Details

sample171.0ms

Algorithm

intervals

Results

44.0ms	40×	body	1280	valid
35.0ms	46×	body	640	valid
21.0ms	138×	body	80	valid
12.0ms	22×	body	320	valid
4.0ms	10×	body	160	valid

simplify475.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
13.5b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite294.0ms

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:

121.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
49.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
120.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series291.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
58.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
141.0ms	(/ (* (* (/ 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

prune598.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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

rewrite194.0ms

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:

23.0ms	(/ (sin (* x 0.5)) (sin x))
110.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
54.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series276.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (sin (* x 0.5)) (sin x))
134.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
64.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify4.2s

Counts

113 → 113

Iterations

Useful iterations: done (4.2s)

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

prune733.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 3 expressions with local error:

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

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-cbrt-cube`
27×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`prod-exp` `cbrt-unprod`
8×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-l` `associate-l/` `-commutative`

Counts

3 → 99

Calls

3 calls:

23.0ms	(/ (sin (* 0.5 x)) 3.0)
30.0ms	(/ (sin (* x 0.5)) (sin x))
73.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

series254.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(/ (sin (* 0.5 x)) 3.0)
62.0ms	(/ (sin (* x 0.5)) (sin x))
126.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

simplify2.8s

Counts

108 → 108

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	193	1725
1	481	1656
2	2894	1361
done	5000	1310

prune809.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (/ (sin (* x 0.5)) (sin x)))
0.2b	(cbrt (/ (sin (* x 0.5)) (sin x)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
0.7b	(* (cbrt (/ (sin (* x 0.5)) (sin x))) (cbrt (/ (sin (* x 0.5)) (sin x))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

90×	`cbrt-prod`
87×	`add-sqr-sqrt`
70×	`times-frac`
58×	`add-cube-cbrt` `*-un-lft-identity`
29×	`associate-l`
19×	`associate-r`
16×	`swap-sqr`
13×	`pow1`
11×	`add-exp-log` `unswap-sqr`
9×	`add-cbrt-cube`
8×	`pow1/3`
7×	`div-inv`
6×	`cbrt-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-l/` `pow-sqr` `-commutative` `pow-prod-up`
1×	`cbrt-undiv` `pow2` `frac-times` `pow-plus` `associate-*r/` `div-exp`

Counts

4 → 162

Calls

4 calls:

6.0ms	(cbrt (/ (sin (* x 0.5)) (sin x)))
6.0ms	(cbrt (/ (sin (* x 0.5)) (sin x)))
55.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
75.0ms	(* (cbrt (/ (sin (* x 0.5)) (sin x))) (cbrt (/ (sin (* x 0.5)) (sin x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

330.0ms	(cbrt (/ (sin (* x 0.5)) (sin x)))
359.0ms	(cbrt (/ (sin (* x 0.5)) (sin x)))
77.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
442.0ms	(* (cbrt (/ (sin (* x 0.5)) (sin x))) (cbrt (/ (sin (* x 0.5)) (sin x))))

simplify2.2s

Counts

174 → 174

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	254	3253
1	528	3078
2	2423	2785
done	5001	2739

prune1.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes93.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.8s	1544×	body	1280	valid
1.2s	1259×	body	640	valid
789.0ms	4260×	body	80	valid
490.0ms	625×	body	320	valid
100.0ms	312×	body	160	valid