Details

sample369.0ms

Algorithm

intervals

Results

132.0ms	50×	body	640	valid
79.0ms	89×	body	1280	valid
41.0ms	73×	body	80	valid
12.0ms	34×	body	320	valid
2.0ms	10×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

150.0ms	(* r (sin b))
109.0ms	(/ (* r (sin b)) (cos (+ a b)))
56.0ms	(cos (+ a b))

series280.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* r (sin b))
198.0ms	(/ (* r (sin b)) (cos (+ a b)))
36.0ms	(cos (+ a b))

simplify598.0ms

Counts

56 → 56

Iterations

Useful iterations: done (596.0ms)

Iter	Nodes	Cost
0	90	535
1	206	525
2	855	455
done	5000	443

prune217.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

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

rewrite130.0ms

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:

13.0ms	(* r (sin b))
40.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
49.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms	(* (sin a) (sin b))

series582.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* r (sin b))
124.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
312.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
75.0ms	(* (sin a) (sin b))

simplify1.2s

Counts

88 → 88

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	140	1256
1	361	1224
2	1706	1084
done	5000	1028

prune558.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite221.0ms

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:

37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
117.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
14.0ms	(* (sin a) (sin b))

series730.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
173.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
348.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
71.0ms	(* (sin a) (sin b))

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	170	2072
1	435	2028
2	1856	1842
done	5001	1770

prune638.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (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)
29.7b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`times-frac`
8×	`cbrt-prod`
6×	`associate-l`
4×	`prod-exp` `cbrt-unprod` `sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `pow-prod-down` `associate-/r/` `unswap-sqr`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-exp` `*-commutative` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow1/3` `associate-*r/` `div-exp` `cos-mult` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv`

Counts

4 → 95

Calls

4 calls:

146.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
14.0ms	(* (sin b) (sin a))
10.0ms	(pow (* (sin b) (sin a)) 3)
5.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series551.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
57.0ms	(* (sin b) (sin a))
89.0ms	(pow (* (sin b) (sin a)) 3)
83.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.6s

Counts

107 → 107

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	188	1602
1	516	1322
2	2496	1192
done	5000	1188

prune656.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes209.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.1s	2913×	body	1280	valid
1.0s	1797×	body	640	valid
793.0ms	788×	body	320	valid
375.0ms	2129×	body	80	valid
86.0ms	374×	body	160	valid