Details

sample313.0ms

Algorithm

intervals

Results

39.0ms	91×	body	1280	valid
12.0ms	51×	body	640	valid
5.0ms	31×	body	320	valid
4.0ms	75×	body	80	valid
1.0ms	8×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	15	9
3	19	9
4	20	9
done	20	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.3b	(cos (+ a b))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series161.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify2.2s

Counts

76 → 76

Iterations

Useful iterations: 3 (423.0ms)

Iter	Nodes	Cost
0	116	909
1	253	883
2	648	793
3	1972	785
done	5001	785

prune217.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
24.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series454.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* (sin a) (sin b))
215.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
114.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.0s

Counts

112 → 112

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	170	2072
1	404	2024
2	1174	1834
3	3716	1715
done	5001	1714

prune401.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`associate-/r/`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 77

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos a) (cos b))
81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* (sin a) (sin b))
219.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.2s

Counts

89 → 89

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	155	1300
1	370	1256
2	1199	1114
3	4429	1027
done	5001	1026

prune302.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`add-cube-cbrt` `times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cos-mult` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

6.0ms	(* (cos b) (cos a))
9.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
4.0ms	(/ (* (cos b) (cos a)) (sin b))
13.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos b) (cos a))
82.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
58.0ms	(/ (* (cos b) (cos a)) (sin b))
181.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify2.5s

Counts

104 → 104

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	171	1607
1	365	1558
2	1045	1432
3	4477	1424
done	5001	1423

prune289.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes156.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	20	18
done	20	18

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2913×	body	1280	valid
591.0ms	1767×	body	640	valid
136.0ms	773×	body	320	valid
126.0ms	2210×	body	80	valid
51.0ms	337×	body	160	valid