Details

sample98.0ms

Algorithm

intervals

Results

36.0ms	46×	body	1280	valid
18.0ms	34×	body	640	valid
16.0ms	140×	body	80	valid
8.0ms	21×	body	320	valid
4.0ms	15×	body	160	valid

simplify365.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	43	16
3	89	16
4	168	16
5	257	16
6	273	16
done	273	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize20.0ms

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)))
13.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite219.0ms

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:

85.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
93.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series240.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
59.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
116.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.3s

Counts

94 → 94

Iterations

Useful iterations: 2 (239.0ms)

Iter	Nodes	Cost
0	169	1554
1	405	1349
2	1480	1080
done	5000	1080

prune379.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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)))

rewrite143.0ms

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:

14.0ms	(/ (sin (* x 0.5)) (sin x))
80.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
46.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series280.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (sin (* x 0.5)) (sin x))
133.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
65.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.9s

Counts

113 → 113

Iterations

Useful iterations: 2 (376.0ms)

Iter	Nodes	Cost
0	189	1786
1	447	1612
2	1605	1349
done	5001	1349

prune468.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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)))

rewrite110.0ms

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:

20.0ms	(/ (sin (* 0.5 x)) 3.0)
29.0ms	(/ (sin (* x 0.5)) (sin x))
55.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

series283.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (sin (* 0.5 x)) 3.0)
66.0ms	(/ (sin (* x 0.5)) (sin x))
146.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

simplify1.8s

Counts

108 → 108

Iterations

Useful iterations: 2 (307.0ms)

Iter	Nodes	Cost
0	193	1725
1	435	1646
2	1549	1310
done	5000	1310

prune454.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (cbrt (pow (/ (sin (* x 0.5)) (sin x)) 3)))
0.4b	(pow (/ (sin (* x 0.5)) (sin x)) 3)
0.8b	(cbrt (pow (/ (sin (* x 0.5)) (sin x)) 3))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
63×	`times-frac`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
35×	`associate-r`
18×	`add-exp-log`
15×	`add-cbrt-cube`
10×	`pow1`
7×	`div-inv`
5×	`prod-exp` `cbrt-unprod`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `cube-mult` `pow-unpow` `cbrt-div` `unpow3` `associate-r/` `div-exp` `pow-prod-down` `associate-/r` `associate-/l*` `sqr-pow`
2×	`pow-exp` `rem-cube-cbrt`
1×	`frac-times` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `associate-l` `associate-l/` `clear-num` `-commutative` `rem-cbrt-cube`

Counts

4 → 178

Calls

4 calls:

17.0ms	(/ (sin (* x 0.5)) (sin x))
76.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (cbrt (pow (/ (sin (* x 0.5)) (sin x)) 3)))
13.0ms	(pow (/ (sin (* x 0.5)) (sin x)) 3)
12.0ms	(cbrt (pow (/ (sin (* x 0.5)) (sin x)) 3))

series397.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (sin (* x 0.5)) (sin x))
141.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (cbrt (pow (/ (sin (* x 0.5)) (sin x)) 3)))
110.0ms	(pow (/ (sin (* x 0.5)) (sin x)) 3)
63.0ms	(cbrt (pow (/ (sin (* x 0.5)) (sin x)) 3))

simplify1.6s

Counts

190 → 190

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	240	3449
1	590	2887
2	2149	2452
done	5001	2437

prune623.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes46.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.0s	1542×	body	1280	valid
1.1s	4318×	body	80	valid
862.0ms	1200×	body	640	valid
466.0ms	644×	body	320	valid
148.0ms	296×	body	160	valid