Details

sample193.0ms

Algorithm

intervals

Results

49.0ms	79×	body	1280	valid
26.0ms	67×	body	640	valid
8.0ms	77×	body	80	valid
6.0ms	22×	body	320	valid
3.0ms	11×	body	160	valid

simplify95.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.0b	(cos (+ a b))

rewrite82.0ms

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×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `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 → 73

Calls

3 calls:

20.0ms	(* r (/ (sin b) (cos (+ a b))))
20.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

series239.0ms

Counts

3 → 9

Calls

3 calls:

156.0ms	(* r (/ (sin b) (cos (+ a b))))
47.0ms	(/ (sin b) (cos (+ a b)))
36.0ms	(cos (+ a b))

simplify3.6s

Counts

82 → 82

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	122	955
1	260	924
2	659	834
3	1814	830
done	5001	824

prune376.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

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

rewrite219.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

31.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
111.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
42.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
28.0ms	(* (sin a) (sin b))

series762.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
359.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
189.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
92.0ms	(* (sin a) (sin b))

simplify2.7s

Counts

122 → 122

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	181	2200
1	430	2141
2	1243	1949
3	3731	1826
done	5000	1821

prune747.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
0.2b	(* (sin b) (sin a))
0.3b	(pow (* (sin b) (sin a)) 3)
26.7b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
8×	`cbrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `associate-r` `associate-l` `associate-/r` `associate-/r/` `associate-/l`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `div-exp` `clear-num` `cos-mult` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

63.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
13.0ms	(* (sin b) (sin a))
14.0ms	(pow (* (sin b) (sin a)) 3)
9.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series385.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
71.0ms	(* (sin b) (sin a))
83.0ms	(pow (* (sin b) (sin a)) 3)
69.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.3s

Counts

110 → 110

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	171	1632
1	360	1333
2	1239	1243
done	5001	1219

prune710.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r` `add-cbrt-cube`
18×	`times-frac`
13×	`prod-exp`
12×	`pow1`
8×	`associate-/r/`
7×	`cbrt-unprod` `sin-mult`
6×	`div-exp` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `associate-/r` `frac-sub` `flip--` `associate-/l` `sub-div`
2×	`*-commutative` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num` `un-div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

27.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
54.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms	(* (sin a) (sin b))
146.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
168.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
61.0ms	(* (sin a) (sin b))
361.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify2.1s

Counts

132 → 132

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	193	2402
1	488	2203
2	1514	1937
done	5000	1885

prune611.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes241.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	23	18
2	25	18
done	25	18

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.1s	2908×	body	1280	valid
1.5s	1810×	body	640	valid
453.0ms	766×	body	320	valid
215.0ms	2127×	body	80	valid
183.0ms	392×	body	160	valid