Details

sample265.0ms

Algorithm

intervals

Results

80.0ms	89×	body	1280	valid
34.0ms	55×	body	640	valid
12.0ms	31×	body	320	valid
8.0ms	67×	body	80	valid
4.0ms	14×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite56.0ms

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:

16.0ms	(* r (sin b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
13.0ms	(cos (+ a b))

series430.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(* r (sin b))
225.0ms	(/ (* r (sin b)) (cos (+ a b)))
47.0ms	(cos (+ a b))

simplify2.1s

Counts

59 → 59

Iterations

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

prune326.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize54.0ms

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

rewrite117.0ms

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:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms	(* r (sin b))
29.0ms	(* (sin a) (sin b))
55.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms	(* r (sin b))
61.0ms	(* (sin a) (sin b))
287.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1237
1	365
0	145

prune607.0ms

Pruning

14 alts after pruning (14 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	(* (sin a) (sin b))
0.3b	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
0.3b	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

rewrite111.0ms

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:

32.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
13.0ms	(* (sin a) (sin b))
42.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
20.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
72.0ms	(* (sin a) (sin b))
178.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
328.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify1.8s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
2	1999
1	633
0	244

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

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

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-l`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-r` `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-*l/`

Counts

4 → 104

Calls

4 calls:

22.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
36.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))
102.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

series819.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
278.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
82.0ms	(* (sin a) (sin b))
341.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

simplify1.7s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	1381
1	437
0	175

prune735.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes341.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.2s	2893×	body	1280	valid
1.5s	1826×	body	640	valid
370.0ms	765×	body	320	valid
332.0ms	2174×	body	80	valid
128.0ms	343×	body	160	valid