Details

sample657.0ms

Algorithm

intervals

Results

315.0ms	59×	body	640	valid
154.0ms	95×	body	1280	valid
52.0ms	32×	body	320	valid
8.0ms	61×	body	80	valid
3.0ms	9×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize71.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
4.9b	(cos (+ a b))

rewrite99.0ms

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:

52.0ms	(* r (/ (sin b) (cos (+ a b))))
14.0ms	(/ (sin b) (cos (+ a b)))
26.0ms	(cos (+ a b))

series255.0ms

Counts

3 → 9

Calls

3 calls:

153.0ms	(* r (/ (sin b) (cos (+ a b))))
52.0ms	(/ (sin b) (cos (+ a b)))
50.0ms	(cos (+ a b))

simplify5.3s

Counts

76 → 76

Iterations

Useful iterations: 4 (3.8s)

Iter	Nodes	Cost
0	116	909
1	249	883
2	638	793
3	1727	785
4	4912	783
done	5000	783

prune362.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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))))

rewrite208.0ms

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:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
121.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
31.0ms	(* (sin a) (sin b))
33.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series699.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
342.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
59.0ms	(* (sin a) (sin b))
159.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.6s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	170	2072
1	403	2024
2	1162	1856
3	3369	1715
done	5001	1715

prune701.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

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:

10.0ms	(* r (sin b))
33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
26.0ms	(* (sin a) (sin b))
38.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series658.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* r (sin b))
158.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
71.0ms	(* (sin a) (sin b))
371.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.1s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	140	1256
1	345	1224
2	1091	1076
3	3874	989
done	5000	989

prune435.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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

rewrite138.0ms

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:

13.0ms	(* (cos b) (cos a))
50.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
28.0ms	(/ (* (cos b) (cos a)) (sin b))
44.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (cos b) (cos a))
168.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
86.0ms	(/ (* (cos b) (cos a)) (sin b))
269.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify3.5s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	171	1607
1	364	1558
2	1038	1432
3	3870	1424
done	5000	1424

prune456.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes274.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	56
1	28	56
done	28	56

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.5s	2939×	body	1280	valid
1.2s	1778×	body	640	valid
302.0ms	811×	body	320	valid
291.0ms	2138×	body	80	valid
95.0ms	335×	body	160	valid