Details

sample95.0ms

Algorithm

intervals

Results

37.0ms	259×	body	80	valid
3.0ms	6×	body	320	valid
2.0ms	4×	body	640	valid
2.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify8.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	4997
5	1382
4	501
3	198
2	91
1	50
0	21

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize106.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ m n) (/ K 2.0))
0.0b	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.7b	(cos (- (* (+ m n) (/ K 2.0)) M))

rewrite650.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`associate-r`
11×	`times-frac`
10×	`add-exp-log`
9×	`add-cbrt-cube` `add-log-exp`
7×	`pow1` `unpow-prod-down`
5×	`difference-of-squares`
4×	`associate-l` `insert-posit16` `distribute-lft-out--`
3×	`pow-unpow` `sub-neg` `diff-log`
2×	`frac-times` `cos-sum` `flip3-+` `associate-*l/` `prod-exp` `associate--l+` `cbrt-unprod` `flip-+` `unswap-sqr` `sqr-pow`
1×	`associate--l-` `cos-diff` `pow-to-exp` `cbrt-undiv` `pow-pow` `flip3--` `div-exp` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `div-inv` `flip--` `distribute-lft-out`

Counts

4 → 92

Calls

4 calls:

46.0ms	(* (+ m n) (/ K 2.0))
380.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
131.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
80.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

series1.2s

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (+ m n) (/ K 2.0))
399.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
548.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
190.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

simplify3.0s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
2	1522
1	568
0	231

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.7b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (fabs (- m n)) l)
0.0b	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite526.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`unpow-prod-down`
6×	`difference-of-squares`
5×	`add-cube-cbrt` `distribute-lft-out--`
4×	`pow1` `diff-log` `add-exp-log`
3×	`pow-unpow` `sub-neg` `add-cbrt-cube` `insert-posit16`
2×	`flip3--` `associate--l+` `flip--` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow-pow` `times-frac` `pow-exp`

Counts

3 → 58

Calls

3 calls:

9.0ms	(- (fabs (- m n)) l)
400.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
113.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series930.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(- (fabs (- m n)) l)
331.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
555.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify3.9s

Counts

67 → 67

Iterations

Iter	Nodes
done	5026
3	1910
2	719
1	331
0	141

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.7b

localize73.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fabs (- m n)) l)
0.0b	(- (- (fabs (- m n)) l) (posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
25.6b	(posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-log-exp`
6×	`unpow-prod-down` `add-cube-cbrt`
5×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`add-cbrt-cube` `diff-log` `insert-posit16` `difference-of-squares`
3×	`pow-unpow` `sub-neg`
2×	`flip3--` `associate--l+` `flip--`
1×	`associate--l-` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `remove-posit16` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

16.0ms	(- (fabs (- m n)) l)
100.0ms	(- (- (fabs (- m n)) l) (posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0))))
117.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.0ms	(posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (fabs (- m n)) l)
359.0ms	(- (- (fabs (- m n)) l) (posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0))))
575.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
579.0ms	(posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0)))

simplify3.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
3	1876
2	714
1	330
0	146

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.7b

localize190.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
32.9b	(cos (- (* (* (+ m n) (/ (* (cbrt K) (cbrt K)) (sqrt 2.0))) (/ (cbrt K) (sqrt 2.0))) M))

rewrite482.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt K)
2.0ms	(cbrt K)
2.0ms	(cbrt K)
475.0ms	(cos (- (* (* (+ m n) (/ (* (cbrt K) (cbrt K)) (sqrt 2.0))) (/ (cbrt K) (sqrt 2.0))) M))

series1.8s

Counts

4 → 12

Calls

4 calls:

321.0ms	(cbrt K)
287.0ms	(cbrt K)
296.0ms	(cbrt K)
899.0ms	(cos (- (* (* (+ m n) (/ (* (cbrt K) (cbrt K)) (sqrt 2.0))) (/ (cbrt K) (sqrt 2.0))) M))

simplify4.8s

Counts

59 → 59

Iterations

Iter	Nodes
done	5003
4	2696
3	806
2	316
1	139
0	73

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 1.7b

regimes2.4s

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.9s	8088×	body	80	valid
139.0ms	121×	body	1280	valid
98.0ms	151×	body	640	valid
46.0ms	103×	body	320	valid
19.0ms	62×	body	160	valid
6.0ms	4×	body	2560	valid