Details

sample392.0ms

Algorithm

intervals

Results

44.0ms	98×	body	1280	valid
25.0ms	25×	body	320	valid
16.0ms	64×	body	640	valid
3.0ms	60×	body	80	valid
1.0ms	9×	body	160	valid

simplify11.0ms

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: 17.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.5b	(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))))
9.0ms	(/ (sin b) (cos (+ a b)))
12.0ms	(cos (+ a b))

series175.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(* r (/ (sin b) (cos (+ a b))))
41.0ms	(/ (sin b) (cos (+ a b)))
32.0ms	(cos (+ a b))

simplify38.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

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

prune197.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

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)))
25.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
71.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms	(* (sin a) (sin b))

series479.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
118.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
228.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms	(* (sin a) (sin b))

simplify53.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

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

prune366.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ (sin b) (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1))
0.2b	(* r (/ (sin b) (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1)))
0.2b	(* (sin a) (sin b))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
32.0ms	(/ (sin b) (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1))
90.0ms	(* r (/ (sin b) (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1)))
12.0ms	(* (sin a) (sin b))

series486.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
120.0ms	(/ (sin b) (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1))
231.0ms	(* r (/ (sin b) (pow (- (* (cos a) (cos b)) (* (sin a) (sin b))) 1)))
47.0ms	(* (sin a) (sin b))

simplify63.0ms

Counts

138 → 138

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	488	1760
1	2076	1517
2	5001	1514
done	5001	1514

prune426.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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

rewrite69.0ms

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))
16.0ms	(- (* (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))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* r (sin b))
88.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms	(* (sin a) (sin b))
233.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify44.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

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

prune268.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes156.0ms

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	21	11
1	21	11
done	21	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2908×	body	1280	valid
462.0ms	1875×	body	640	valid
134.0ms	778×	body	320	valid
122.0ms	2093×	body	80	valid
44.0ms	347×	body	160	valid