Details

sample95.0ms

Algorithm

intervals

Results

57.0ms	263×	body	80	valid
7.0ms	7×	body	1280	valid
5.0ms	5×	body	640	valid
3.0ms	5×	body	320	valid
1.0ms	1×	body	2560	valid

simplify275.0ms

Calls

1 calls:

Slowest

275.0ms

(* (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: 18.2b

localize59.0ms

Local error

Found 4 expressions with local error:

33.7b	(cos (- (/ K (/ 2 (+ m n))) M))
0.2b	(/ K (/ 2 (+ m n)))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b	(/ 2 (+ m n))

rewrite25.0ms

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

18.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
5.0ms	(cos (- (/ K (/ 2 (+ m n))) M))
1.0ms	(/ K (/ 2 (+ m n)))
1.0ms	(/ 2 (+ m n))

series176.0ms

Calls

4 calls:

Slowest

80.0ms	(cos (- (/ K (/ 2 (+ m n))) M))
38.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
30.0ms	(/ K (/ 2 (+ m n)))
28.0ms	(/ 2 (+ m n))

simplify5.4s

Calls

54 calls:

Slowest

466.0ms	(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
439.0ms	(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
395.0ms	(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
386.0ms	(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
317.0ms	(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))

prune2.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.2b

localize3.0ms

Local error

Found 4 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))) l)
0.0b	(- (/ (+ m n) 2) M)
0.0b	(- (/ (+ m n) 2) M)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

39.0ms	(- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)
21.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
7.0ms	(- (/ (+ m n) 2) M)
5.0ms	(- (/ (+ m n) 2) M)

series212.0ms

Calls

4 calls:

Slowest

117.0ms	(- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)
49.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
25.0ms	(- (/ (+ m n) 2) M)
20.0ms	(- (/ (+ m n) 2) M)

simplify5.4s

Calls

42 calls:

Slowest

497.0ms	(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
486.0ms	(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
468.0ms	(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
385.0ms	(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
316.0ms	(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.2b

localize43.0ms

Local error

Found 4 expressions with local error:

60.1b	(posit16->real (real->posit16 (/ 2 (+ m n))))
33.7b	(cos (- (/ K (posit16->real (real->posit16 (/ 2 (+ m n))))) M))
0.2b	(/ K (posit16->real (real->posit16 (/ 2 (+ m n)))))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

18.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
7.0ms	(cos (- (/ K (posit16->real (real->posit16 (/ 2 (+ m n))))) M))
1.0ms	(/ K (posit16->real (real->posit16 (/ 2 (+ m n)))))
0.0ms	(posit16->real (real->posit16 (/ 2 (+ m n))))

series140.0ms

Calls

4 calls:

Slowest

53.0ms	(cos (- (/ K (posit16->real (real->posit16 (/ 2 (+ m n))))) M))
46.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
23.0ms	(/ K (posit16->real (real->posit16 (/ 2 (+ m n)))))
19.0ms	(posit16->real (real->posit16 (/ 2 (+ m n))))

simplify5.2s

Calls

45 calls:

Slowest

496.0ms	(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
410.0ms	(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
376.0ms	(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
375.0ms	(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
339.0ms	(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))

prune2.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

localize36.0ms

Local error

Found 4 expressions with local error:

60.1b	(posit16->real (real->posit16 (/ 2 (+ m n))))
60.1b	(posit16->real (real->posit16 (/ 2 (+ m n))))
60.1b	(posit16->real (real->posit16 (/ 2 (+ m n))))
33.6b	(cos (- (/ (/ K (* (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n)))))) M))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`remove-posit16`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Calls

4 calls:

Slowest

49.0ms	(cos (- (/ (/ K (* (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n)))))) M))
0.0ms	(posit16->real (real->posit16 (/ 2 (+ m n))))
0.0ms	(posit16->real (real->posit16 (/ 2 (+ m n))))
0.0ms	(posit16->real (real->posit16 (/ 2 (+ m n))))

series275.0ms

Calls

4 calls:

Slowest

213.0ms	(cos (- (/ (/ K (* (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n)))))) M))
25.0ms	(posit16->real (real->posit16 (/ 2 (+ m n))))
19.0ms	(posit16->real (real->posit16 (/ 2 (+ m n))))
18.0ms	(posit16->real (real->posit16 (/ 2 (+ m n))))

simplify418.0ms

Calls

15 calls:

Slowest

112.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
100.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
68.0ms	(* (cos (/ (/ K (* (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))))) (cos (- M)))
64.0ms	(* (cos (/ (/ K (* (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))))) (cos M))
62.0ms	(* (cos (/ (/ K (* (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))))) (cbrt (posit16->real (real->posit16 (/ 2 (+ m n))))))) (cos (- M)))

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

regimes520.0ms

Accuracy

0% (0.3b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch5.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.3s	8089×	body	80	valid
554.0ms	141×	body	640	valid
180.0ms	130×	body	1280	valid
109.0ms	101×	body	320	valid
28.0ms	53×	body	160	valid
4.0ms	2×	body	2560	valid