Details

sample806.0ms

Algorithm

intervals

Results

699.0ms	91×	body	1280	valid
23.0ms	60×	body	640	valid
8.0ms	31×	body	320	valid
6.0ms	65×	body	80	valid
1.0ms	9×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

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)))
2.3b	(cos (+ a b))

rewrite98.0ms

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:

56.0ms	(* r (/ (sin b) (cos (+ a b))))
16.0ms	(/ (sin b) (cos (+ a b)))
20.0ms	(cos (+ a b))

series270.0ms

Counts

3 → 9

Calls

3 calls:

184.0ms	(* r (/ (sin b) (cos (+ a b))))
48.0ms	(/ (sin b) (cos (+ a b)))
38.0ms	(cos (+ a b))

simplify2.2s

Counts

82 → 82

Iterations

Iter	Nodes
done	5012
3	3284
2	879
1	280
0	123

prune579.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

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

rewrite168.0ms

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:

28.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
96.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))

series676.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
346.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
154.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
72.0ms	(* (sin a) (sin b))

simplify1.7s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	1531
1	462
0	182

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

384×	`times-frac`
295×	`add-sqr-sqrt`
260×	`*-un-lft-identity`
250×	`add-cube-cbrt`
132×	`prod-diff`
44×	`fma-neg`
23×	`associate-/r*` `div-inv`
15×	`difference-of-squares`
13×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
7×	`associate-/r/`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`flip3--` `flip--`
1×	`quot-tan` `sub-neg` `diff-log`

Counts

4 → 343

Calls

4 calls:

57.0ms	(- (/ (cos a) (/ (sin b) (cos b))) (sin a))
7.0ms	(/ (sin b) (cos b))
73.0ms	(/ r (- (/ (cos a) (/ (sin b) (cos b))) (sin a)))
20.0ms	(/ (cos a) (/ (sin b) (cos b)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(- (/ (cos a) (/ (sin b) (cos b))) (sin a))
24.0ms	(/ (sin b) (cos b))
266.0ms	(/ r (- (/ (cos a) (/ (sin b) (cos b))) (sin a)))
95.0ms	(/ (cos a) (/ (sin b) (cos b)))

simplify2.0s

Counts

355 → 355

Iterations

Iter	Nodes
done	5003
2	2887
1	999
0	435

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
0.2b	(* (/ (cos a) (sin b)) (cos b))
0.2b	(/ (cos a) (sin b))
0.2b	(/ r (+ (- (* (/ (cos a) (sin b)) (cos b)) (sin a)) (fma (sin a) -1 (sin a))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
31×	`times-frac`
30×	`add-cube-cbrt`
13×	`add-cbrt-cube` `associate-l` `add-exp-log`
7×	`associate-/r*`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out`
3×	`cbrt-undiv` `div-exp` `associate-r` `prod-diff` `div-inv`
2×	`clear-num` `frac-2neg` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3-+` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `flip--`

Counts

4 → 116

Calls

4 calls:

13.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
20.0ms	(* (/ (cos a) (sin b)) (cos b))
14.0ms	(/ (cos a) (sin b))
81.0ms	(/ r (+ (- (* (/ (cos a) (sin b)) (cos b)) (sin a)) (fma (sin a) -1 (sin a))))

series735.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
141.0ms	(* (/ (cos a) (sin b)) (cos b))
59.0ms	(/ (cos a) (sin b))
406.0ms	(/ r (+ (- (* (/ (cos a) (sin b)) (cos b)) (sin a)) (fma (sin a) -1 (sin a))))

simplify1.8s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	1498
1	501
0	217

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes426.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	16

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.3s	2868×	body	1280	valid
1.2s	1875×	body	640	valid
275.0ms	2150×	body	80	valid
252.0ms	768×	body	320	valid
81.0ms	339×	body	160	valid