Details

sample88.0ms

Algorithm

intervals

Results

60.0ms	272×	body	80	valid
2.0ms	2×	body	1280	valid
2.0ms	5×	body	320	valid
1.0ms	1×	body	640	valid

simplify672.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

671.0ms

(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize59.0ms

Local error

Found 4 expressions with local error:

34.0b	(cos (- (/ (* K (+ m n)) 2) M))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
0.0b	(* K (+ m n))
0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))

rewrite820.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `add-cbrt-cube` `diff-log`
4×	`associate-r` `insert-posit16`
3×	`pow-unpow` `sub-neg` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `neg-log` `associate-*r/` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `flip3--` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `unpow2` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

Slowest

723.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
62.0ms	(pow (- (/ (+ m n) 2) M) 2)
19.0ms	(cos (- (/ (* K (+ m n)) 2) M))
13.0ms	(* K (+ m n))

series423.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

202.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
100.0ms	(pow (- (/ (+ m n) 2) M) 2)
78.0ms	(cos (- (/ (* K (+ m n)) 2) M))
43.0ms	(* K (+ m n))

simplify6.2s

Counts

53 → 94

Calls

53 calls:

Slowest

516.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
460.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
393.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
384.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
358.0ms	(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize67.0ms

Local error

Found 3 expressions with local error:

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

rewrite759.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
15×	`add-log-exp`
14×	`add-sqr-sqrt`
8×	`distribute-lft-out--`
7×	`diff-log`
6×	`unpow-prod-down`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `difference-of-squares`
3×	`pow-unpow` `sub-neg` `add-cbrt-cube` `insert-posit16`
2×	`distribute-rgt-neg-in` `flip3--` `neg-log` `flip--` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `unpow2` `associate--r-` `sqr-pow`

Counts

3 → 62

Calls

3 calls:

Slowest

708.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
41.0ms	(pow (- (/ (+ m n) 2) M) 2)
8.0ms	(- l (fabs (- m n)))

series350.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

225.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
112.0ms	(pow (- (/ (+ m n) 2) M) 2)
13.0ms	(- l (fabs (- m n)))

simplify5.1s

Counts

36 → 71

Calls

36 calls:

Slowest

444.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
443.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
435.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
400.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
328.0ms	(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize95.0ms

Local error

Found 4 expressions with local error:

51.7b	(posit16->real (real->posit16 (* K (+ m n))))
34.0b	(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
0.0b	(* K (+ m n))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube`
4×	`associate-r` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-l`
2×	`cos-sum` `associate-*r/` `difference-of-squares`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `remove-posit16` `distribute-lft-out` `distribute-lft-out--` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

Slowest

59.0ms	(pow (- (/ (+ m n) 2) M) 2)
14.0ms	(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
13.0ms	(* K (+ m n))
0.0ms	(posit16->real (real->posit16 (* K (+ m n))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(pow (- (/ (+ m n) 2) M) 2)
96.0ms	(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
41.0ms	(posit16->real (real->posit16 (* K (+ m n))))
40.0ms	(* K (+ m n))

simplify2.7s

Counts

40 → 78

Calls

40 calls:

Slowest

371.0ms	(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)
267.0ms	(pow (+ (sqrt (/ (+ m n) 2)) (sqrt M)) 2)
252.0ms	(pow (* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M))) 2)
198.0ms	(- (pow M 2) (+ (* m M) (* M n)))
187.0ms	(+ (* 1/2 (* m n)) (+ (* 1/4 (pow m 2)) (* 1/4 (pow n 2))))

prune2.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize113.0ms

Local error

Found 4 expressions with local error:

51.7b	(posit16->real (real->posit16 (* K (+ m n))))
34.0b	(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
32.5b	(posit16->real (real->posit16 (cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))))
0.0b	(pow (- (/ (+ m n) 2) M) 2)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`unpow-prod-down` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`pow-unpow`
2×	`cos-sum` `remove-posit16` `difference-of-squares`
1×	`cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `times-frac` `pow-exp` `distribute-lft-out--` `unpow2` `sqr-pow`

Counts

4 → 51

Calls

4 calls:

Slowest

57.0ms	(pow (- (/ (+ m n) 2) M) 2)
25.0ms	(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
0.0ms	(posit16->real (real->posit16 (cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))))
0.0ms	(posit16->real (real->posit16 (* K (+ m n))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

102.0ms	(pow (- (/ (+ m n) 2) M) 2)
99.0ms	(posit16->real (real->posit16 (cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))))
91.0ms	(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
37.0ms	(posit16->real (real->posit16 (* K (+ m n))))

simplify2.4s

Counts

26 → 63

Calls

26 calls:

Slowest

332.0ms	(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)
214.0ms	(pow (* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M))) 2)
201.0ms	(- (pow M 2) (+ (* m M) (* M n)))
185.0ms	(pow (+ (sqrt (/ (+ m n) 2)) (sqrt M)) 2)
178.0ms	(- (pow M 2) (+ (* m M) (* M n)))

prune2.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes486.0ms

Accuracy

0% (0.2b remaining)

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

bsearch5.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.3s	8056×	body	80	valid
676.0ms	173×	body	640	valid
192.0ms	133×	body	1280	valid
72.0ms	103×	body	320	valid
29.0ms	59×	body	160	valid
2.0ms	2×	body	2560	valid