Details

sample129.0ms

Algorithm

intervals

Results

76.0ms	257×	body	80	valid
10.0ms	8×	body	640	valid
10.0ms	6×	body	1280	valid
2.0ms	3×	body	160	valid
1.0ms	1×	body	320	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
5	2910
4	776
3	248
2	100
1	51
0	21

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
0.0b	(* (+ m n) K)
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
37.2b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

102.0ms	(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
28.0ms	(* (+ m n) K)
173.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
50.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series511.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
47.0ms	(* (+ m n) K)
116.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
102.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify1.2s

Counts

130 → 130

Iterations

Iter	Nodes
2	3338
1	852
0	260

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize58.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))))
0.0b	(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

rewrite779.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
26×	`flip3--` `flip--`
17×	`add-cube-cbrt`
16×	`times-frac` `frac-add`
12×	`frac-times`
11×	`pow1`
8×	`swap-sqr` `add-log-exp` `difference-of-squares`
7×	`add-cbrt-cube`
6×	`associate-r` `associate-l` `associate-l/` `associate-r/` `add-exp-log` `distribute-lft-out--`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `associate-/r*` `distribute-lft-in` `exp-sum` `pow-flip`
3×	`exp-prod` `insert-posit16` `associate-/l*`
2×	`associate-+r+` `associate-+r-` `sum-log` `div-exp`
1×	`pow2` `cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `exp-diff` `diff-log` `1-exp` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `inv-pow` `unswap-sqr`

Counts

3 → 125

Calls

3 calls:

480.0ms	(/ 1 (exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))))
114.0ms	(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
183.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series613.0ms

Counts

3 → 9

Calls

3 calls:

232.0ms	(/ 1 (exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))))
274.0ms	(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
108.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify1.5s

Counts

134 → 134

Iterations

Iter	Nodes
2	3677
1	860
0	264

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

localize88.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (exp (+ (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))) (- l (fabs (- m n))))))
0.0b	(+ (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))) (- l (fabs (- m n))))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
23.0b	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

rewrite382.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
16×	`times-frac`
12×	`pow1`
9×	`add-log-exp`
8×	`add-cbrt-cube` `swap-sqr` `distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
6×	`flip3--` `associate-r` `associate-l` `pow-flip` `flip--`
5×	`exp-prod`
4×	`frac-times` `associate-/r*` `exp-sum` `insert-posit16` `distribute-lft-out`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `associate-+r+` `associate-+r-` `sum-log` `distribute-lft-in` `div-exp` `associate-l/` `associate-r/`
1×	`pow2` `cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `exp-diff` `diff-log` `1-exp` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `remove-posit16` `inv-pow` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

133.0ms	(/ 1 (exp (+ (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))) (- l (fabs (- m n))))))
21.0ms	(+ (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))) (- l (fabs (- m n))))
224.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0ms	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

series626.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ 1 (exp (+ (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))) (- l (fabs (- m n))))))
240.0ms	(+ (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))) (- l (fabs (- m n))))
110.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
86.0ms	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

simplify7.6s

Counts

130 → 130

Iterations

Iter	Nodes
3	9869
2	1816
1	515
0	205

prune3.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (/ 1 (exp (+ (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))) (- l (fabs (- m n)))))))
23.0b	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
23.0b	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
23.0b	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

17×	`cbrt-prod`
12×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`exp-sum` `remove-posit16`
1×	`cbrt-div` `associate-+r-` `exp-diff` `pow1/3` `associate-/r/` `div-inv`

Counts

4 → 54

Calls

4 calls:

89.0ms	(cbrt (/ 1 (exp (+ (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))) (- l (fabs (- m n)))))))
0.0ms	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
0.0ms	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
0.0ms	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

series672.0ms

Counts

4 → 12

Calls

4 calls:

349.0ms	(cbrt (/ 1 (exp (+ (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))) (- l (fabs (- m n)))))))
95.0ms	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
105.0ms	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
123.0ms	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

simplify3.3s

Counts

66 → 66

Iterations

Iter	Nodes
4	7876
3	1744
2	523
1	245
0	130

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

regimes547.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 0.9b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	18
1	18
0	16

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.8s	8120×	body	80	valid
190.0ms	116×	body	1280	valid
158.0ms	164×	body	640	valid
74.0ms	96×	body	320	valid
63.0ms	54×	body	160	valid