Details

sample395.0ms

Algorithm

intervals

Results

59.0ms	91×	body	1280	valid
14.0ms	56×	body	640	valid
6.0ms	65×	body	80	valid
5.0ms	29×	body	320	valid
2.0ms	15×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
4.4b	(cos (+ a b))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 67

Calls

3 calls:

17.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(/ (sin b) (cos (+ a b)))
12.0ms	(cos (+ a b))

series178.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(* r (/ (sin b) (cos (+ a b))))
41.0ms	(/ (sin b) (cos (+ a b)))
33.0ms	(cos (+ a b))

simplify39.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477
done	5001	477

prune201.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
72.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms	(* (sin a) (sin b))
26.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
232.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
50.0ms	(* (sin a) (sin b))
123.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify53.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5001	1173
done	5001	1173

prune381.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

9.0ms	(* r (sin b))
17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
30.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* r (sin b))
88.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
239.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663
done	5001	663

prune275.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
0.3b	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`add-cbrt-cube`
21×	`associate-r`
20×	`times-frac`
14×	`pow1` `prod-exp`
9×	`associate-l`
8×	`associate-/r/` `cbrt-unprod`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`associate-*r/` `cos-mult` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `un-div-inv` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 118

Calls

4 calls:

34.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
74.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
12.0ms	(* (sin a) (sin b))
79.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
235.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
47.0ms	(* (sin a) (sin b))
122.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify57.0ms

Counts

130 → 130

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	458	1487
1	2005	1272
2	5001	1240
done	5001	1240

prune328.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes143.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	12
1	17	12
done	17	12

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2893×	body	1280	valid
486.0ms	1909×	body	640	valid
131.0ms	766×	body	320	valid
125.0ms	2141×	body	80	valid
36.0ms	292×	body	160	valid