Details

sample57.0ms

Algorithm

intervals

Results

23.0ms	50×	body	1280	valid
11.0ms	37×	body	640	valid
8.0ms	128×	body	80	valid
4.0ms	20×	body	320	valid
3.0ms	21×	body	160	valid

simplify183.0ms

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: 14.7b

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)))
14.6b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite56.0ms

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:

20.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
13.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
20.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series185.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
82.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.1s

Counts

94 → 94

Iterations

Useful iterations: 2 (217.0ms)

Iter	Nodes	Cost
0	169	1554
1	414	1349
2	1620	1080
done	5000	1080

prune262.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin (* x 0.5)) (sin x))
0.3b	(* (* (sin (* 0.5 x)) (/ 8.0 3.0)) (/ (sin (* x 0.5)) (sin x)))
0.4b	(* (sin (* 0.5 x)) (/ 8.0 3.0))

rewrite38.0ms

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` `associate-r*`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`associate-r/` `associate-l*` `pow-prod-down`
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-*l/` `clear-num`

Counts

3 → 104

Calls

3 calls:

4.0ms	(/ (sin (* x 0.5)) (sin x))
20.0ms	(* (* (sin (* 0.5 x)) (/ 8.0 3.0)) (/ (sin (* x 0.5)) (sin x)))
10.0ms	(* (sin (* 0.5 x)) (/ 8.0 3.0))

series166.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (sin (* x 0.5)) (sin x))
83.0ms	(* (* (sin (* 0.5 x)) (/ 8.0 3.0)) (/ (sin (* x 0.5)) (sin x)))
43.0ms	(* (sin (* 0.5 x)) (/ 8.0 3.0))

simplify1.0s

Counts

113 → 113

Iterations

Useful iterations: 2 (382.0ms)

Iter	Nodes	Cost
0	196	1801
1	495	1699
2	1959	1357
done	5000	1357

prune354.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

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:

5.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
4.0ms	(/ (sin (* x 0.5)) (sin x))
16.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
42.0ms	(/ (sin (* x 0.5)) (sin x))
85.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify1.0s

Counts

109 → 109

Iterations

Useful iterations: 2 (280.0ms)

Iter	Nodes	Cost
0	184	1811
1	471	1731
2	1823	1375
done	5001	1375

prune355.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

99×	`times-frac`
92×	`add-exp-log`
74×	`add-sqr-sqrt`
61×	`add-cbrt-cube`
55×	`add-cube-cbrt` `*-un-lft-identity`
38×	`cbrt-undiv` `div-exp`
35×	`cbrt-prod`
34×	`associate-l`
28×	`prod-exp` `cbrt-unprod`
18×	`div-inv`
13×	`associate-r`
10×	`associate-/r*`
9×	`associate-/l*`
6×	`pow1` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 207

Calls

4 calls:

10.0ms	(/ (* (sin (* 0.5 x)) 8.0) (* (cbrt 3.0) (cbrt 3.0)))
4.0ms	(/ (sin (* x 0.5)) (sin x))
40.0ms	(* (/ (/ (* (sin (* 0.5 x)) 8.0) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) (/ (sin (* x 0.5)) (sin x)))
10.0ms	(/ (/ (* (sin (* 0.5 x)) 8.0) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))

series582.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (* (sin (* 0.5 x)) 8.0) (* (cbrt 3.0) (cbrt 3.0)))
52.0ms	(/ (sin (* x 0.5)) (sin x))
194.0ms	(* (/ (/ (* (sin (* 0.5 x)) 8.0) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) (/ (sin (* x 0.5)) (sin x)))
146.0ms	(/ (/ (* (sin (* 0.5 x)) 8.0) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))

simplify1.7s

Counts

219 → 219

Iterations

Useful iterations: 2 (804.0ms)

Iter	Nodes	Cost
0	316	5241
1	889	4564
2	3711	3605
done	5001	3605

prune747.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes42.0ms

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: 0 (0.0ms)

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

end0.0ms

sample1.9s

Algorithm

intervals

Results

686.0ms	1449×	body	1280	valid
524.0ms	4315×	body	80	valid
398.0ms	1309×	body	640	valid
122.0ms	599×	body	320	valid
46.0ms	328×	body	160	valid