Details

Time bar (total: 7.7s)

analyze2.3s

Algorithm
search

sample48.0ms

Algorithm
intervals
Results
27.0ms255×body80valid
2.0ms3×body1280invalid
1.0ms2×body320invalid
0.0ms1×body640invalid
0.0ms4×body80invalid
0.0ms2×body160invalid
0.0ms1×body160valid

simplify48.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (7.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115

prune13.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 15.3b

Counts
2 → 1

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
36.8b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
7×add-cube-cbrt
6×pow1 add-exp-log unpow-prod-down
5×add-cbrt-cube
4×associate-*r*
3×pow-unpow associate-*l* add-log-exp
2×cos-sum associate-*r/ difference-of-squares
1×distribute-rgt-in cos-diff pow-to-exp sub-neg pow-pow distribute-lft-in flip3-+ times-frac pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out distribute-lft-out-- unswap-sqr sqr-pow
Counts
3 → 53
Calls
3 calls:
6.0ms
(* K (+ m n))
11.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
11.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series69.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(* K (+ m n))
40.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
21.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify101.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
0332372
11107346
24408342
35002339

prune126.0ms

Filtered
44 candidates to 62 candidates (-40.9%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New60262
Fresh000
Picked101
Done000
Total61263

Merged error: 0.2b

Counts
63 → 2

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:
11.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series40.0ms

Counts
1 → 3
Calls
1 calls:
40.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify45.0ms

Algorithm
egg-herbie
Counts
23 → 23
Iterations

Useful iterations: 3 (41.0ms)

IterNodesCost
0170174
1470169
21593165
35002157

prune50.0ms

Filtered
17 candidates to 23 candidates (-35.3%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New23023
Fresh011
Picked011
Done000
Total23225

Merged error: 0.2b

Counts
25 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
2.1b
(exp (log (* K (+ m n))))
10.2b
(log (* K (+ m n)))
19.3b
(cos (- (/ (exp (log (* K (+ m n)))) 2.0) M))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×pow1
9×*-un-lft-identity
8×add-exp-log
7×add-cube-cbrt
6×unpow-prod-down
5×exp-prod
4×log-div associate-*r/ log-pow add-cbrt-cube add-log-exp
3×pow-unpow
2×cos-sum log-prod flip3-+ exp-diff rem-log-exp pow-prod-down flip-+ difference-of-squares
1×cos-diff pow-to-exp sub-neg pow-pow times-frac exp-sum pow-exp prod-exp rem-exp-log distribute-lft-out-- sqr-pow
Counts
4 → 60
Calls
4 calls:
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms
(exp (log (* K (+ m n))))
5.0ms
(log (* K (+ m n)))
13.0ms
(cos (- (/ (exp (log (* K (+ m n)))) 2.0) M))

series80.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms
(exp (log (* K (+ m n))))
12.0ms
(log (* K (+ m n)))
21.0ms
(cos (- (/ (exp (log (* K (+ m n)))) 2.0) M))

simplify70.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0338482
1925442
22965434
35002431

prune138.0ms

Filtered
51 candidates to 72 candidates (-41.2%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New71172
Fresh000
Picked101
Done011
Total72274

Merged error: 0.2b

Counts
74 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.2b
(+ (log K) (log n))
1.0b
(exp (+ (log K) (log n)))
7.7b
(cos (- (/ (exp (+ (log K) (log n))) 2.0) M))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
14×add-sqr-sqrt
13×pow1
9×add-cube-cbrt
8×log-pow distribute-lft-out
7×exp-prod
6×unpow-prod-down log-prod
5×add-exp-log add-log-exp
4×add-cbrt-cube
3×pow-unpow associate-+l+ associate-+r+
2×cos-sum sum-log rem-exp-log difference-of-squares
1×+-commutative cos-diff pow-to-exp sub-neg pow-pow flip3-+ times-frac exp-sum pow-exp flip-+ distribute-lft-out-- sqr-pow
Counts
4 → 68
Calls
4 calls:
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
5.0ms
(+ (log K) (log n))
5.0ms
(exp (+ (log K) (log n)))
14.0ms
(cos (- (/ (exp (+ (log K) (log n))) 2.0) M))

series103.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
11.0ms
(+ (log K) (log n))
16.0ms
(exp (+ (log K) (log n)))
34.0ms
(cos (- (/ (exp (+ (log K) (log n))) 2.0) M))

simplify82.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0378568
11048520
23942476
35001461

prune138.0ms

Filtered
54 candidates to 80 candidates (-48.1%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New79180
Fresh000
Picked101
Done011
Total80282

Merged error: 0.2b

Counts
82 → 2

regimes303.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02010
12010

end0.0ms

analyze2.3s

Algorithm
search

sample1.4s

Algorithm
intervals
Results
862.0ms7823×body80valid
41.0ms62×body1280invalid
36.0ms83×body640invalid
35.0ms77×body640valid
34.0ms48×body1280valid
30.0ms258×body80invalid
18.0ms56×body320invalid
12.0ms37×body320valid
5.0ms5×body2560invalid
5.0ms21×body160invalid
4.0ms15×body160valid

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