Details

Time bar (total: 4.8s)

sample49.0ms

Algorithm
intervals
Results
25.0ms259×body80valid
3.0ms6×body1280valid
2.0ms4×body640valid
2.0ms6×body320valid
1.0ms4×body160valid

simplify48.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115

prune9.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 14.7b

Counts
2 → 1

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
33.3b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite56.0ms

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:
13.0ms
(- (/ (* K (+ m n)) 2.0) M)
10.0ms
(* K (+ m n))
17.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
14.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series418.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (/ (* K (+ m n)) 2.0) M)
30.0ms
(* K (+ m n))
249.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
60.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify53.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0378485
11267447
25002443

prune316.0ms

Filtered
79 candidates to 56 candidates (70.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New74579
Fresh000
Picked101
Done000
Total75580

Merged error: 1.1b

Counts
80 → 5

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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:
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series258.0ms

Counts
1 → 3
Calls
1 calls:
258.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify41.0ms

Algorithm
egg-herbie
Counts
23 → 23
Iterations

Useful iterations: 3 (38.0ms)

IterNodesCost
0156164
1433159
21446158
35001155

prune82.0ms

Filtered
23 candidates to 17 candidates (73.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New23023
Fresh044
Picked011
Done000
Total23528

Merged error: 1.1b

Counts
28 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
33.3b
(cos (- (/ (* K (+ m n)) 2.0) M))
33.3b
(cos (- (/ (* K (+ m n)) 2.0) M))
33.3b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
6×cos-sum
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod cos-diff sub-neg
1×pow1/3
Counts
4 → 41
Calls
4 calls:
2.0ms
(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
8.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))
8.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))
8.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series293.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
50.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))
53.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))
53.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify124.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 6 (118.0ms)

IterNodesCost
083464
1123418
2183416
3334416
41040416
53218416
65001397

prune242.0ms

Filtered
53 candidates to 44 candidates (83.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New53053
Fresh033
Picked011
Done011
Total53558

Merged error: 1.1b

Counts
58 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

13.4b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
13.4b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
13.4b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
44.2b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

rewrite31.0ms

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:
8.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
8.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
8.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
6.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

series763.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
226.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
242.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
56.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

simplify48.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (39.0ms)

IterNodesCost
0214792
1511722
21517713
35001704

prune315.0ms

Filtered
64 candidates to 56 candidates (87.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New61364
Fresh112
Picked101
Done112
Total64569

Merged error: 1.1b

Counts
69 → 5

regimes193.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02010
12010

end0.0ms

sample1.3s

Algorithm
intervals
Results
798.0ms8097×body80valid
70.0ms161×body640valid
69.0ms117×body1280valid
30.0ms100×body320valid
13.0ms63×body160valid
4.0ms5×body2560valid

Profiling

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