Details

sample402.0ms

Algorithm

intervals

Results

36.0ms	87×	body	1280	valid
13.0ms	53×	body	640	valid
7.0ms	75×	body	80	valid
4.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid

simplify21.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
2.9b	(cos (+ a b))

rewrite44.0ms

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:

10.0ms	(/ (sin b) (cos (+ a b)))
18.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(cos (+ a b))

series180.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (sin b) (cos (+ a b)))
107.0ms	(* r (/ (sin b) (cos (+ a b))))
32.0ms	(cos (+ a b))

simplify3.6s

Counts

76 → 76

Iterations

Useful iterations: 4 (2.4s)

Iter	Nodes	Cost
0	116	909
1	249	883
2	634	793
3	1708	785
4	4906	783
done	5000	783

prune193.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

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:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
73.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
232.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
121.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.7s

Counts

112 → 112

Iterations

Useful iterations: 3 (782.0ms)

Iter	Nodes	Cost
0	170	2072
1	403	2024
2	1167	1862
3	3369	1715
done	5001	1715

prune374.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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

rewrite71.0ms

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:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* r (sin b))
12.0ms	(* (sin a) (sin b))
31.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms	(* r (sin b))
48.0ms	(* (sin a) (sin b))
240.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.1s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	140	1256
1	345	1224
2	1091	1076
3	3873	989
done	5000	989

prune267.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

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

rewrite85.0ms

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:

11.0ms	(* (cos a) (cos b))
23.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
14.0ms	(/ (* (cos a) (cos b)) (sin b))
34.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos a) (cos b))
97.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
75.0ms	(/ (* (cos a) (cos b)) (sin b))
211.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify2.2s

Counts

104 → 104

Iterations

Useful iterations: 3 (979.0ms)

Iter	Nodes	Cost
0	174	1613
1	365	1564
2	1055	1436
3	4014	1430
done	5000	1430

prune312.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes143.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	15	16
done	15	16

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	2872×	body	1280	valid
433.0ms	1763×	body	640	valid
140.0ms	796×	body	320	valid
118.0ms	2210×	body	80	valid
44.0ms	361×	body	160	valid