Details

sample321.0ms

Algorithm

intervals

Results

110.0ms	83×	body	1280	valid
103.0ms	68×	body	640	valid
14.0ms	76×	body	80	valid
14.0ms	21×	body	320	valid
4.0ms	8×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune476.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
3.0b	(cos (+ a b))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

38.0ms	(/ (sin b) (cos (+ a b)))
45.0ms	(* r (/ (sin b) (cos (+ a b))))
17.0ms	(cos (+ a b))

series252.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ (sin b) (cos (+ a b)))
159.0ms	(* r (/ (sin b) (cos (+ a b))))
28.0ms	(cos (+ a b))

simplify1.9s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
3	3065
2	913
1	293
0	128

prune456.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite685.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
67×	`times-frac`
44×	`associate-r`
42×	`associate-l`
40×	`add-cube-cbrt`
39×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
17×	`associate-*r/`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult` `associate-/l*`
6×	`cos-mult` `add-log-exp`
4×	`insert-posit16`
3×	`clear-num` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `sub-div`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `un-div-inv` `*-commutative` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 186

Calls

4 calls:

105.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
122.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
21.0ms	(* (sin b) (sin a))
424.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
177.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
50.0ms	(* (sin b) (sin a))
337.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

simplify2.0s

Counts

198 → 198

Iterations

Iter	Nodes
done	5001
2	1794
1	578
0	240

prune947.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite645.0ms

Algorithm

rewrite-expression-head

Rules

163×	`add-sqr-sqrt`
111×	`*-un-lft-identity`
70×	`times-frac`
53×	`associate-l`
50×	`associate-r`
44×	`add-cube-cbrt` `unswap-sqr`
34×	`add-exp-log`
32×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*` `add-cbrt-cube`
17×	`associate-*r/`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-/l*`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`cos-mult` `*-commutative` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `clear-num` `1-exp` `un-div-inv`
2×	`frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`pow-flip` `inv-pow`

Counts

4 → 209

Calls

4 calls:

9.0ms	(* r (sin b))
156.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
453.0ms	(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
19.0ms	(* (sin b) (sin a))

series611.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* r (sin b))
152.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
304.0ms	(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
89.0ms	(* (sin b) (sin a))

simplify2.3s

Counts

221 → 221

Iterations

Iter	Nodes
done	5000
2	2253
1	709
0	255

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

253×	`add-sqr-sqrt`
169×	`*-un-lft-identity`
132×	`times-frac`
98×	`associate-l`
70×	`unswap-sqr`
57×	`add-cube-cbrt`
56×	`distribute-lft-out--` `difference-of-squares`
42×	`associate-r`
14×	`*-commutative`
13×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/l*`
11×	`associate-/r*`
8×	`pow1`
6×	`add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult` `insert-posit16`
3×	`prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `frac-sub` `flip--` `sub-div`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-inv`

Counts

4 → 236

Calls

4 calls:

103.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
11.0ms	(* (sin b) r)
126.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
13.0ms	(* (sin b) (sin a))

series540.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
44.0ms	(* (sin b) r)
332.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
60.0ms	(* (sin b) (sin a))

simplify2.6s

Counts

248 → 248

Iterations

Iter	Nodes
done	5001
2	2316
1	718
0	307

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes263.0ms

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	17
1	17
0	14

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.5s	2839×	body	1280	valid
1.6s	1837×	body	640	valid
413.0ms	2216×	body	80	valid
400.0ms	766×	body	320	valid
164.0ms	344×	body	160	valid