Details

sample318.0ms

Algorithm

intervals

Results

44.0ms	99×	body	1280	valid
15.0ms	64×	body	640	valid
4.0ms	24×	body	320	valid
3.0ms	59×	body	80	valid
1.0ms	10×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	15	9
3	19	9
4	20	9
done	20	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.3b	(cos (+ a b))

rewrite32.0ms

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:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series155.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(* r (/ (sin b) (cos (+ a b))))
36.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify1.1s

Counts

76 → 76

Iterations

Useful iterations: 3 (314.0ms)

Iter	Nodes	Cost
0	116	909
1	253	883
2	648	793
3	1972	785
done	5000	785

prune214.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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

rewrite45.0ms

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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
24.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
220.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms	(* (sin a) (sin b))
110.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.8s

Counts

112 → 112

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	170	2072
1	404	2024
2	1174	1834
3	3750	1715
done	5000	1714

prune408.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

4.0ms	(* (cos b) (cos a))
35.0ms	(* r (/ 1 (- (/ (* (cos b) (cos a)) (sin b)) (sin a))))
4.0ms	(/ (* (cos b) (cos a)) (sin b))
14.0ms	(/ 1 (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos b) (cos a))
181.0ms	(* r (/ 1 (- (/ (* (cos b) (cos a)) (sin b)) (sin a))))
63.0ms	(/ (* (cos b) (cos a)) (sin b))
96.0ms	(/ 1 (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify2.3s

Counts

138 → 138

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	205	2215
1	469	1997
2	1174	1799
3	4405	1793
done	5000	1792

prune364.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

149×	`times-frac`
148×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
78×	`add-cube-cbrt`
27×	`associate-r`
24×	`add-exp-log`
23×	`associate-/r*`
21×	`difference-of-squares`
18×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp` `div-inv`
7×	`pow1` `distribute-lft-out--`
6×	`cbrt-undiv`
5×	`associate-/r/`
4×	`prod-exp` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num` `unswap-sqr`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `cbrt-unprod`
1×	`pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 196

Calls

4 calls:

92.0ms	(* r (/ 1 (- (/ (cos b) (/ (sin b) (cos a))) (sin a))))
3.0ms	(/ (sin b) (cos a))
6.0ms	(/ (cos b) (/ (sin b) (cos a)))
45.0ms	(/ 1 (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* r (/ 1 (- (/ (cos b) (/ (sin b) (cos a))) (sin a))))
45.0ms	(/ (sin b) (cos a))
62.0ms	(/ (cos b) (/ (sin b) (cos a)))
94.0ms	(/ 1 (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))

simplify866.0ms

Counts

208 → 208

Iterations

Useful iterations: done (861.0ms)

Iter	Nodes	Cost
0	319	3647
1	702	3329
2	1775	3121
done	5000	3119

prune645.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes141.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	16	15
done	16	15

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	2963×	body	1280	valid
474.0ms	1882×	body	640	valid
126.0ms	733×	body	320	valid
117.0ms	2086×	body	80	valid
42.0ms	339×	body	160	valid