Details

sample263.0ms

Algorithm

intervals

Results

96.0ms	62×	body	640	valid
76.0ms	94×	body	1280	valid
8.0ms	21×	body	320	valid
7.0ms	68×	body	80	valid
6.0ms	11×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ r (cos (+ b a)))
0.2b	(* (sin b) (/ r (cos (+ b a))))
2.2b	(cos (+ b a))

rewrite54.0ms

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:

6.0ms	(/ r (cos (+ b a)))
17.0ms	(* (sin b) (/ r (cos (+ b a))))
25.0ms	(cos (+ b a))

series356.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(/ r (cos (+ b a)))
206.0ms	(* (sin b) (/ r (cos (+ b a))))
40.0ms	(cos (+ b a))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1471
1	277
0	118

prune538.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

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

rewrite157.0ms

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:

26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
34.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
66.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
25.0ms	(* (sin a) (sin b))

series879.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
298.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
367.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
69.0ms	(* (sin a) (sin b))

simplify1.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	2275
1	445
0	172

prune877.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

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:

23.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
50.0ms	(/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r)
10.0ms	(* (sin b) (sin a))
14.0ms	(/ (sin b) (/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r))

series772.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
181.0ms	(/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r)
55.0ms	(* (sin b) (sin a))
410.0ms	(/ (sin b) (/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r))

simplify1.9s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	3521
1	655
0	248

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

35×	`associate-l`
30×	`sin-mult`
28×	`cos-mult`
27×	`frac-times`
21×	`add-sqr-sqrt`
19×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1` `flip3-+` `associate-r` `frac-add` `flip-+`
9×	`associate-l/` `associate-r/`
8×	`flip3--` `frac-sub` `flip--` `sub-div`
7×	`prod-exp` `cbrt-unprod`
4×	`pow-prod-down` `*-commutative` `add-log-exp` `unswap-sqr`
3×	`times-frac`
2×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-exp`
1×	`div-inv`

Counts

4 → 131

Calls

4 calls:

9.0ms	(* (sin b) (sin a))
9.0ms	(* (sin a) (sin b))
317.0ms	(* (/ r (* (- (* (cos b) (cos a)) (* (sin b) (sin a))) (+ (* (cos b) (cos a)) (* (sin b) (sin a))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
75.0ms	(* (- (* (cos b) (cos a)) (* (sin b) (sin a))) (+ (* (cos b) (cos a)) (* (sin b) (sin a))))

series891.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin b) (sin a))
87.0ms	(* (sin a) (sin b))
450.0ms	(* (/ r (* (- (* (cos b) (cos a)) (* (sin b) (sin a))) (+ (* (cos b) (cos a)) (* (sin b) (sin a))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
286.0ms	(* (- (* (cos b) (cos a)) (* (sin b) (sin a))) (+ (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify527.0ms

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
1	1051
0	262

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes359.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.7s	2960×	body	1280	valid
1.6s	1897×	body	640	valid
763.0ms	707×	body	320	valid
273.0ms	2060×	body	80	valid
138.0ms	376×	body	160	valid