Details

Time bar (total: 20.4s)

sample121.0ms

Algorithm
intervals
Results
73.0ms261×body80valid
8.0ms5×body1280valid
3.0ms3×body640valid
3.0ms4×body320valid
2.0ms1×body2560valid
1.0ms2×body160valid

simplify970.0ms

Counts
1 → 1
Iterations
IterNodes
52910
4776
3248
2100
151
021

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
37.1b
(cos (- (/ (* K (+ m n)) 2) M))

rewrite882.0ms

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:
771.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
28.0ms
(* K (+ m n))
57.0ms
(pow (- (/ (+ m n) 2) M) 2)
25.0ms
(cos (- (/ (* K (+ m n)) 2) M))

series458.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
47.0ms
(* K (+ m n))
123.0ms
(pow (- (/ (+ m n) 2) M) 2)
66.0ms
(cos (- (/ (* K (+ m n)) 2) M))

simplify1.3s

Counts
94 → 94
Iterations
IterNodes
33410
21061
1411
0175

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize38.0ms

Local error

Found 2 expressions with local error:

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

rewrite867.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×add-log-exp
11×add-sqr-sqrt
7×distribute-lft-out--
6×unpow-prod-down diff-log
4×add-cube-cbrt
3×pow1 pow-unpow add-exp-log difference-of-squares
2×sub-neg distribute-rgt-neg-in add-cbrt-cube neg-log insert-posit16 associate--r+
1×associate--l- neg-sub0 pow-to-exp pow-pow times-frac flip3-- pow-exp flip-- unpow2 associate--r- sqr-pow
Counts
2 → 47
Calls
2 calls:
803.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
63.0ms
(pow (- (/ (+ m n) 2) M) 2)

series339.0ms

Counts
2 → 6
Calls
2 calls:
214.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
125.0ms
(pow (- (/ (+ m n) 2) M) 2)

simplify2.5s

Counts
53 → 53
Iterations
IterNodes
46839
31773
2597
1251
0107

prune740.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
37.1b
(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
49.9b
(posit16->real (real->posit16 (* K (+ m n))))

rewrite67.0ms

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:
13.0ms
(* K (+ m n))
32.0ms
(pow (- (/ (+ m n) 2) M) 2)
20.0ms
(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
0.0ms
(posit16->real (real->posit16 (* K (+ m n))))

series251.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* K (+ m n))
113.0ms
(pow (- (/ (+ m n) 2) M) 2)
72.0ms
(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
33.0ms
(posit16->real (real->posit16 (* K (+ m n))))

simplify846.0ms

Counts
78 → 78
Iterations
IterNodes
32281
2793
1316
0140

prune2.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize120.0ms

Local error

Found 4 expressions with local error:

37.7b
(cos (- (/ (* (* (cbrt (posit16->real (real->posit16 (* K (+ m n))))) (cbrt (posit16->real (real->posit16 (* K (+ m n)))))) (cbrt (posit16->real (real->posit16 (* K (+ m n)))))) 2) M))
49.9b
(posit16->real (real->posit16 (* K (+ m n))))
49.9b
(posit16->real (real->posit16 (* K (+ m n))))
49.9b
(posit16->real (real->posit16 (* K (+ m n))))

rewrite32.0ms

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
Counts
4 → 38
Calls
4 calls:
31.0ms
(cos (- (/ (* (* (cbrt (posit16->real (real->posit16 (* K (+ m n))))) (cbrt (posit16->real (real->posit16 (* K (+ m n)))))) (cbrt (posit16->real (real->posit16 (* K (+ m n)))))) 2) M))
0.0ms
(posit16->real (real->posit16 (* K (+ m n))))
0.0ms
(posit16->real (real->posit16 (* K (+ m n))))
0.0ms
(posit16->real (real->posit16 (* K (+ m n))))

series187.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(cos (- (/ (* (* (cbrt (posit16->real (real->posit16 (* K (+ m n))))) (cbrt (posit16->real (real->posit16 (* K (+ m n)))))) (cbrt (posit16->real (real->posit16 (* K (+ m n)))))) 2) M))
34.0ms
(posit16->real (real->posit16 (* K (+ m n))))
44.0ms
(posit16->real (real->posit16 (* K (+ m n))))
37.0ms
(posit16->real (real->posit16 (* K (+ m n))))

simplify885.0ms

Counts
50 → 50
Iterations
IterNodes
42401
3522
2163
180
050

prune1.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

regimes353.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
219
119
017

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.7s8128×body80valid
187.0ms146×body640valid
167.0ms128×body1280valid
149.0ms94×body320valid
27.0ms56×body160valid
6.0ms4×body2560valid