Details

Time bar (total: 4.5s)

sample50.0ms

Algorithm
intervals
Results
25.0ms261×body80valid
3.0ms6×body640valid
2.0ms4×body1280valid
1.0ms1×body2560valid
1.0ms3×body320valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (9.0ms)

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: 15.7b

Counts
2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
32.8b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
15×add-sqr-sqrt
9×add-log-exp
8×add-cube-cbrt
7×pow1 add-exp-log
6×unpow-prod-down add-cbrt-cube
4×associate-*r*
3×pow-unpow associate-*l* distribute-lft-out
2×sub-neg cos-sum associate-+r+ flip3-+ associate-*r/ sum-log flip-+ distribute-lft-out-- difference-of-squares
1×+-commutative distribute-rgt-in cos-diff pow-to-exp associate-+r- pow-pow distribute-lft-in times-frac diff-log pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod unswap-sqr sqr-pow
Counts
4 → 70
Calls
4 calls:
6.0ms
(* K (+ m n))
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
17.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
9.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series506.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* K (+ m n))
252.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
173.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
57.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify42.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0411566
11369528
25001523

prune281.0ms

Filtered
82 candidates to 58 candidates (70.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New77582
Fresh000
Picked101
Done000
Total78583

Merged error: 0.8b

Counts
83 → 5

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
9×add-sqr-sqrt
7×add-log-exp
6×unpow-prod-down
4×add-cube-cbrt
3×pow1 add-exp-log pow-unpow
2×associate-+r+ sum-log add-cbrt-cube distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative pow-to-exp associate-+r- sub-neg pow-pow flip3-+ times-frac diff-log pow-exp flip-+ sqr-pow
Counts
2 → 37
Calls
2 calls:
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
17.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

series426.0ms

Counts
2 → 6
Calls
2 calls:
252.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
174.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

simplify74.0ms

Algorithm
egg-herbie
Counts
43 → 43
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0253368
1720351
22937346
35002343

prune128.0ms

Filtered
43 candidates to 31 candidates (72.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New43043
Fresh044
Picked011
Done000
Total43548

Merged error: 0.8b

Counts
48 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
32.8b
(cos (- (/ (* K (+ m n)) 2.0) M))
32.8b
(cos (- (/ (* K (+ m n)) 2.0) M))
32.8b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite28.0ms

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))

series294.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
54.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))
51.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))
55.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify125.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 6 (119.0ms)

IterNodesCost
083464
1123418
2183416
3334416
41040416
53218416
65001397

prune246.0ms

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: 0.8b

Counts
58 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

15.9b
(cbrt (* K (+ m n)))
15.9b
(cbrt (* K (+ m n)))
15.9b
(cbrt (* K (+ m n)))
32.9b
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-div associate-*r/
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cbrt-prod flip3-+ pow1/3 flip-+
2×cos-sum
1×cos-diff sub-neg
Counts
4 → 43
Calls
4 calls:
5.0ms
(cbrt (* K (+ m n)))
4.0ms
(cbrt (* K (+ m n)))
4.0ms
(cbrt (* K (+ m n)))
10.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series354.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (* K (+ m n)))
98.0ms
(cbrt (* K (+ m n)))
100.0ms
(cbrt (* K (+ m n)))
57.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify52.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 4 (46.0ms)

IterNodesCost
0186496
1357446
2740422
31608419
45001407

prune234.0ms

Filtered
55 candidates to 46 candidates (83.6%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New53255
Fresh112
Picked101
Done022
Total55560

Merged error: 0.8b

Counts
60 → 5

regimes176.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.2b 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
794.0ms8088×body80valid
68.0ms158×body640valid
65.0ms114×body1280valid
36.0ms112×body320valid
13.0ms49×body160valid
2.0ms3×body2560valid