	48×	body	1280	valid
14.0ms	45×	body	640	valid
9.0ms	140×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

simplify125.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	42	16
3	90	16
4	168	16
5	237	16
6	255	16
done	255	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize12.0ms

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)))
14.9b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite55.0ms

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:

21.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
21.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series191.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
46.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
87.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify700.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (217.0ms)

Iter	Nodes	Cost
0	169	1554
1	413	1349
2	1629	1080
done	5000	1080

prune274.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))

rewrite34.0ms

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:

9.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
4.0ms	(/ (sin (* x 0.5)) (sin x))
17.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series170.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
49.0ms	(/ (sin (* x 0.5)) (sin x))
82.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify723.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (285.0ms)

Iter	Nodes	Cost
0	181	1823
1	463	1671
2	1787	1392
done	5001	1392

prune299.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0)) (cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0)))
0.6b	(cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0))
0.6b	(cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0))
0.6b	(cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

53×	`cbrt-prod`
30×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 111

Calls

4 calls:

12.0ms	(* (cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0)) (cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0)))
2.0ms	(cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0))
2.0ms	(cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0))
2.0ms	(cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0))

series961.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(* (cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0)) (cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0)))
221.0ms	(cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0))
223.0ms	(cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0))
238.0ms	(cbrt (/ (* 8.0 (sin (* x 0.5))) 3.0))

simplify1.8s

Counts

123 → 123

Iterations

Useful iterations: 3 (564.0ms)

Iter	Nodes	Cost
0	141	2385
1	287	2248
2	914	2077
3	4414	1831
done	5000	1831

prune470.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 2.6666666666666665 (/ (pow (sin (* 0.5 x)) 2) (sin x)))
0.3b	(pow (sin (* 0.5 x)) 2)
14.9b	(/ (pow (sin (* 0.5 x)) 2) (sin x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
50×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `*-un-lft-identity`
28×	`associate-r`
25×	`unpow-prod-down`
19×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`unpow2` `sqr-pow`
8×	`associate-/l*`
6×	`pow1` `div-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`expm1-log1p-u` `pow-to-exp` `pow-unpow` `associate-l` `pow-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv`
1×	`pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 125

Calls

3 calls:

16.0ms	(* 2.6666666666666665 (/ (pow (sin (* 0.5 x)) 2) (sin x)))
2.0ms	(pow (sin (* 0.5 x)) 2)
6.0ms	(/ (pow (sin (* 0.5 x)) 2) (sin x))

series196.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(* 2.6666666666666665 (/ (pow (sin (* 0.5 x)) 2) (sin x)))
39.0ms	(pow (sin (* 0.5 x)) 2)
71.0ms	(/ (pow (sin (* 0.5 x)) 2) (sin x))

simplify1.9s

Counts

134 → 134

Iterations

Useful iterations: 2 (166.0ms)

Iter	Nodes	Cost
0	193	1962
1	420	1776
2	1093	1599
3	3759	1599
done	5001	1599

prune314.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	14	16
done	14	16

end0.0ms

sample1.8s

Algorithm

intervals

Results

750.0ms	1459×	body	1280	valid
393.0ms	1212×	body	640	valid
280.0ms	4339×	body	80	valid
154.0ms	649×	body	320	valid
58.0ms	341×	body	160	valid