Details

sample183.0ms

Algorithm

intervals

Results

89.0ms	94×	body	1280	valid
24.0ms	60×	body	640	valid
7.0ms	30×	body	320	valid
6.0ms	65×	body	80	valid
1.0ms	7×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.9b	(cos (+ a b))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

27.0ms	(* r (sin b))
16.0ms	(/ (* r (sin b)) (cos (+ a b)))
13.0ms	(cos (+ a b))

series192.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* r (sin b))
116.0ms	(/ (* r (sin b)) (cos (+ a b)))
29.0ms	(cos (+ a b))

simplify3.5s

Counts

56 → 56

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	90	535
1	198	525
2	550	447
3	2112	443
done	5001	439

prune241.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))))

rewrite140.0ms

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×	`cos-mult` `sin-mult`
4×	`associate-/r/`
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 → 77

Calls

4 calls:

22.0ms	(* (cos a) (cos b))
38.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
36.0ms	(* (sin a) (sin b))
40.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series642.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos a) (cos b))
137.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
57.0ms	(* (sin a) (sin b))
388.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.4s

Counts

89 → 89

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	155	1300
1	372	1256
2	1192	1114
3	4114	1027
done	5000	1027

prune505.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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

rewrite142.0ms

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:

12.0ms	(* (cos a) (cos b))
48.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
63.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
16.0ms	(/ (* (cos a) (cos b)) (sin b))

series582.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos a) (cos b))
126.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
287.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
105.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify3.2s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	174	1613
1	365	1564
2	1052	1436
3	4003	1430
done	5000	1430

prune548.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
111×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
66×	`add-cube-cbrt`
23×	`associate-/r*`
15×	`difference-of-squares`
13×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
7×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
4×	`pow1`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`flip3--` `flip--`
1×	`sub-neg` `quot-tan` `diff-log`

Counts

4 → 159

Calls

4 calls:

90.0ms	(- (/ (cos a) (/ (sin b) (cos b))) (sin a))
11.0ms	(/ (sin b) (cos b))
17.0ms	(/ (cos a) (/ (sin b) (cos b)))
77.0ms	(/ r (- (/ (cos a) (/ (sin b) (cos b))) (sin a)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (/ (cos a) (/ (sin b) (cos b))) (sin a))
36.0ms	(/ (sin b) (cos b))
105.0ms	(/ (cos a) (/ (sin b) (cos b)))
303.0ms	(/ r (- (/ (cos a) (/ (sin b) (cos b))) (sin a)))

simplify3.6s

Counts

171 → 171

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	282	2980
1	573	2867
2	1592	2729
3	4604	2721
done	5000	2721

prune766.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
done	9	10

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.0s	2916×	body	1280	valid
1.0s	1826×	body	640	valid
764.0ms	784×	body	320	valid
295.0ms	2134×	body	80	valid
115.0ms	341×	body	160	valid