Details

sample96.0ms

Algorithm

intervals

Results

49.0ms	107×	body	1280	valid
16.0ms	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

localize11.0ms

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))

series52.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(sin b)
30.0ms	(* r (/ (sin b) (cos (+ a b))))
13.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify693.0ms

Counts

86 → 86

Iterations

Useful iterations: 3 (305.0ms)

Iter	Nodes	Cost
0	126	956
1	279	936
2	854	848
3	2564	830
done	5001	830

prune138.0ms

Filtered

66 candidates to 86 candidates (-30.3%)

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))

rewrite36.0ms

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)))
13.0ms	(* 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))

series117.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
55.0ms	(* 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))

simplify1.2s

Counts

112 → 112

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	169	2072
1	416	2031
2	1404	1847
3	4433	1763
done	5000	1725

prune205.0ms

Filtered

91 candidates to 112 candidates (-23.1%)

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

localize14.0ms

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)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos b) (cos a))
21.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
19.0ms	(/ (* (cos b) (cos a)) (sin b))
49.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify1.3s

Counts

104 → 104

Iterations

Useful iterations: 3 (438.0ms)

Iter	Nodes	Cost
0	171	1607
1	374	1563
2	1158	1438
3	4951	1424
done	5000	1424

prune153.0ms

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)))

rewrite57.0ms

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:

17.0ms	(- (/ 1 (/ (sin b) (* (cos b) (cos a)))) (sin a))
8.0ms	(/ 1 (/ (sin b) (* (cos b) (cos a))))
19.0ms	(/ r (- (/ 1 (/ (sin b) (* (cos b) (cos a)))) (sin a)))
7.0ms	(/ (sin b) (* (cos b) (cos a)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(- (/ 1 (/ (sin b) (* (cos b) (cos a)))) (sin a))
16.0ms	(/ 1 (/ (sin b) (* (cos b) (cos a))))
53.0ms	(/ r (- (/ 1 (/ (sin b) (* (cos b) (cos a)))) (sin a)))
17.0ms	(/ (sin b) (* (cos b) (cos a)))

simplify1.2s

Counts

160 → 160

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	254	2978
1	552	2826
2	1807	2608
done	5000	2394

prune118.0ms

Filtered

96 candidates to 160 candidates (-66.7%)

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

regimes268.0ms

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

1.4s	2997×	body	1280	valid
529.0ms	1845×	body	640	valid
152.0ms	720×	body	320	valid
148.0ms	2116×	body	80	valid
50.0ms	327×	body	160	valid

Details

sample96.0ms

simplify9.0ms

prune4.0ms

localize11.0ms

rewrite21.0ms

series52.0ms

simplify693.0ms

prune138.0ms

localize16.0ms

rewrite36.0ms

series117.0ms

simplify1.2s

prune205.0ms

localize14.0ms

rewrite31.0ms

series97.0ms

simplify1.3s

prune153.0ms

localize16.0ms

rewrite57.0ms

series107.0ms

simplify1.2s

prune118.0ms

regimes268.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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