Details

sample94.0ms

Algorithm

intervals

Results

60.0ms	250×	body	80	valid
4.0ms	4×	body	640	valid
4.0ms	3×	body	1280	valid
3.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
5	3045
4	783
3	250
2	102
1	51
0	21

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* (+ m n) K) 2) M)
0.0b	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
33.6b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`pow1`
10×	`difference-of-squares`
9×	`add-cube-cbrt`
8×	`swap-sqr` `distribute-lft-out--`
7×	`flip3--` `flip--`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`exp-prod` `sub-neg`
4×	`frac-times` `times-frac` `insert-posit16`
3×	`diff-log` `rem-exp-log`
2×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `exp-sum` `associate-l/` `associate-r/`
1×	`pow2` `cos-diff` `sum-log` `pow-plus` `exp-diff` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

24.0ms	(- (/ (* (+ m n) K) 2) M)
103.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
208.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
48.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series402.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (/ (* (+ m n) K) 2) M)
143.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
103.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
79.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify2.3s

Counts

106 → 106

Iterations

Iter	Nodes
3	7142
2	1542
1	479
0	191

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.5b

localize48.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
0.0b	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
14×	`add-log-exp`
10×	`pow1` `difference-of-squares`
8×	`swap-sqr` `add-cube-cbrt` `distribute-lft-out--`
7×	`flip3--` `flip--`
6×	`associate-r` `associate-l`
5×	`exp-prod` `add-cbrt-cube` `add-exp-log`
4×	`frac-times` `sub-neg` `times-frac` `diff-log`
3×	`insert-posit16` `rem-exp-log`
2×	`distribute-rgt-in` `sum-log` `distribute-lft-in` `exp-sum` `associate-l/` `associate-r/`
1×	`pow2` `pow-plus` `exp-diff` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate--r+` `unswap-sqr`

Counts

3 → 85

Calls

3 calls:

63.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
90.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
202.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series443.0ms

Counts

3 → 9

Calls

3 calls:

205.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
136.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
102.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify2.2s

Counts

94 → 94

Iterations

Iter	Nodes
3	6911
2	1463
1	438
0	158

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
33.3b	(posit16->real (real->posit16 (cos (- (/ (* (+ m n) K) 2) M))))
33.6b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
11×	`pow1`
10×	`add-log-exp`
9×	`add-cube-cbrt` `difference-of-squares`
8×	`swap-sqr`
7×	`distribute-lft-out--`
6×	`flip3--` `add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `flip--`
5×	`exp-prod`
4×	`frac-times` `sub-neg` `times-frac` `insert-posit16`
3×	`rem-exp-log`
2×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `diff-log` `exp-sum` `associate-l/` `associate-r/`
1×	`pow2` `cos-diff` `sum-log` `pow-plus` `exp-diff` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `remove-posit16` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

58.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
192.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0ms	(posit16->real (real->posit16 (cos (- (/ (* (+ m n) K) 2) M))))
25.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series350.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
82.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
77.0ms	(posit16->real (real->posit16 (cos (- (/ (* (+ m n) K) 2) M))))
71.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify2.1s

Counts

100 → 100

Iterations

Iter	Nodes
3	6492
2	1399
1	429
0	174

prune2.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.5b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
33.6b	(cos (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M))))
52.9b	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
11×	`pow1`
10×	`add-log-exp`
9×	`add-cube-cbrt` `difference-of-squares`
8×	`swap-sqr`
7×	`distribute-lft-out--`
6×	`flip3--` `add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `flip--`
5×	`exp-prod`
4×	`frac-times` `times-frac` `insert-posit16`
3×	`sub-neg` `rem-exp-log`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `exp-sum` `associate-l/` `associate-r/`
1×	`pow2` `sum-log` `pow-plus` `exp-diff` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `remove-posit16` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

79.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
208.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
2.0ms	(cos (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M))))
0.0ms	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
112.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
97.0ms	(cos (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M))))
80.0ms	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))

simplify2.1s

Counts

97 → 97

Iterations

Iter	Nodes
3	6719
2	1436
1	428
0	169

prune3.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.5b

regimes717.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	21
1	21
0	16

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.7s	8063×	body	80	valid
199.0ms	121×	body	1280	valid
179.0ms	167×	body	640	valid
85.0ms	117×	body	320	valid
48.0ms	52×	body	160	valid
6.0ms	3×	body	2560	valid