Details

sample266.0ms

Algorithm

intervals

Results

81.0ms	88×	body	1280	valid
38.0ms	68×	body	640	valid
11.0ms	26×	body	320	valid
9.0ms	68×	body	80	valid
2.0ms	6×	body	160	valid

simplify89.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

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)))
4.6b	(cos (+ a b))

rewrite69.0ms

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:

30.0ms	(* r (/ (sin b) (cos (+ a b))))
16.0ms	(/ (sin b) (cos (+ a b)))
20.0ms	(cos (+ a b))

series261.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(* r (/ (sin b) (cos (+ a b))))
77.0ms	(/ (sin b) (cos (+ a b)))
47.0ms	(cos (+ a b))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	1053
1	274
0	117

prune508.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (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))

rewrite189.0ms

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)))
101.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
40.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms	(* (sin a) (sin b))

series776.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
376.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
187.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
60.0ms	(* (sin a) (sin b))

simplify1.4s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	1878
1	441
0	171

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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×	`associate-/r/` `cos-mult`
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` `diff-log` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

9.0ms	(* r (sin b))
13.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms	(* (sin a) (sin b))

series664.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* r (sin b))
153.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
385.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
68.0ms	(* (sin a) (sin b))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1579
1	365
0	141

prune841.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

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)))
31.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
10.0ms	(* (sin a) (sin b))
29.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series729.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
188.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
83.0ms	(* (sin a) (sin b))
333.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify1.7s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	2953
1	639
0	240

prune992.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes417.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	19
1	19
0	14

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.9s	2888×	body	1280	valid
1.5s	1804×	body	640	valid
367.0ms	2179×	body	80	valid
296.0ms	782×	body	320	valid
85.0ms	347×	body	160	valid