Details

sample225.0ms

Algorithm

intervals

Results

52.0ms	91×	body	1280	valid
19.0ms	56×	body	640	valid
6.0ms	25×	body	320	valid
6.0ms	75×	body	80	valid
1.0ms	9×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize47.0ms

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))

rewrite37.0ms

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:

14.0ms	(* r (/ (sin b) (cos (+ a b))))
7.0ms	(/ (sin b) (cos (+ a b)))
11.0ms	(cos (+ a b))

series228.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms	(* r (/ (sin b) (cos (+ a b))))
46.0ms	(/ (sin b) (cos (+ a b)))
38.0ms	(cos (+ a b))

simplify622.0ms

Counts

76 → 76

Iterations

Useful iterations: done (619.0ms)

Iter	Nodes	Cost
0	117	909
1	274	887
2	1053	801
done	5001	787

prune433.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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))))

rewrite131.0ms

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:

24.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
17.0ms	(* (sin b) (sin a))
63.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
25.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
65.0ms	(* (sin b) (sin a))
342.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
145.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.5s

Counts

112 → 112

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	176	2072
1	443	2028
2	2006	1842
done	5000	1767

prune778.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

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:

26.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
15.0ms	(* (sin b) r)
20.0ms	(* (sin b) (sin a))
49.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series612.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
49.0ms	(* (sin b) r)
75.0ms	(* (sin b) (sin a))
376.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify955.0ms

Counts

88 → 88

Iterations

Useful iterations: done (952.0ms)

Iter	Nodes	Cost
0	143	1255
1	361	1223
2	1824	1083
done	5002	1075

prune564.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

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

rewrite179.0ms

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:

18.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
19.0ms	(* (sin b) (sin a))
33.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
106.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

series967.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
56.0ms	(* (sin b) (sin a))
343.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
410.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	175	2028
1	443	1984
2	2178	1800
done	5001	1788

prune829.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes341.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	15	16
done	15	16

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.3s	2928×	body	1280	valid
1.1s	1797×	body	640	valid
593.0ms	339×	body	160	valid
293.0ms	2178×	body	80	valid
273.0ms	758×	body	320	valid