Details

sample303.0ms

Algorithm

intervals

Results

100.0ms	94×	body	1280	valid
47.0ms	69×	body	640	valid
12.0ms	26×	body	320	valid
8.0ms	57×	body	80	valid
3.0ms	10×	body	160	valid

simplify54.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize40.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.4b	(cos (+ a b))

rewrite62.0ms

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:

11.0ms	(* r (sin b))
21.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

series196.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* r (sin b))
118.0ms	(/ (* r (sin b)) (cos (+ a b)))
36.0ms	(cos (+ a b))

simplify2.2s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
3	3024
2	671
1	212
0	95

prune335.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite114.0ms

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:

20.0ms	(* r (sin b))
31.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms	(* (sin a) (sin b))
47.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series644.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* r (sin b))
111.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
79.0ms	(* (sin a) (sin b))
392.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	4930
2	1132
1	367
0	145

prune650.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
0.2b	(* (sin a) (sin b))
0.3b	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 139

Calls

4 calls:

20.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
18.0ms	(* (sin a) (sin b))
33.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series690.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
301.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
80.0ms	(* (sin a) (sin b))
186.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify1.8s

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
2	2004
1	634
0	244

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

23.0ms	(* (cos a) (cos b))
28.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
58.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
26.0ms	(/ (* (cos a) (cos b)) (sin b))

series589.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos a) (cos b))
136.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
281.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
119.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify2.6s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
3	4569
2	1080
1	378
0	174

prune668.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes308.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.0s	2824×	body	1280	valid
1.4s	1836×	body	640	valid
481.0ms	2216×	body	80	valid
278.0ms	785×	body	320	valid
137.0ms	341×	body	160	valid