Details

sample248.0ms

Algorithm

intervals

Results

111.0ms	100×	body	1280	valid
28.0ms	56×	body	640	valid
17.0ms	23×	body	320	valid
7.0ms	62×	body	80	valid
4.0ms	15×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	20
5	20
4	19
3	17
2	14
1	12
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize37.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.2b	(cos (+ a b))

rewrite34.0ms

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:

8.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series183.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(* r (sin b))
113.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify611.0ms

Counts

59 → 59

Iterations

Iter	Nodes
3	2151
2	565
1	203
0	95

prune697.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

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

rewrite98.0ms

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:

21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* r (sin b))
16.0ms	(* (sin a) (sin b))
52.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series600.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms	(* r (sin b))
65.0ms	(* (sin a) (sin b))
357.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.7s

Counts

92 → 92

Iterations

Iter	Nodes
3	4272
2	1111
1	358
0	145

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite179.0ms

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:

9.0ms	(* r (sin b))
32.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))
112.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series621.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* r (sin b))
166.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
67.0ms	(* (sin a) (sin b))
325.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify8.4s

Counts

130 → 130

Iterations

Iter	Nodes
3	4621
2	1533
1	497
0	187

prune1.9s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize112.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (* (cos a) (cos b)) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b))))))
0.3b	(/ (* r (sin b)) (/ (- (* (* (cos a) (cos b)) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b)))))))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

224×	`cos-mult`
168×	`sin-mult`
150×	`associate-*r/`
142×	`frac-times`
92×	`associate-*l/`
82×	`pow1`
81×	`frac-add`
75×	`times-frac`
70×	`associate-/r/` `associate-/l/`
49×	`frac-sub`
42×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
34×	`pow-prod-down`
29×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
21×	`flip3-+` `flip-+`
20×	`cube-unmult`
19×	`sub-div`
18×	`prod-exp` `cbrt-unprod`
10×	`difference-cubes`
8×	`pow-sqr` `pow-prod-up`
7×	`cbrt-undiv` `div-exp`
5×	`associate-/l*`
4×	`pow-plus` `insert-posit16` `div-inv` `add-log-exp`
2×	`pow2` `clear-num` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 301

Calls

4 calls:

876.0ms	(/ (- (* (* (cos a) (cos b)) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b))))))
399.0ms	(/ (* r (sin b)) (/ (- (* (* (cos a) (cos b)) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b)))))))
53.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
45.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series1.5s

Counts

4 → 12

Calls

4 calls:

477.0ms	(/ (- (* (* (cos a) (cos b)) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b))))))
926.0ms	(/ (* r (sin b)) (/ (- (* (* (cos a) (cos b)) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b)))))))
67.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
79.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify8.4s

Counts

313 → 313

Iterations

Iter	Nodes
2	7219
1	1458
0	459

prune6.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes338.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	18
1	18
0	14

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.6s	2885×	body	1280	valid
2.2s	1883×	body	640	valid
475.0ms	732×	body	320	valid
417.0ms	2174×	body	80	valid
176.0ms	328×	body	160	valid