Details

sample180.0ms

Algorithm

intervals

Results

72.0ms	41×	body	1280	valid
34.0ms	40×	body	640	valid
26.0ms	138×	body	80	valid
16.0ms	26×	body	320	valid
5.0ms	11×	body	160	valid

simplify421.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize38.0ms

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)))
13.9b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite270.0ms

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:

106.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
58.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
103.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series322.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
74.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
141.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify2.0s

Counts

94 → 94

Iterations

Useful iterations: done (2.0s)

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

prune462.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)))

rewrite213.0ms

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:

26.0ms	(/ (sin (* x 0.5)) (sin x))
132.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
47.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series272.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/ (sin (* x 0.5)) (sin x))
130.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
78.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify3.4s

Counts

113 → 113

Iterations

Useful iterations: done (3.4s)

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

prune679.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize43.0ms

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)))

rewrite92.0ms

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:

13.0ms	(/ (sin (* 0.5 x)) 3.0)
14.0ms	(/ (sin (* x 0.5)) (sin x))
61.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

series299.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(/ (sin (* 0.5 x)) 3.0)
86.0ms	(/ (sin (* x 0.5)) (sin x))
130.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

simplify2.4s

Counts

108 → 108

Iterations

Useful iterations: done (2.4s)

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

prune621.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

39×	`exp-prod`
37×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`times-frac`
28×	`log-pow`
17×	`associate-r`
15×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`log-prod`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`frac-2neg` `associate-r/` `rem-log-exp` `associate-l` `associate-l/` `clear-num` `*-commutative` `rem-exp-log`

Counts

4 → 122

Calls

4 calls:

19.0ms	(/ (sin (* x 0.5)) (sin x))
10.0ms	(exp (/ (sin (* x 0.5)) (sin x)))
22.0ms	(log (exp (/ (sin (* x 0.5)) (sin x))))
86.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (log (exp (/ (sin (* x 0.5)) (sin x)))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (sin (* x 0.5)) (sin x))
148.0ms	(exp (/ (sin (* x 0.5)) (sin x)))
54.0ms	(log (exp (/ (sin (* x 0.5)) (sin x))))
134.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (log (exp (/ (sin (* x 0.5)) (sin x)))))

simplify2.1s

Counts

134 → 134

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	208	2119
1	492	1944
2	2613	1730
done	5000	1648

prune669.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes68.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	18
1	17	18
done	17	18

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.9s	1468×	body	1280	valid
1.1s	4310×	body	80	valid
842.0ms	1283×	body	640	valid
279.0ms	635×	body	320	valid
75.0ms	304×	body	160	valid