Details

sample221.0ms

Algorithm

intervals

Results

103.0ms	91×	body	1280	valid
21.0ms	56×	body	640	valid
7.0ms	25×	body	320	valid
6.0ms	75×	body	80	valid
2.0ms	9×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize50.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.3b	(cos (+ a b))

rewrite68.0ms

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

Calls

3 calls:

29.0ms	(* r (/ (sin b) (cos (+ a b))))
15.0ms	(/ (sin b) (cos (+ a b)))
19.0ms	(cos (+ a b))

series233.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(* r (/ (sin b) (cos (+ a b))))
49.0ms	(/ (sin b) (cos (+ a b)))
54.0ms	(cos (+ a b))

simplify753.0ms

Counts

82 → 82

Iterations

Useful iterations: done (749.0ms)

Iter	Nodes	Cost
0	123	955
1	284	929
2	1076	843
done	5001	836

prune507.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

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

rewrite149.0ms

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

Counts

4 → 110

Calls

4 calls:

19.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
10.0ms	(* (sin b) (sin a))
73.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
41.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series739.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
87.0ms	(* (sin b) (sin a))
386.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
151.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.5s

Counts

122 → 122

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	188	2200
1	468	2146
2	2059	1958
done	5001	1868

prune869.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

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×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

14.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
9.0ms	(* r (sin b))
26.0ms	(* (sin b) (sin a))
32.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series539.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
42.0ms	(* r (sin b))
64.0ms	(* (sin b) (sin a))
326.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify879.0ms

Counts

98 → 98

Iterations

Useful iterations: done (877.0ms)

Iter	Nodes	Cost
0	158	1364
1	398	1324
2	1926	1182
done	5000	1174

prune550.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-cbrt-cube` `add-exp-log`
18×	`add-sqr-sqrt`
16×	`times-frac`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
10×	`associate-/r*`
8×	`pow1` `prod-exp` `associate-*r/` `cbrt-unprod`
6×	`associate-r` `associate-l`
5×	`sin-mult`
4×	`expm1-log1p-u` `cos-mult` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `prod-diff` `pow-prod-down` `-commutative` `frac-sub` `flip--` `associate-/l` `sub-div` `unswap-sqr`
1×	`associate-/r/`

Counts

4 → 118

Calls

4 calls:

9.0ms	(* (sin b) (sin a))
19.0ms	(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (fma (cos a) (cos b) (* (sin b) (sin a)))))
43.0ms	(* (fma (cos a) (cos b) (* (sin b) (sin a))) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
56.0ms	(/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (fma (cos a) (cos b) (* (sin b) (sin a))))

series827.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin b) (sin a))
344.0ms	(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (fma (cos a) (cos b) (* (sin b) (sin a)))))
271.0ms	(* (fma (cos a) (cos b) (* (sin b) (sin a))) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
141.0ms	(/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (fma (cos a) (cos b) (* (sin b) (sin a))))

simplify2.7s

Counts

130 → 130

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	229	4577
1	673	4528
2	4941	3685
done	5000	3685

prune965.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes341.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	38
1	19	38
done	19	38

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.6s	2928×	body	1280	valid
1.5s	1797×	body	640	valid
854.0ms	2178×	body	80	valid
314.0ms	758×	body	320	valid
111.0ms	339×	body	160	valid