Details

sample103.0ms

Algorithm

intervals

Results

64.0ms	253×	body	80	valid
13.0ms	9×	body	1280	valid
2.0ms	3×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify750.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize80.0ms

Local error

Found 4 expressions with local error:

32.1b	(cos (- (/ (* (+ m n) K) 2) M))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b	(/ (* (+ m n) K) 2)
0.0b	(* (exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))) (cos (- (/ (* (+ m n) K) 2) M)))

rewrite608.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

Slowest

307.0ms	(* (exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))) (cos (- (/ (* (+ m n) K) 2) M)))
256.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
23.0ms	(/ (* (+ m n) K) 2)
20.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series534.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

346.0ms	(* (exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))) (cos (- (/ (* (+ m n) K) 2) M)))
81.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
69.0ms	(cos (- (/ (* (+ m n) K) 2) M))
38.0ms	(/ (* (+ m n) K) 2)

simplify873.0ms

Counts: 120 → 120

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.8b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

Slowest

240.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
47.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
41.0ms	(- (/ (+ m n) 2) M)
38.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

204.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
143.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
119.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
28.0ms	(- (/ (+ m n) 2) M)

simplify2.6s

Counts: 113 → 113

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.8b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

Slowest

216.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
64.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
57.0ms	(- (/ (+ m n) 2) M)
56.0ms	(- (/ (+ m n) 2) M)

series432.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

219.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
118.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
50.0ms	(- (/ (+ m n) 2) M)
45.0ms	(- (/ (+ m n) 2) M)

simplify1.8s

Counts: 110 → 110

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.8b

localize69.0ms

Local error

Found 4 expressions with local error:

0.8b	(posit16->real (real->posit16 (exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
0.0b	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

Slowest

214.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
92.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
37.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
0.0ms	(posit16->real (real->posit16 (exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))))

series641.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

224.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
167.0ms	(posit16->real (real->posit16 (exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))))
150.0ms	(exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))
100.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify3.2s

Counts: 106 → 106

prune3.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.8b

regimes564.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch5.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.9s	8087×	body	80	valid
298.0ms	167×	body	640	valid
232.0ms	139×	body	1280	valid
81.0ms	103×	body	320	valid
26.0ms	51×	body	160	valid
6.0ms	4×	body	2560	valid