Details

sample91.0ms

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

simplify8.0ms

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

prune9.0ms

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)
0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

4 → 54

Calls

4 calls:

2.0ms	(sin b)
4.0ms	(* r (sin b))
6.0ms	(/ (* r (sin b)) (cos (+ a b)))
4.0ms	(cos (+ a b))

series42.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(sin b)
8.0ms	(* r (sin b))
27.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify610.0ms

Counts

66 → 66

Iterations

Useful iterations: 3 (221.0ms)

Iter	Nodes	Cost
0	101	582
1	227	572
2	700	490
3	2833	486
done	5000	486

prune110.0ms

Filtered

48 candidates to 66 candidates (-37.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Merged error: 0.2b

Counts

67 → 8

localize16.0ms

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))))

rewrite27.0ms

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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* r (sin b))
5.0ms	(* (sin a) (sin b))
10.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* r (sin b))
11.0ms	(* (sin a) (sin b))
59.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.0s

Counts

88 → 88

Iterations

Useful iterations: 3 (394.0ms)

Iter	Nodes	Cost
0	140	1256
1	355	1224
2	1181	1076
3	4482	989
done	5000	989

prune152.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 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))

rewrite38.0ms

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))))
8.0ms	(* (sin a) (sin b))

series118.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
31.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))

simplify970.0ms

Counts

112 → 112

Iterations

Useful iterations: done (967.0ms)

Iter	Nodes	Cost
0	169	2072
1	416	2024
2	1297	1834
3	4235	1715
done	5000	1714

prune155.0ms

Filtered

85 candidates to 112 candidates (-31.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	111	12	123

Merged error: 0.0b

Counts

123 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-l`
22×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
21×	`add-sqr-sqrt` `frac-times`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`flip3--` `flip--` `sin-mult`
11×	`flip3-+` `associate-r` `frac-add` `cos-mult` `flip-+`
10×	`pow1` `associate-*l/`
9×	`associate-*r/`
7×	`prod-exp` `cbrt-unprod`
6×	`times-frac`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `-commutative` `associate-/l` `unswap-sqr`
2×	`sub-neg` `div-inv`
1×	`frac-2neg` `clear-num` `associate-/r*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 132

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
16.0ms	(* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
29.0ms	(* (/ r (* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms	(/ r (* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin a) (sin b))
45.0ms	(* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
52.0ms	(* (/ r (* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
107.0ms	(/ r (* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))

simplify1.0s

Counts

144 → 144

Iterations

Useful iterations: 2 (293.0ms)

Iter	Nodes	Cost
0	249	5079
1	849	4928
2	4105	4327
done	5000	4327

prune187.0ms

Filtered

113 candidates to 144 candidates (-27.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	142	14	156

Merged error: 0b

Counts

156 → 14

regimes326.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	2997×	body	1280	valid
536.0ms	1845×	body	640	valid
153.0ms	2116×	body	80	valid
148.0ms	720×	body	320	valid
49.0ms	327×	body	160	valid

Details

sample91.0ms

simplify8.0ms

prune9.0ms

localize10.0ms

rewrite18.0ms

series42.0ms

simplify610.0ms

prune110.0ms

localize16.0ms

rewrite27.0ms

series96.0ms

simplify1.0s

prune152.0ms

localize16.0ms

rewrite38.0ms

series118.0ms

simplify970.0ms

prune155.0ms

localize19.0ms

rewrite72.0ms

series214.0ms

simplify1.0s

prune187.0ms

regimes326.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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