Details

sample251.0ms

Algorithm

intervals

Results

122.0ms	87×	body	1280	valid
25.0ms	54×	body	640	valid
13.0ms	29×	body	320	valid
7.0ms	73×	body	80	valid
4.0ms	13×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 14.5b

localize29.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.8b	(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×	`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:

38.0ms	(* r (/ (sin b) (cos (+ a b))))
17.0ms	(/ (sin b) (cos (+ a b)))
22.0ms	(cos (+ a b))

series244.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(* r (/ (sin b) (cos (+ a b))))
72.0ms	(/ (sin b) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify701.0ms

Counts

76 → 76

Iterations

Useful iterations: done (689.0ms)

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

prune332.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite290.0ms

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:

31.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
161.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
25.0ms	(* (sin b) (sin a))
68.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series661.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
335.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
55.0ms	(* (sin b) (sin a))
156.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.7s

Counts

112 → 112

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	175	2072
1	439	2028
2	2027	1838
done	5001	1753

prune640.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

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:

22.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
10.0ms	(* r (sin b))
22.0ms	(* (sin b) (sin a))
32.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
52.0ms	(* r (sin b))
75.0ms	(* (sin b) (sin a))
300.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.0s

Counts

88 → 88

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	145	1256
1	370	1224
2	1883	1084
done	5001	1080

prune445.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
27×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
18×	`times-frac` `prod-exp`
17×	`add-cube-cbrt`
10×	`pow1`
8×	`div-exp` `associate-/r*`
7×	`1-exp`
6×	`cbrt-unprod` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`cbrt-undiv` `associate-/l*`
3×	`rec-exp` `associate-r/` `associate-l*` `pow-prod-down` `un-div-inv`
2×	`flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--` `div-inv`
1×	`sub-neg` `pow-flip` `diff-log` `associate-r` `cos-mult` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 106

Calls

4 calls:

25.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
15.0ms	(/ (* (cos a) (cos b)) (sin b))
127.0ms	(* r (* 1 (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))))
73.0ms	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series716.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
114.0ms	(/ (* (cos a) (cos b)) (sin b))
310.0ms	(* r (* 1 (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))))
156.0ms	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify1.4s

Counts

118 → 118

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	197	2123
1	486	1936
2	1981	1708
done	5000	1662

prune376.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes454.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	17
1	19	15
2	20	15
done	20	15

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.2s	2880×	body	1280	valid
1.6s	1895×	body	640	valid
281.0ms	2139×	body	80	valid
255.0ms	728×	body	320	valid
90.0ms	359×	body	160	valid