Details

sample365.0ms

Algorithm

intervals

Results

108.0ms	99×	body	1280	valid
90.0ms	12×	body	160	valid
31.0ms	61×	body	640	valid
12.0ms	65×	body	80	valid
5.0ms	19×	body	320	valid

simplify78.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize40.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.2b	(cos (+ a b))

rewrite110.0ms

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×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `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 → 73

Calls

3 calls:

61.0ms	(* r (/ (sin b) (cos (+ a b))))
20.0ms	(/ (sin b) (cos (+ a b)))
23.0ms	(cos (+ a b))

series251.0ms

Counts

3 → 9

Calls

3 calls:

149.0ms	(* r (/ (sin b) (cos (+ a b))))
58.0ms	(/ (sin b) (cos (+ a b)))
44.0ms	(cos (+ a b))

simplify929.0ms

Counts

82 → 82

Iterations

Useful iterations: done (923.0ms)

Iter	Nodes	Cost
0	122	955
1	283	928
2	1071	842
done	5000	836

prune249.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite249.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

38.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
116.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
64.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
25.0ms	(* (sin b) (sin a))

series762.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
370.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
208.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
61.0ms	(* (sin b) (sin a))

simplify1.2s

Counts

122 → 122

Iterations

Useful iterations: 2 (374.0ms)

Iter	Nodes	Cost
0	187	2200
1	466	2145
2	2145	1953
done	5000	1953

prune647.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-r`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
8×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`distribute-lft-neg-out` `neg-mul-1` `frac-2neg` `associate-*r/` `clear-num` `fma-udef`

Counts

4 → 101

Calls

4 calls:

1.0ms	(fma (cos a) (cos b) (* (- (sin a)) (sin b)))
33.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b)))))
16.0ms	(/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b))))
30.0ms	(* (- (sin a)) (sin b))

series773.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(fma (cos a) (cos b) (* (- (sin a)) (sin b)))
350.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b)))))
179.0ms	(/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b))))
96.0ms	(* (- (sin a)) (sin b))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: 2 (331.0ms)

Iter	Nodes	Cost
0	159	1900
1	383	1865
2	1703	1673
done	5001	1673

prune709.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`distribute-lft-neg-out` `neg-mul-1` `frac-2neg` `clear-num` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

1.0ms	(fma (cos a) (cos b) (* (- (sin a)) (sin b)))
11.0ms	(* (sin b) r)
12.0ms	(/ (* (sin b) r) (fma (cos a) (cos b) (* (- (sin a)) (sin b))))
31.0ms	(* (- (sin a)) (sin b))

series646.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(fma (cos a) (cos b) (* (- (sin a)) (sin b)))
49.0ms	(* (sin b) r)
346.0ms	(/ (* (sin b) r) (fma (cos a) (cos b) (* (- (sin a)) (sin b))))
103.0ms	(* (- (sin a)) (sin b))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	135	1155
1	321	1134
2	1767	982
done	5000	978

prune496.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes226.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	18	18
2	22	18
3	23	18
done	23	18

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.1s	2984×	body	1280	valid
1.6s	1805×	body	640	valid
231.0ms	716×	body	320	valid
222.0ms	2162×	body	80	valid
80.0ms	335×	body	160	valid