Details

Time bar (total: 4.8s)

sample48.0ms

Algorithm
intervals
Results
25.0ms262×body80valid
2.0ms4×body1280valid
2.0ms5×body640valid
1.0ms1×body2560valid
1.0ms2×body320valid
1.0ms3×body160valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115

prune10.0ms

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: 15.6b

Counts
2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.2b
(/ (* K (+ m n)) 2.0)
34.6b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×*-un-lft-identity
12×add-exp-log
11×add-cbrt-cube
10×add-cube-cbrt
7×pow1
6×unpow-prod-down
4×times-frac associate-*r/ associate-*r* add-log-exp
3×pow-unpow associate-*l* associate-/r*
2×cbrt-undiv cos-sum flip3-+ div-exp prod-exp cbrt-unprod flip-+ associate-/l/ difference-of-squares
1×distribute-rgt-in cos-diff pow-to-exp sub-neg pow-pow frac-2neg distribute-lft-in pow-prod-down pow-exp clear-num *-commutative div-inv distribute-lft-out associate-/l* distribute-lft-out-- unswap-sqr sqr-pow
Counts
4 → 76
Calls
4 calls:
6.0ms
(* K (+ m n))
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms
(/ (* K (+ m n)) 2.0)
8.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series375.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* K (+ m n))
256.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
39.0ms
(/ (* K (+ m n)) 2.0)
56.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify48.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0411487
11722437
25001437

prune302.0ms

Filtered
88 candidates to 63 candidates (71.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New85388
Fresh000
Picked101
Done000
Total86389

Merged error: 0.4b

Counts
89 → 3

localize18.0ms

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)

series267.0ms

Counts
1 → 3
Calls
1 calls:
267.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify44.0ms

Algorithm
egg-herbie
Counts
23 → 23
Iterations

Useful iterations: 3 (41.0ms)

IterNodesCost
0156164
1433159
21446158
35002155

prune75.0ms

Filtered
23 candidates to 17 candidates (73.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New23023
Fresh022
Picked011
Done000
Total23326

Merged error: 0.4b

Counts
26 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(/ 2.0 (+ m n))
0.2b
(/ K (/ 2.0 (+ m n)))
34.6b
(cos (- (/ K (/ 2.0 (+ m n))) M))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
115×times-frac
100×*-un-lft-identity
71×add-sqr-sqrt
66×add-cube-cbrt
22×associate-/r*
16×distribute-lft-out
12×add-exp-log
11×associate-/r/ add-cbrt-cube
6×unpow-prod-down div-inv associate-/l*
5×pow1 flip3-+ flip-+
4×cbrt-undiv div-exp add-log-exp
3×pow-unpow
2×cos-sum frac-2neg clear-num difference-of-squares
1×cos-diff pow-to-exp sub-neg pow-pow pow-exp distribute-lft-out-- sqr-pow
Counts
4 → 153
Calls
4 calls:
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
5.0ms
(/ 2.0 (+ m n))
12.0ms
(/ K (/ 2.0 (+ m n)))
21.0ms
(cos (- (/ K (/ 2.0 (+ m n))) M))

series396.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
37.0ms
(/ 2.0 (+ m n))
46.0ms
(/ K (/ 2.0 (+ m n)))
52.0ms
(cos (- (/ K (/ 2.0 (+ m n))) M))

simplify72.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06021150
125641095
250011093

prune570.0ms

Filtered
165 candidates to 120 candidates (72.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1641165
Fresh011
Picked101
Done011
Total1653168

Merged error: 0.4b

Counts
168 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (cos (- (/ K (/ 2.0 (+ m n))) M)))
0.2b
(/ K (/ 2.0 (+ m n)))
0.6b
(log (exp (cos (- (/ K (/ 2.0 (+ m n))) M))))
34.6b
(cos (- (/ K (/ 2.0 (+ m n))) M))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
82×*-un-lft-identity
58×add-sqr-sqrt add-cube-cbrt
18×associate-/r*
12×distribute-lft-out
9×add-exp-log associate-/r/ add-cbrt-cube
6×cos-sum exp-prod
5×pow1 div-inv add-log-exp
4×log-prod flip3-+ exp-diff log-pow flip-+
3×cbrt-undiv cos-diff sub-neg div-exp associate-/l*
2×log-div exp-sum
1×frac-2neg rem-log-exp clear-num rem-exp-log
Counts
4 → 132
Calls
4 calls:
23.0ms
(exp (cos (- (/ K (/ 2.0 (+ m n))) M)))
8.0ms
(/ K (/ 2.0 (+ m n)))
21.0ms
(log (exp (cos (- (/ K (/ 2.0 (+ m n))) M))))
21.0ms
(cos (- (/ K (/ 2.0 (+ m n))) M))

series228.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(exp (cos (- (/ K (/ 2.0 (+ m n))) M)))
39.0ms
(/ K (/ 2.0 (+ m n)))
55.0ms
(log (exp (cos (- (/ K (/ 2.0 (+ m n))) M))))
51.0ms
(cos (- (/ K (/ 2.0 (+ m n))) M))

simplify59.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
05001162
119061091
250011088

prune575.0ms

Filtered
144 candidates to 107 candidates (74.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1431144
Fresh011
Picked101
Done011
Total1443147

Merged error: 0.4b

Counts
147 → 3

regimes129.0ms

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
804.0ms8117×body80valid
67.0ms117×body1280valid
62.0ms143×body640valid
27.0ms89×body320valid
13.0ms66×body160valid
4.0ms5×body2560valid

Profiling

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