Details

sample378.0ms

Algorithm

intervals

Results

84.0ms	99×	body	1280	valid
66.0ms	61×	body	640	valid
7.0ms	65×	body	80	valid
7.0ms	19×	body	320	valid
4.0ms	12×	body	160	valid

simplify97.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.2b	(cos (+ a b))

rewrite88.0ms

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:

34.0ms	(* r (/ (sin b) (cos (+ a b))))
22.0ms	(/ (sin b) (cos (+ a b)))
18.0ms	(cos (+ a b))

series223.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(* r (/ (sin b) (cos (+ a b))))
58.0ms	(/ (sin b) (cos (+ a b)))
39.0ms	(cos (+ a b))

simplify824.0ms

Counts

76 → 76

Iterations

Useful iterations: done (821.0ms)

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

prune305.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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

rewrite193.0ms

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:

24.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
98.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
45.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
21.0ms	(* (sin b) (sin a))

series715.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
332.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
176.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
80.0ms	(* (sin b) (sin a))

simplify1.6s

Counts

112 → 112

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	175	2072
1	439	2028
2	1991	1842
done	5001	1761

prune640.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

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:

26.0ms	(* (cos b) (cos a))
40.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
14.0ms	(/ (* (cos b) (cos a)) (sin b))
38.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos b) (cos a))
135.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
101.0ms	(/ (* (cos b) (cos a)) (sin b))
262.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify1.3s

Counts

104 → 104

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	171	1607
1	377	1558
2	1492	1434
done	5000	1424

prune622.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))
0.3b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
22×	`add-exp-log` `add-cbrt-cube`
20×	`pow-prod-down`
16×	`add-sqr-sqrt`
11×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `add-log-exp`
3×	`sin-mult` `unswap-sqr`
2×	`pow-plus`
1×	`pow2` `frac-times` `associate-r/` `swap-sqr` `associate-l/`

Counts

4 → 94

Calls

4 calls:

21.0ms	(* (sin b) (sin a))
13.0ms	(* (sin b) (sin a))
20.0ms	(* (sin b) (sin a))
62.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin b) (sin a))
95.0ms	(* (sin b) (sin a))
87.0ms	(* (sin b) (sin a))
94.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify919.0ms

Counts

106 → 106

Iterations

Useful iterations: done (916.0ms)

Iter	Nodes	Cost
0	88	981
1	229	868
2	1088	732
done	5001	700

prune485.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes262.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	13	15
1	17	13
2	18	13
done	18	13

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.7s	2984×	body	1280	valid
1.0s	1805×	body	640	valid
386.0ms	2162×	body	80	valid
316.0ms	716×	body	320	valid
84.0ms	335×	body	160	valid