Details

sample56.0ms

Algorithm

intervals

Results

20.0ms	42×	body	1280	valid
15.0ms	52×	body	640	valid
9.0ms	140×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid

simplify117.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize11.0ms

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)))
16.6b	(/ (* (* (/ 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×	`associate-/r*` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 79

Calls

3 calls:

20.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
19.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
73.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify634.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (201.0ms)

Iter	Nodes	Cost
0	163	1474
1	403	1285
2	1604	1016
done	5000	1016

prune209.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
0.2b	(/ (sin x) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
13×	`cbrt-undiv` `div-exp` `associate-l`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1` `div-inv`
4×	`associate-/l*`
3×	`associate-r` `add-log-exp`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 110

Calls

3 calls:

11.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
3.0ms	(/ (sin x) (sin (* x 0.5)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
38.0ms	(/ (sin x) (sin (* x 0.5)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.1s

Counts

119 → 119

Iterations

Useful iterations: 2 (396.0ms)

Iter	Nodes	Cost
0	211	2048
1	528	1898
2	2053	1604
done	5000	1604

prune269.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

59×	`times-frac`
50×	`add-sqr-sqrt`
43×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
32×	`associate-l`
28×	`sqrt-prod`
16×	`associate-/r*`
11×	`pow1`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
9×	`sqrt-div`
7×	`associate-*l/`
6×	`div-inv`
4×	`associate-r` `pow-prod-down` `associate-/l*` `add-log-exp`
3×	`associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-r/` `clear-num` `-commutative`
1×	`associate-/r/`

Counts

4 → 148

Calls

4 calls:

14.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
27.0ms	(/ (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin x) (sin (* x 0.5))))
3.0ms	(/ (sin x) (sin (* x 0.5)))
28.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
151.0ms	(/ (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin x) (sin (* x 0.5))))
38.0ms	(/ (sin x) (sin (* x 0.5)))
91.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

simplify967.0ms

Counts

160 → 160

Iterations

Useful iterations: 2 (393.0ms)

Iter	Nodes	Cost
0	255	3172
1	641	2638
2	2498	2206
done	5001	2206

prune423.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
0.2b	(/ (sin (* x 0.5)) (sin x))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite40.0ms

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×	`associate-/r` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 98

Calls

3 calls:

21.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
3.0ms	(/ (sin (* x 0.5)) (sin x))
12.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series153.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
41.0ms	(/ (sin (* x 0.5)) (sin x))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify795.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (325.0ms)

Iter	Nodes	Cost
0	183	1718
1	453	1555
2	1762	1306
done	5001	1306

prune222.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: done (1.0ms)

Iter	Nodes	Cost
0	14	20
1	20	18
done	20	16

end0.0ms

sample1.7s

Algorithm

intervals

Results

724.0ms	1513×	body	1280	valid
387.0ms	1231×	body	640	valid
273.0ms	4339×	body	80	valid
139.0ms	622×	body	320	valid
43.0ms	295×	body	160	valid