Details

sample123.0ms

Algorithm

intervals

Results

81.0ms	258×	body	80	valid
5.0ms	5×	body	320	valid
3.0ms	3×	body	640	valid
3.0ms	2×	body	1280	valid
1.0ms	2×	body	160	valid

simplify261.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

260.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize57.0ms

Local error

Found 4 expressions with local error:

34.9b	(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))))

rewrite887.0ms

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

802.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
38.0ms	(pow (- (/ (+ m n) 2) M) 2)
32.0ms	(cos (- (/ (* K (+ m n)) 2) M))
13.0ms	(* K (+ m n))

series431.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

208.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
93.0ms	(cos (- (/ (* K (+ m n)) 2) M))
90.0ms	(pow (- (/ (+ m n) 2) M) 2)
40.0ms	(* K (+ m n))

simplify6.4s

Counts

53 → 94

Calls

53 calls:

Slowest

523.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
478.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
451.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
438.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
395.0ms	(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.8b

localize44.0ms

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)))

rewrite794.0ms

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

743.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
46.0ms	(pow (- (/ (+ m n) 2) M) 2)
4.0ms	(- l (fabs (- m n)))

series351.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

222.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
105.0ms	(pow (- (/ (+ m n) 2) M) 2)
24.0ms	(- l (fabs (- m n)))

simplify5.1s

Counts

36 → 71

Calls

36 calls:

Slowest

441.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
440.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
431.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
420.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
372.0ms	(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.8b

localize93.0ms

Local error

Found 4 expressions with local error:

19.2b	(posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
0.0b	(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
0.0b	(- l (fabs (- m n)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
16×	`add-log-exp`
15×	`add-sqr-sqrt`
8×	`distribute-lft-out--`
7×	`diff-log`
6×	`unpow-prod-down` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `difference-of-squares`
3×	`pow-unpow` `sub-neg`
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` `remove-posit16` `unpow2` `associate--r-` `sqr-pow`

Counts

4 → 71

Calls

4 calls:

Slowest

32.0ms	(pow (- (/ (+ m n) 2) M) 2)
24.0ms	(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
7.0ms	(- l (fabs (- m n)))
0.0ms	(posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

225.0ms	(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
101.0ms	(posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))
92.0ms	(pow (- (/ (+ m n) 2) M) 2)
15.0ms	(- l (fabs (- m n)))

simplify6.1s

Counts

40 → 83

Calls

40 calls:

Slowest

537.0ms	(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
497.0ms	(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
471.0ms	(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
454.0ms	(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
378.0ms	(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)

prune2.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize103.0ms

Local error

Found 4 expressions with local error:

42.6b	(posit16->real (real->posit16 (* (* (+ (sqrt (/ (+ n m) 2)) (sqrt M)) (+ (sqrt (/ (+ n m) 2)) (sqrt M))) (pow (- (sqrt (/ (+ m n) 2)) (sqrt M)) 2))))
0.1b	(pow (- (sqrt (/ (+ m n) 2)) (sqrt M)) 2)
0.1b	(* (+ (sqrt (/ (+ n m) 2)) (sqrt M)) (+ (sqrt (/ (+ n m) 2)) (sqrt M)))
0.0b	(sqrt (/ (+ m n) 2))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
33×	`sqrt-prod`
18×	`add-cube-cbrt`
15×	`times-frac`
13×	`pow1` `distribute-lft-out`
11×	`unpow-prod-down`
7×	`swap-sqr` `add-exp-log`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `difference-of-squares`
5×	`associate-r` `associate-l`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `associate-l/` `associate-r/` `distribute-lft-out--`
1×	`pow2` `distribute-rgt-in` `pow-to-exp` `pow-pow` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-prod-down` `pow-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `remove-posit16` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 109

Calls

4 calls:

Slowest

168.0ms	(* (+ (sqrt (/ (+ n m) 2)) (sqrt M)) (+ (sqrt (/ (+ n m) 2)) (sqrt M)))
46.0ms	(pow (- (sqrt (/ (+ m n) 2)) (sqrt M)) 2)
5.0ms	(sqrt (/ (+ m n) 2))
1.0ms	(posit16->real (real->posit16 (* (* (+ (sqrt (/ (+ n m) 2)) (sqrt M)) (+ (sqrt (/ (+ n m) 2)) (sqrt M))) (pow (- (sqrt (/ (+ m n) 2)) (sqrt M)) 2))))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

652.0ms	(posit16->real (real->posit16 (* (* (+ (sqrt (/ (+ n m) 2)) (sqrt M)) (+ (sqrt (/ (+ n m) 2)) (sqrt M))) (pow (- (sqrt (/ (+ m n) 2)) (sqrt M)) 2))))
266.0ms	(* (+ (sqrt (/ (+ n m) 2)) (sqrt M)) (+ (sqrt (/ (+ n m) 2)) (sqrt M)))
262.0ms	(pow (- (sqrt (/ (+ m n) 2)) (sqrt M)) 2)
95.0ms	(sqrt (/ (+ m n) 2))

simplify6.5s

Counts

94 → 121

Calls

94 calls:

Slowest

451.0ms	(* (- (* (sqrt (/ (+ n m) 2)) (sqrt (/ (+ n m) 2))) (* (sqrt M) (sqrt M))) (+ (pow (sqrt (/ (+ n m) 2)) 3) (pow (sqrt M) 3)))
413.0ms	(+ (sqrt (/ (+ n m) 2)) (sqrt M))
394.0ms	(* (+ (* (sqrt (/ (+ n m) 2)) (sqrt (/ (+ n m) 2))) (- (* (sqrt M) (sqrt M)) (* (sqrt (/ (+ n m) 2)) (sqrt M)))) (+ (* (sqrt (/ (+ n m) 2)) (sqrt (/ (+ n m) 2))) (- (* (sqrt M) (sqrt M)) (* (sqrt (/ (+ n m) 2)) (sqrt M)))))
319.0ms	(- (+ (* (pow n 2) (pow (sqrt 1/2) 4)) (* 2 (* m (* n (pow (sqrt 1/2) 4))))) (* 2 (* M (* n (pow (sqrt 1/2) 2)))))
277.0ms	(* (- (* (sqrt (/ (+ n m) 2)) (sqrt (/ (+ n m) 2))) (* (sqrt M) (sqrt M))) (- (* (sqrt (/ (+ n m) 2)) (sqrt (/ (+ n m) 2))) (* (sqrt M) (sqrt M))))

prune4.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

regimes596.0ms

Accuracy

0% (0.2b remaining)

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

bsearch7.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.8s	8090×	body	80	valid
166.0ms	114×	body	1280	valid
163.0ms	152×	body	640	valid
111.0ms	100×	body	320	valid
97.0ms	57×	body	160	valid
3.0ms	1×	body	2560	valid