Details

sample97.0ms

Algorithm

intervals

Results

49.0ms	107×	body	1280	valid
22.0ms	56×	body	640	valid
5.0ms	68×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 17.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin b)
0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
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

4 → 74

Calls

4 calls:

2.0ms	(sin b)
8.0ms	(* r (/ (sin b) (cos (+ a b))))
5.0ms	(/ (sin b) (cos (+ a b)))
5.0ms	(cos (+ a b))

series51.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(sin b)
31.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify2.5s

Counts

86 → 86

Iterations

Useful iterations: 3 (647.0ms)

Iter	Nodes	Cost
0	126	956
1	274	930
2	709	836
3	2109	828
done	5000	828

prune131.0ms

Filtered

68 candidates to 86 candidates (-26.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	75	11	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	11	87

Merged error: 0.2b

Counts

87 → 11

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

rewrite35.0ms

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:

6.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series115.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
54.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))

simplify2.2s

Counts

112 → 112

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	169	2072
1	404	2024
2	1176	1834
3	3746	1715
done	5000	1714

prune191.0ms

Filtered

89 candidates to 112 candidates (-25.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 0.0b

Counts

123 → 14

localize17.0ms

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)))

rewrite31.0ms

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:

5.0ms	(* (cos b) (cos a))
8.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
6.0ms	(/ (* (cos b) (cos a)) (sin b))
9.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos b) (cos a))
20.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
18.0ms	(/ (* (cos b) (cos a)) (sin b))
48.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify2.7s

Counts

104 → 104

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	171	1607
1	365	1558
2	1045	1432
3	4482	1424
done	5000	1423

prune151.0ms

Filtered

73 candidates to 104 candidates (-42.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 0.0b

Counts

118 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac`
71×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
36×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`associate-/r*`
15×	`div-exp` `difference-of-squares`
12×	`div-inv`
10×	`distribute-lft-out--`
9×	`associate-/l*`
8×	`cbrt-undiv` `associate-/r/`
6×	`add-log-exp`
5×	`pow1` `cos-mult`
4×	`prod-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
2×	`flip3--` `flip--` `cbrt-unprod`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

4 → 148

Calls

4 calls:

16.0ms	(- (/ 1 (/ (sin b) (* (cos b) (cos a)))) (sin a))
8.0ms	(/ 1 (/ (sin b) (* (cos b) (cos a))))
16.0ms	(/ r (- (/ 1 (/ (sin b) (* (cos b) (cos a)))) (sin a)))
6.0ms	(/ (sin b) (* (cos b) (cos a)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(- (/ 1 (/ (sin b) (* (cos b) (cos a)))) (sin a))
15.0ms	(/ 1 (/ (sin b) (* (cos b) (cos a))))
52.0ms	(/ r (- (/ 1 (/ (sin b) (* (cos b) (cos a)))) (sin a)))
16.0ms	(/ (sin b) (* (cos b) (cos a)))

simplify1.4s

Counts

160 → 160

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	254	2978
1	539	2776
2	1358	2394
done	5000	2360

prune110.0ms

Filtered

94 candidates to 160 candidates (-70.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	160	11	171

Merged error: 0.0b

Counts

171 → 11

regimes256.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	2997×	body	1280	valid
524.0ms	1845×	body	640	valid
144.0ms	720×	body	320	valid
142.0ms	2116×	body	80	valid
53.0ms	327×	body	160	valid

Details

sample97.0ms

simplify9.0ms

prune4.0ms

localize10.0ms

rewrite21.0ms

series51.0ms

simplify2.5s

prune131.0ms

localize16.0ms

rewrite35.0ms

series115.0ms

simplify2.2s

prune191.0ms

localize17.0ms

rewrite31.0ms

series96.0ms

simplify2.7s

prune151.0ms

localize16.0ms

rewrite52.0ms

series104.0ms

simplify1.4s

prune110.0ms

regimes256.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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