Details

sample380.0ms

Algorithm

intervals

Results

154.0ms	76×	body	80	valid
80.0ms	68×	body	640	valid
75.0ms	83×	body	1280	valid
10.0ms	21×	body	320	valid
3.0ms	8×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
5	20
4	19
3	17
2	14
1	12
0	8

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize40.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.0b	(cos (+ a b))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
36×	`times-frac`
30×	`*-un-lft-identity` `add-cube-cbrt`
15×	`associate-r` `associate-l`
12×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `*-commutative` `unswap-sqr`
3×	`associate-/r*` `insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `cos-sum` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `clear-num` `frac-2neg` `pow-prod-down` `div-inv`

Counts

3 → 95

Calls

3 calls:

20.0ms	(* r (sin b))
44.0ms	(/ (* r (sin b)) (cos (+ a b)))
28.0ms	(cos (+ a b))

series212.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* r (sin b))
144.0ms	(/ (* r (sin b)) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify2.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	5003
3	4128
2	1128
1	359
0	157

prune579.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

253×	`add-sqr-sqrt`
169×	`*-un-lft-identity`
132×	`times-frac`
98×	`associate-l`
70×	`unswap-sqr`
57×	`add-cube-cbrt`
56×	`distribute-lft-out--` `difference-of-squares`
42×	`associate-r`
14×	`*-commutative`
13×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/l*`
11×	`associate-/r*`
8×	`pow1`
6×	`add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult` `insert-posit16`
3×	`prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `frac-sub` `flip--` `sub-div`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-inv`

Counts

4 → 236

Calls

4 calls:

62.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* r (sin b))
155.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
28.0ms	(* (sin a) (sin b))

series641.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
72.0ms	(* r (sin b))
362.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
70.0ms	(* (sin a) (sin b))

simplify2.0s

Counts

248 → 248

Iterations

Iter	Nodes
done	5001
2	2393
1	724
0	305

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

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

rewrite636.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
67×	`times-frac`
44×	`associate-r`
42×	`associate-l`
40×	`add-cube-cbrt`
39×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
17×	`associate-*r/`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult` `associate-/l*`
6×	`cos-mult` `add-log-exp`
4×	`insert-posit16`
3×	`clear-num` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `sub-div`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `un-div-inv` `*-commutative` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 186

Calls

4 calls:

85.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
108.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms	(* (sin a) (sin b))
411.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series637.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
162.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
66.0ms	(* (sin a) (sin b))
305.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify1.8s

Counts

198 → 198

Iterations

Iter	Nodes
done	5000
2	1840
1	581
0	237

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
3.8b	(log (exp (* (sin a) (sin b))))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

146×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
108×	`times-frac`
65×	`associate-l`
55×	`add-cube-cbrt`
52×	`distribute-lft-out--`
40×	`log-pow`
39×	`associate-r`
35×	`pow1`
26×	`difference-of-squares` `unswap-sqr`
14×	`add-exp-log`
13×	`add-cbrt-cube` `*-commutative`
12×	`exp-prod` `associate-/l*`
9×	`associate-/r*`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`log-prod` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `rem-log-exp` `pow-prod-down` `associate-/r/`
1×	`clear-num` `frac-2neg` `flip3--` `exp-to-pow` `div-inv` `flip--` `sin-mult`

Counts

4 → 212

Calls

4 calls:

18.0ms	(* r (sin b))
14.0ms	(* (sin a) (sin b))
158.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
19.0ms	(log (exp (* (sin a) (sin b))))

series475.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* r (sin b))
62.0ms	(* (sin a) (sin b))
306.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
59.0ms	(log (exp (* (sin a) (sin b))))

simplify2.0s

Counts

224 → 224

Iterations

Iter	Nodes
done	5004
2	2000
1	621
0	275

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes273.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.3s	2839×	body	1280	valid
1.5s	1837×	body	640	valid
478.0ms	2216×	body	80	valid
426.0ms	766×	body	320	valid
153.0ms	344×	body	160	valid