Details

Time bar (total: 9.3s)

sample43.0ms

Algorithm
intervals
Results
19.0ms260×body80valid
1.0ms3×body1280valid
1.0ms4×body640valid
1.0ms4×body320valid
0.0ms1×body160valid

simplify48.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115
done500115

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b
(* K (+ m n))
36.1b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.0s

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 diff-log add-cbrt-cube
4×associate-*r*
3×sub-neg pow-unpow associate-*l* difference-of-squares
2×cos-sum distribute-rgt-neg-in associate-*r/ neg-log associate--r+
1×associate--l- neg-sub0 distribute-rgt-in cos-diff pow-to-exp flip3-- pow-pow distribute-lft-in flip3-+ times-frac pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out associate--r- unswap-sqr sqr-pow
Counts
4 → 77
Calls
4 calls:
55.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
934.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
22.0ms
(* K (+ m n))
28.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series563.0ms

Counts
4 → 12
Calls
4 calls:
275.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
193.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
32.0ms
(* K (+ m n))
63.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify42.0ms

Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0435667
11447621
25001620
done5001620

prune365.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

rewrite1.0s

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 add-exp-log pow-unpow difference-of-squares
2×sub-neg distribute-rgt-neg-in neg-log add-cbrt-cube associate--r+
1×associate--l- neg-sub0 pow-to-exp flip3-- pow-pow times-frac pow-exp flip-- associate--r- sqr-pow
Counts
2 → 44
Calls
2 calls:
55.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
986.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series475.0ms

Counts
2 → 6
Calls
2 calls:
283.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
192.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify85.0ms

Counts
50 → 50
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0277469
1798444
23368435
35001432
done5001432

prune185.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.6b
(* (cbrt (+ m n)) (cbrt (+ m n)))
35.7b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod *-un-lft-identity
22×add-sqr-sqrt
16×cbrt-div
14×add-cube-cbrt
11×pow1
9×swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×cos-sum associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 cos-diff sub-neg pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 91
Calls
4 calls:
4.0ms
(cbrt (+ m n))
5.0ms
(cbrt (+ m n))
35.0ms
(* (cbrt (+ m n)) (cbrt (+ m n)))
261.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series563.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(cbrt (+ m n))
136.0ms
(cbrt (+ m n))
183.0ms
(* (cbrt (+ m n)) (cbrt (+ m n)))
108.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify163.0ms

Counts
103 → 103
Iterations

Useful iterations: 3 (155.0ms)

IterNodesCost
0308808
11031751
24783705
35001701
done5001701

prune493.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.9b
(pow (cbrt (cbrt (+ m n))) 4)
35.7b
(cos (- (/ (* (* K (* (pow (cbrt (cbrt (+ m n))) 4) (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
19×cbrt-prod
16×*-un-lft-identity
10×add-sqr-sqrt add-cube-cbrt unpow-prod-down
5×pow1 add-exp-log
4×cbrt-div add-cbrt-cube add-log-exp
3×pow-unpow pow1/3 distribute-lft-out
2×cos-sum pow-pow flip3-+ flip-+
1×cos-diff pow-to-exp sub-neg pow-exp sqr-pow
Counts
4 → 63
Calls
4 calls:
4.0ms
(cbrt (+ m n))
4.0ms
(cbrt (+ m n))
11.0ms
(pow (cbrt (cbrt (+ m n))) 4)
999.0ms
(cos (- (/ (* (* K (* (pow (cbrt (cbrt (+ m n))) 4) (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

series732.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(cbrt (+ m n))
137.0ms
(cbrt (+ m n))
341.0ms
(pow (cbrt (cbrt (+ m n))) 4)
109.0ms
(cos (- (/ (* (* K (* (pow (cbrt (cbrt (+ m n))) 4) (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

simplify105.0ms

Counts
75 → 75
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0322708
1893647
23613636
35001624
done5001624

prune464.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

regimes257.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12310
22310
done2310

end0.0ms

sample1.2s

Algorithm
intervals
Results
616.0ms8107×body80valid
61.0ms127×body1280valid
55.0ms163×body640valid
21.0ms94×body320valid
7.0ms44×body160valid
2.0ms3×body2560valid