Details

sample357.0ms

Algorithm

intervals

Results

142.0ms	103×	body	1280	valid
88.0ms	43×	body	640	valid
25.0ms	30×	body	320	valid
15.0ms	73×	body	80	valid
3.0ms	7×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
5	20
4	19
3	17
2	14
1	12
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

12.0ms	(* r (sin b))
13.0ms	(/ (* r (sin b)) (cos (+ a b)))
9.0ms	(cos (+ a b))

series224.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* r (sin b))
125.0ms	(/ (* r (sin b)) (cos (+ a b)))
50.0ms	(cos (+ a b))

simplify507.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	2010
2	671
1	212
0	95

prune362.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult` `insert-posit16`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-inv` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms	(* r (sin b))
40.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series504.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* r (sin b))
288.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
58.0ms	(* (sin a) (sin b))

simplify861.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	2021
2	1215
1	366
0	145

prune652.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/`

Counts

4 → 104

Calls

4 calls:

31.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
107.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
33.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series623.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
284.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
168.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
71.0ms	(* (sin a) (sin b))

simplify923.0ms

Counts

116 → 116

Iterations

Iter	Nodes
done	2016
2	1478
1	439
0	175

prune804.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`cos-mult` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `associate-/r` `1-exp` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `div-inv` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow`

Counts

4 → 118

Calls

4 calls:

17.0ms	(* r (sin b))
42.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
116.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms	(* (sin a) (sin b))

series543.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* r (sin b))
116.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
304.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
53.0ms	(* (sin a) (sin b))

simplify919.0ms

Counts

130 → 130

Iterations

Iter	Nodes
done	2021
2	1511
1	499
0	187

prune583.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes351.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	20
1	20
0	14

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.6s	2956×	body	1280	valid
2.0s	1821×	body	640	valid
765.0ms	2115×	body	80	valid
413.0ms	766×	body	320	valid
118.0ms	343×	body	160	valid