Details

sample284.0ms

Algorithm

intervals

Results

89.0ms	89×	body	1280	valid
31.0ms	52×	body	640	valid
14.0ms	33×	body	320	valid
10.0ms	69×	body	80	valid
4.0ms	13×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

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

prune142.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize78.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite60.0ms

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*` `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 → 47

Calls

3 calls:

16.0ms	(* r (sin b))
21.0ms	(/ (* r (sin b)) (cos (+ a b)))
18.0ms	(cos (+ a b))

series289.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* r (sin b))
183.0ms	(/ (* r (sin b)) (cos (+ a b)))
51.0ms	(cos (+ a b))

simplify2.7s

Counts

56 → 56

Iterations

Iter	Nodes
done	5020
3	2390
2	589
1	211
0	92

prune405.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

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))))

rewrite94.0ms

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`
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 → 76

Calls

4 calls:

14.0ms	(* r (sin b))
26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
19.0ms	(* (sin a) (sin b))
31.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series592.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* r (sin b))
124.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
72.0ms	(* (sin a) (sin b))
325.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	4913
2	1129
1	362
0	141

prune784.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

71.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
28.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
24.0ms	(* (sin a) (sin b))
40.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series820.0ms

Counts

4 → 12

Calls

4 calls:

396.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
136.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
79.0ms	(* (sin a) (sin b))
208.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.0s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4737
2	1464
1	438
0	171

prune813.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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

rewrite101.0ms

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` `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 → 135

Calls

4 calls:

25.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
19.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
39.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
9.0ms	(* (sin a) (sin b))

series702.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
324.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
188.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
72.0ms	(* (sin a) (sin b))

simplify1.9s

Counts

147 → 147

Iterations

Iter	Nodes
done	5005
2	2101
1	633
0	240

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes449.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.3s	2858×	body	1280	valid
1.9s	1820×	body	640	valid
561.0ms	2173×	body	80	valid
344.0ms	797×	body	320	valid
130.0ms	352×	body	160	valid