Details

Time bar (total: 5.3s)

sample41.0ms

Algorithm
intervals
Results
19.0ms254×body80valid
2.0ms5×body1280valid
0.0ms2×body320valid
0.0ms2×body160valid
0.0ms1×body640valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115
done500115

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(* K (+ m n))
34.4b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×*-un-lft-identity
8×add-cube-cbrt
7×pow1 add-exp-log
6×unpow-prod-down add-cbrt-cube add-log-exp
4×associate-*r*
3×pow-unpow associate-*l* difference-of-squares
2×sub-neg cos-sum associate-*r/ distribute-lft-out--
1×distribute-rgt-in cos-diff pow-to-exp flip3-- pow-pow distribute-lft-in flip3-+ times-frac diff-log pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 67
Calls
4 calls:
18.0ms
(- (/ (* K (+ m n)) 2.0) M)
58.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
19.0ms
(* K (+ m n))
29.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series418.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (/ (* K (+ m n)) 2.0) M)
261.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
30.0ms
(* K (+ m n))
63.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify40.0ms

Counts
79 → 79
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0378485
11267447
25002443
done5002443

prune322.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×unpow-prod-down
5×*-un-lft-identity
3×add-cube-cbrt pow-unpow
2×pow1 add-exp-log difference-of-squares
1×pow-to-exp pow-pow times-frac pow-exp add-cbrt-cube distribute-lft-out-- add-log-exp sqr-pow
Counts
1 → 20
Calls
1 calls:
57.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series262.0ms

Counts
1 → 3
Calls
1 calls:
262.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify43.0ms

Counts
23 → 23
Iterations

Useful iterations: 3 (40.0ms)

IterNodesCost
0156164
1433159
21446158
35001155
done5001155

prune92.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

localize28.0ms

Local error

Found 4 expressions with local error:

16.2b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
16.2b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
16.2b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
42.9b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 52
Calls
4 calls:
12.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
13.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
12.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
60.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

series825.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
258.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
249.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
63.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

simplify48.0ms

Counts
64 → 64
Iterations

Useful iterations: 3 (41.0ms)

IterNodesCost
0214792
1511722
21517713
35001704
done5001704

prune389.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

localize35.0ms

Local error

Found 4 expressions with local error:

16.2b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
42.9b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))
42.9b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))
42.9b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity
5×cbrt-prod add-cube-cbrt
4×pow1 add-exp-log add-cbrt-cube add-log-exp
2×cbrt-div
1×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 36
Calls
4 calls:
12.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
58.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))
57.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))
59.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
63.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))
66.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))
64.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

simplify46.0ms

Counts
48 → 48
Iterations

Useful iterations: 3 (40.0ms)

IterNodesCost
0214808
1511686
21517683
35001680
done5001680

prune336.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

regimes208.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12310
22310
done2310

end0.0ms

sample1.1s

Algorithm
intervals
Results
599.0ms8088×body80valid
53.0ms117×body1280valid
44.0ms139×body640valid
24.0ms108×body320valid
9.0ms56×body160valid
2.0ms3×body2560valid