Details

sample102.0ms

Algorithm

intervals

Results

60.0ms	258×	body	80	valid
11.0ms	4×	body	1280	valid
3.0ms	4×	body	320	valid
2.0ms	3×	body	640	valid
1.0ms	2×	body	160	valid

simplify303.0ms

Calls

1 calls:

Slowest

302.0ms

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize39.0ms

Local error

Found 4 expressions with local error:

31.5b	(cos (- (/ K (/ 2 (+ m n))) M))
0.3b	(/ K (/ 2 (+ m n)))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b	(/ 2 (+ m n))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `associate-/r*`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`flip3--` `add-cbrt-cube` `add-exp-log` `flip--`
5×	`associate-/r/`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`sub-neg` `associate-r` `associate-l` `div-inv`
2×	`distribute-rgt-in` `cos-sum` `clear-num` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l/` `associate-r/` `flip-+`
1×	`pow2` `cos-diff` `pow-plus` `pow-prod-down` `prod-exp` `*-commutative` `pow-prod-up` `cbrt-unprod`

Calls

4 calls:

Slowest

28.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
5.0ms	(cos (- (/ K (/ 2 (+ m n))) M))
1.0ms	(/ 2 (+ m n))
1.0ms	(/ K (/ 2 (+ m n)))

series313.0ms

Calls

4 calls:

Slowest

117.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
85.0ms	(cos (- (/ K (/ 2 (+ m n))) M))
59.0ms	(/ 2 (+ m n))
51.0ms	(/ K (/ 2 (+ m n)))

simplify6.0s

Calls

54 calls:

Slowest

488.0ms	(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
455.0ms	(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
414.0ms	(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
347.0ms	(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))
337.0ms	(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize4.0ms

Local error

Found 3 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

3 calls:

Slowest

22.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
18.0ms	(- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)
5.0ms	(- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))

series459.0ms

Calls

3 calls:

Slowest

226.0ms	(- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)
134.0ms	(- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
98.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify6.9s

Calls

46 calls:

Slowest

527.0ms	(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
491.0ms	(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
488.0ms	(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
421.0ms	(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
362.0ms	(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize23.0ms

Local error

Found 4 expressions with local error:

31.6b	(cos (- (/ K (* (* (cbrt (/ 2 (+ m n))) (cbrt (/ 2 (+ m n)))) (cbrt (/ 2 (+ m n))))) M))
0.6b	(cbrt (/ 2 (+ m n)))
0.6b	(cbrt (/ 2 (+ m n)))
0.6b	(cbrt (/ 2 (+ m n)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r/`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Calls

4 calls:

Slowest

45.0ms	(cos (- (/ K (* (* (cbrt (/ 2 (+ m n))) (cbrt (/ 2 (+ m n)))) (cbrt (/ 2 (+ m n))))) M))
3.0ms	(cbrt (/ 2 (+ m n)))
1.0ms	(cbrt (/ 2 (+ m n)))
1.0ms	(cbrt (/ 2 (+ m n)))

series893.0ms

Calls

4 calls:

Slowest

267.0ms	(cos (- (/ K (* (* (cbrt (/ 2 (+ m n))) (cbrt (/ 2 (+ m n)))) (cbrt (/ 2 (+ m n))))) M))
224.0ms	(cbrt (/ 2 (+ m n)))
213.0ms	(cbrt (/ 2 (+ m n)))
189.0ms	(cbrt (/ 2 (+ m n)))

simplify2.0s

Calls

36 calls:

Slowest

294.0ms	(- (+ (* (pow (/ 1 n) 1/3) (cbrt 2)) (* 2/9 (* (* (pow m 2) (cbrt 2)) (pow (/ 1 (pow n 7)) 1/3)))) (* 1/3 (* (* m (cbrt 2)) (pow (/ 1 (pow n 4)) 1/3))))
266.0ms	(- (+ (* (pow (/ 1 n) 1/3) (cbrt 2)) (* 2/9 (* (* (pow m 2) (cbrt 2)) (pow (/ 1 (pow n 7)) 1/3)))) (* 1/3 (* (* m (cbrt 2)) (pow (/ 1 (pow n 4)) 1/3))))
245.0ms	(- (+ (* (pow (/ 1 n) 1/3) (cbrt 2)) (* 2/9 (* (* (pow m 2) (cbrt 2)) (pow (/ 1 (pow n 7)) 1/3)))) (* 1/3 (* (* m (cbrt 2)) (pow (/ 1 (pow n 4)) 1/3))))
161.0ms	(cbrt (/ 2 (- (* m m) (* n n))))
140.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize34.0ms

Local error

Found 4 expressions with local error:

32.4b	(posit16->real (real->posit16 (cos (- (/ K (* (* (cbrt (/ 2 (+ m n))) (cbrt (/ 2 (+ m n)))) (cbrt (/ 2 (+ m n))))) M))))
31.6b	(cos (- (/ K (* (* (cbrt (/ 2 (+ m n))) (cbrt (/ 2 (+ m n)))) (cbrt (/ 2 (+ m n))))) M))
0.6b	(cbrt (/ 2 (+ m n)))
0.6b	(cbrt (/ 2 (+ m n)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `associate-/r/` `insert-posit16` `add-log-exp`
2×	`cbrt-div` `cos-sum` `flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`cos-diff` `sub-neg` `remove-posit16`

Calls

4 calls:

Slowest

60.0ms	(cos (- (/ K (* (* (cbrt (/ 2 (+ m n))) (cbrt (/ 2 (+ m n)))) (cbrt (/ 2 (+ m n))))) M))
1.0ms	(cbrt (/ 2 (+ m n)))
1.0ms	(cbrt (/ 2 (+ m n)))
0.0ms	(posit16->real (real->posit16 (cos (- (/ K (* (* (cbrt (/ 2 (+ m n))) (cbrt (/ 2 (+ m n)))) (cbrt (/ 2 (+ m n))))) M))))

series1.0s

Calls

4 calls:

Slowest

272.0ms	(posit16->real (real->posit16 (cos (- (/ K (* (* (cbrt (/ 2 (+ m n))) (cbrt (/ 2 (+ m n)))) (cbrt (/ 2 (+ m n))))) M))))
268.0ms	(cos (- (/ K (* (* (cbrt (/ 2 (+ m n))) (cbrt (/ 2 (+ m n)))) (cbrt (/ 2 (+ m n))))) M))
232.0ms	(cbrt (/ 2 (+ m n)))
231.0ms	(cbrt (/ 2 (+ m n)))

simplify1.8s

Calls

30 calls:

Slowest

353.0ms	(- (+ (* (pow (/ 1 n) 1/3) (cbrt 2)) (* 2/9 (* (* (pow m 2) (cbrt 2)) (pow (/ 1 (pow n 7)) 1/3)))) (* 1/3 (* (* m (cbrt 2)) (pow (/ 1 (pow n 4)) 1/3))))
298.0ms	(- (+ (* (pow (/ 1 n) 1/3) (cbrt 2)) (* 2/9 (* (* (pow m 2) (cbrt 2)) (pow (/ 1 (pow n 7)) 1/3)))) (* 1/3 (* (* m (cbrt 2)) (pow (/ 1 (pow n 4)) 1/3))))
130.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
121.0ms	(cbrt (/ 2 (- (* m m) (* n n))))
114.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

regimes403.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.5s	8083×	body	80	valid
176.0ms	166×	body	640	valid
150.0ms	103×	body	1280	valid
121.0ms	122×	body	320	valid
17.0ms	38×	body	160	valid
5.0ms	2×	body	2560	valid