Details

sample275.0ms

Algorithm

intervals

Results

87.0ms	85×	body	1280	valid
67.0ms	61×	body	640	valid
8.0ms	73×	body	80	valid
8.0ms	20×	body	320	valid
5.0ms	17×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	21
5	21
4	20
3	18
2	16
1	12
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize48.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
5.4b	(cos (+ a b))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

26.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
9.0ms	(cos (+ a b))

series213.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(* r (/ (sin b) (cos (+ a b))))
57.0ms	(/ (sin b) (cos (+ a b)))
40.0ms	(cos (+ a b))

simplify4.0s

Counts

79 → 79

Iterations

Iter	Nodes
4	7297
3	1943
2	743
1	266
0	120

prune820.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite186.0ms

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`
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-*r/`

Counts

4 → 104

Calls

4 calls:

34.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
97.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
14.0ms	(* (sin a) (sin b))
38.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series665.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
313.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
81.0ms	(* (sin a) (sin b))
150.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.4s

Counts

116 → 116

Iterations

Iter	Nodes
3	3772
2	1354
1	435
0	175

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

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

rewrite102.0ms

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:

20.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
9.0ms	(* (sin b) r)
12.0ms	(* (sin b) (sin a))
59.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series979.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
46.0ms	(* (sin b) r)
83.0ms	(* (sin b) (sin a))
741.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
3	4733
2	1116
1	365
0	147

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite201.0ms

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`
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-*r/`

Counts

4 → 104

Calls

4 calls:

33.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
22.0ms	(* (sin b) (sin a))
118.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
25.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series842.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
75.0ms	(* (sin b) (sin a))
352.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
296.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.2s

Counts

116 → 116

Iterations

Iter	Nodes
3	3419
2	1228
1	440
0	179

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes291.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.1s	2891×	body	1280	valid
1.6s	1855×	body	640	valid
834.0ms	762×	body	320	valid
492.0ms	2148×	body	80	valid
126.0ms	344×	body	160	valid