Details

sample337.0ms

Algorithm

intervals

Results

97.0ms	100×	body	1280	valid
31.0ms	53×	body	640	valid
11.0ms	27×	body	320	valid
8.0ms	62×	body	80	valid
4.0ms	14×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 15.9b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.2b	(cos (+ a b))

rewrite103.0ms

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:

39.0ms	(* r (/ (sin b) (cos (+ a b))))
20.0ms	(/ (sin b) (cos (+ a b)))
23.0ms	(cos (+ a b))

series221.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(* r (/ (sin b) (cos (+ a b))))
61.0ms	(/ (sin b) (cos (+ a b)))
45.0ms	(cos (+ a b))

simplify764.0ms

Counts

76 → 76

Iterations

Useful iterations: done (761.0ms)

Iter	Nodes	Cost
0	116	909
1	272	887
2	1040	801
done	5000	791

prune308.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

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:

35.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
23.0ms	(* (sin b) (sin a))
93.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
46.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series712.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
80.0ms	(* (sin b) (sin a))
326.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
193.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.6s

Counts

112 → 112

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	175	2072
1	438	2028
2	2023	1842
done	5000	1761

prune617.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

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:

11.0ms	(* r (sin b))
25.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
29.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
30.0ms	(* (sin b) (sin a))

series530.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* r (sin b))
111.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
315.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
55.0ms	(* (sin b) (sin a))

simplify1.4s

Counts

88 → 88

Iterations

Useful iterations: 2 (355.0ms)

Iter	Nodes	Cost
0	145	1256
1	370	1224
2	1869	1076
done	5000	1076

prune464.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

10.0ms	(* (cos a) (cos b))
30.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
60.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
15.0ms	(/ (* (cos a) (cos b)) (sin b))

series621.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (cos a) (cos b))
132.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
328.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
89.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify1.5s

Counts

104 → 104

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	174	1613
1	382	1564
2	1556	1438
done	5000	1430

prune495.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes242.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	17	18
done	17	18

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.1s	2983×	body	1280	valid
1.5s	1826×	body	640	valid
338.0ms	2093×	body	80	valid
318.0ms	738×	body	320	valid
123.0ms	360×	body	160	valid