Details

sample331.0ms

Algorithm

intervals

Results

91.0ms	96×	body	1280	valid
38.0ms	63×	body	640	valid
9.0ms	70×	body	80	valid
9.0ms	21×	body	320	valid
2.0ms	6×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.8b

localize31.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ r (cos (+ b a)))
0.2b	(* (sin b) (/ r (cos (+ b a))))
4.1b	(cos (+ b a))

rewrite82.0ms

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:

9.0ms	(/ r (cos (+ b a)))
32.0ms	(* (sin b) (/ r (cos (+ b a))))
21.0ms	(cos (+ b a))

series322.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(/ r (cos (+ b a)))
174.0ms	(* (sin b) (/ r (cos (+ b a))))
33.0ms	(cos (+ b a))

simplify976.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1471
1	277
0	118

prune524.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

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:

14.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
27.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms	(* (sin a) (sin b))
75.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series786.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
287.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
78.0ms	(* (sin a) (sin b))
320.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify1.6s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	2315
1	445
0	172

prune862.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize51.0ms

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

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

22.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* (sin a) (sin b))
26.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r)
36.0ms	(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r))

series853.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
84.0ms	(* (sin a) (sin b))
214.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r)
423.0ms	(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r))

simplify1.5s

Counts

147 → 147

Iterations

Iter	Nodes
done	5002
2	3474
1	659
0	246

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.4b	(pow (* (sin a) (sin b)) 3)
0.5b	(pow (* (cos a) (cos b)) 3)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

88×	`pow1`
36×	`pow-prod-down`
34×	`add-cbrt-cube` `add-exp-log`
18×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `pow-unpow` `*-un-lft-identity` `add-cube-cbrt`
5×	`cos-mult` `sin-mult`
4×	`pow-pow` `pow-plus` `pow-exp` `add-log-exp` `rem-cube-cbrt`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `swap-sqr` `associate-r` `associate-l` `associate-l/` `associate-r/` `*-commutative` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

52.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
38.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
7.0ms	(pow (* (sin a) (sin b)) 3)
7.0ms	(pow (* (cos a) (cos b)) 3)

series355.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
86.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
98.0ms	(pow (* (sin a) (sin b)) 3)
82.0ms	(pow (* (cos a) (cos b)) 3)

simplify2.1s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
2	3659
1	560
0	165

prune712.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes334.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	21

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.4s	2945×	body	1280	valid
947.0ms	1803×	body	640	valid
591.0ms	367×	body	160	valid
338.0ms	2112×	body	80	valid
270.0ms	773×	body	320	valid