Details

Time bar (total: 4.1s)

sample55.0ms

Algorithm
intervals
Results
28.0ms263×body80valid
3.0ms7×body640valid
2.0ms4×body1280valid
1.0ms3×body320valid
0.0ms1×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (7.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115

prune23.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.9b

Counts
2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
33.5b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
25×add-log-exp
13×add-sqr-sqrt
12×diff-log distribute-lft-out--
8×exp-prod
7×add-cube-cbrt
6×pow1 add-exp-log add-cbrt-cube
5×rem-exp-log
4×sub-neg distribute-rgt-neg-in associate-*r* neg-log
3×associate-*l* exp-sum
2×cos-sum associate-*r/ associate--r+ associate--r- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-in cos-diff flip3-- distribute-lft-in flip3-+ exp-diff pow-prod-down prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out unswap-sqr
Counts
4 → 81
Calls
4 calls:
6.0ms
(* K (+ m n))
23.0ms
(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
21.0ms
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
8.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series122.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* K (+ m n))
39.0ms
(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
56.0ms
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
20.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify44.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0393762
11362694
25002690

prune193.0ms

Filtered
61 candidates to 93 candidates (-52.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New88593
Fresh101
Picked101
Done000
Total90595

Merged error: 1.2b

Counts
95 → 5

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
24×add-log-exp
15×add-sqr-sqrt
13×distribute-lft-out--
12×diff-log
8×exp-prod
6×add-cube-cbrt unpow-prod-down
5×rem-exp-log
4×pow1 add-exp-log distribute-rgt-neg-in neg-log difference-of-squares
3×sub-neg pow-unpow exp-sum add-cbrt-cube
2×associate--r+ associate--r-
1×associate--l- neg-sub0 pow-to-exp flip3-- pow-pow times-frac exp-diff pow-exp flip-- sqr-pow
Counts
3 → 68
Calls
3 calls:
12.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms
(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
21.0ms
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series132.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
41.0ms
(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
52.0ms
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify38.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0386730
11179685
25002677

prune143.0ms

Filtered
51 candidates to 77 candidates (-51.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New75277
Fresh044
Picked101
Done000
Total76682

Merged error: 1.2b

Counts
82 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
0.0b
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
0.0b
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
0.0b
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
37×add-log-exp
24×exp-prod
18×diff-log distribute-lft-out--
15×rem-exp-log
14×add-sqr-sqrt
12×exp-sum
8×add-cube-cbrt
6×cbrt-prod distribute-rgt-neg-in neg-log
4×pow1 add-exp-log sub-neg exp-diff add-cbrt-cube associate--r-
3×difference-of-squares
1×cbrt-div pow1/3
Counts
4 → 87
Calls
4 calls:
20.0ms
(cbrt (exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
21.0ms
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
23.0ms
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
21.0ms
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(cbrt (exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
53.0ms
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
52.0ms
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
55.0ms
(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
02251058
1625975
22674964
35001954

prune330.0ms

Filtered
71 candidates to 99 candidates (-39.4%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New99099
Fresh055
Picked011
Done000
Total996105

Merged error: 1.2b

Counts
105 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))
33.7b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt 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
2×cos-sum
1×cos-diff sub-neg
Counts
4 → 52
Calls
4 calls:
5.0ms
(cbrt (+ m n))
3.0ms
(cbrt (+ m n))
3.0ms
(cbrt (+ m n))
16.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series119.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(cbrt (+ m n))
31.0ms
(cbrt (+ m n))
29.0ms
(cbrt (+ m n))
27.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify165.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (36.0ms)

IterNodesCost
0207539
1429499
21164478
34632454
45001454

prune126.0ms

Filtered
53 candidates to 64 candidates (-20.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New61364
Fresh134
Picked101
Done011
Total63770

Merged error: 1.1b

Counts
70 → 7

regimes459.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02535
12735
22735

end0.0ms

sample1.4s

Algorithm
intervals
Results
871.0ms8091×body80valid
77.0ms128×body1280valid
60.0ms141×body640valid
30.0ms97×body320valid
11.0ms51×body160valid
3.0ms4×body2560valid

Profiling

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