Details

sample383.0ms

Algorithm

intervals

Results

148.0ms	89×	body	1280	valid
37.0ms	61×	body	640	valid
11.0ms	26×	body	320	valid
10.0ms	71×	body	80	valid
3.0ms	9×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

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

prune57.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize38.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.8b	(cos (+ a b))

rewrite60.0ms

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` `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 → 67

Calls

3 calls:

24.0ms	(* r (/ (sin b) (cos (+ a b))))
13.0ms	(/ (sin b) (cos (+ a b)))
17.0ms	(cos (+ a b))

series250.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(* r (/ (sin b) (cos (+ a b))))
48.0ms	(/ (sin b) (cos (+ a b)))
54.0ms	(cos (+ a b))

simplify2.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	3075
2	838
1	269
0	117

prune526.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite195.0ms

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:

25.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
111.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
19.0ms	(* (sin a) (sin b))
34.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series678.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
349.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
65.0ms	(* (sin a) (sin b))
147.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.7s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	1488
1	437
0	171

prune904.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

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

rewrite91.0ms

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:

26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
23.0ms	(* r (sin b))
29.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))

series654.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
56.0ms	(* r (sin b))
384.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
71.0ms	(* (sin a) (sin b))

simplify2.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4759
2	1103
1	364
0	141

prune660.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
111×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
66×	`add-cube-cbrt`
23×	`associate-/r*`
15×	`difference-of-squares`
13×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
7×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
4×	`pow1`
3×	`clear-num` `frac-2neg` `associate-/r/`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 158

Calls

4 calls:

66.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
13.0ms	(/ (sin b) (cos a))
108.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
15.0ms	(/ (cos b) (/ (sin b) (cos a)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
72.0ms	(/ (sin b) (cos a))
233.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
123.0ms	(/ (cos b) (/ (sin b) (cos a)))

simplify1.8s

Counts

170 → 170

Iterations

Iter	Nodes
done	5001
2	1928
1	639
0	281

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes331.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.4s	2890×	body	1280	valid
1.4s	1831×	body	640	valid
858.0ms	806×	body	320	valid
271.0ms	2128×	body	80	valid
140.0ms	346×	body	160	valid