Details

Time bar (total: 5.8s)

sample45.0ms

Algorithm
intervals
Results
19.0ms262×body80valid
2.0ms5×body640valid
1.0ms3×body320valid
0.0ms1×body1280valid
0.0ms1×body160valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
05016
19516
221116
355315
4197415
5500115
done500115

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(* K (+ m n))
34.6b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
42×*-un-lft-identity prod-diff
36×add-cube-cbrt
23×cos-sum
22×times-frac
7×pow1 add-exp-log fma-neg div-inv
6×unpow-prod-down add-cbrt-cube add-log-exp
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×pow-unpow associate-*l* difference-of-squares
2×sub-neg associate-*r/ distribute-lft-out--
1×distribute-rgt-in cos-diff pow-to-exp flip3-- pow-pow distribute-lft-in flip3-+ diff-log pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 124
Calls
4 calls:
56.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
23.0ms
(- (/ (* K (+ m n)) 2.0) M)
19.0ms
(* K (+ m n))
39.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series426.0ms

Counts
4 → 12
Calls
4 calls:
275.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
63.0ms
(- (/ (* K (+ m n)) 2.0) M)
27.0ms
(* K (+ m n))
62.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify60.0ms

Counts
136 → 136
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06121660
119071270
250031268
done50031268

prune492.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize21.0ms

Local error

Found 1 expressions with local error:

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

rewrite59.0ms

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×expm1-log1p-u pow-to-exp pow-pow times-frac pow-exp add-cbrt-cube log1p-expm1-u distribute-lft-out-- add-log-exp sqr-pow
Counts
1 → 22
Calls
1 calls:
58.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series266.0ms

Counts
1 → 3
Calls
1 calls:
266.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify45.0ms

Counts
25 → 25
Iterations

Useful iterations: 3 (42.0ms)

IterNodesCost
0159174
1445168
21492167
35001162
done5001162

prune115.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize31.0ms

Local error

Found 4 expressions with local error:

14.1b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
14.1b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
14.1b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
43.0b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

rewrite98.0ms

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 expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 60
Calls
4 calls:
12.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
12.0ms
(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))))

series1.0s

Counts
4 → 12
Calls
4 calls:
441.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
255.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
246.0ms
(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))))

simplify51.0ms

Counts
72 → 72
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0223866
1551793
21664763
35002751
done5002751

prune426.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize41.0ms

Local error

Found 4 expressions with local error:

14.1b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
43.0b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))
43.0b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))
43.0b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity
5×cbrt-prod add-cube-cbrt
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×cbrt-div
1×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 44
Calls
4 calls:
12.0ms
(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))))
59.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))
61.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(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))))
63.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (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))))

simplify53.0ms

Counts
56 → 56
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0223934
1551811
21664801
35002797
done5002797

prune369.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

regimes228.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12310
22310
done2310

end0.0ms

sample1.1s

Algorithm
intervals
Results
618.0ms8077×body80valid
50.0ms155×body640valid
48.0ms103×body1280valid
20.0ms85×body320valid
9.0ms55×body160valid