Details

sample773.0ms

Algorithm

intervals

Results

613.0ms	104×	body	1280	valid
40.0ms	44×	body	640	valid
19.0ms	29×	body	320	valid
14.0ms	70×	body	80	valid
5.0ms	9×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize67.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.2b	(cos (+ a b))

rewrite59.0ms

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:

15.0ms	(* r (sin b))
23.0ms	(/ (* r (sin b)) (cos (+ a b)))
18.0ms	(cos (+ a b))

series200.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* r (sin b))
122.0ms	(/ (* r (sin b)) (cos (+ a b)))
36.0ms	(cos (+ a b))

simplify976.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	2023
3	2023
2	671
1	212
0	95

prune384.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

19.0ms	(* (cos a) (cos b))
17.0ms	(* r (sin b))
58.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms	(* (sin a) (sin b))

series578.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cos a) (cos b))
59.0ms	(* r (sin b))
375.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
79.0ms	(* (sin a) (sin b))

simplify1.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	2010
3	2010
2	1263
1	392
0	162

prune800.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

19.0ms	(* (cos a) (cos b))
142.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
22.0ms	(* (sin a) (sin b))
50.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series698.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos a) (cos b))
343.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
81.0ms	(* (sin a) (sin b))
198.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.4s

Counts

121 → 121

Iterations

Iter	Nodes
done	2003
3	2003
2	1537
1	464
0	192

prune990.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

16.0ms	(* (cos a) (cos b))
20.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
20.0ms	(* (sin a) (sin b))
38.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series673.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos a) (cos b))
352.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
86.0ms	(* (sin a) (sin b))
190.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify1.3s

Counts

156 → 156

Iterations

Iter	Nodes
done	2000
2	2000
1	640
0	257

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes419.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.5s	2954×	body	1280	valid
1.7s	1848×	body	640	valid
893.0ms	2098×	body	80	valid
524.0ms	759×	body	320	valid
227.0ms	343×	body	160	valid