Details

Time bar (total: 7.8s)

sample47.0ms

Algorithm
intervals
Results
21.0ms253×body80valid
2.0ms5×body1280valid
2.0ms5×body640valid
1.0ms3×body320valid
1.0ms4×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.5b

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) (- l (fabs (- m n))))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
36.3b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite459.0ms

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:
19.0ms
(* K (+ m n))
350.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
58.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
29.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series495.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* K (+ m n))
169.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
248.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
54.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify48.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0411566
11369528
25001523

prune340.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
0.0b
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
20×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
8×add-log-exp
6×unpow-prod-down pow-flip
5×pow1 add-exp-log exp-prod add-cbrt-cube
4×exp-sum associate-/r* distribute-lft-out
3×pow-unpow associate-/l* distribute-lft-out--
2×associate-+r- associate-+r+ div-exp sum-log difference-of-squares
1×cbrt-undiv +-commutative pow-to-exp sub-neg rec-exp pow-pow frac-2neg flip3-+ exp-diff diff-log 1-exp pow-exp clear-num associate-/r/ flip-+ div-inv inv-pow sqr-pow
Counts
3 → 78
Calls
3 calls:
1.8s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
347.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
56.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series576.0ms

Counts
3 → 9
Calls
3 calls:
160.0ms
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
162.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
253.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify47.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04121005
11568934
25001910

prune271.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (* K (+ m n))) (sqrt (* K (+ m n))))
11.8b
(sqrt (* K (+ m n)))
11.8b
(sqrt (* K (+ m n)))
19.9b
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
59×pow1
32×sqrt-pow1
22×pow-prod-down
18×associate-*r/
16×sqrt-div
12×pow1/2
10×add-sqr-sqrt pow-prod-up
8×add-cube-cbrt *-un-lft-identity flip3-+ flip-+
6×add-exp-log sqrt-prod pow-sqr add-cbrt-cube
4×frac-times swap-sqr associate-*r* associate-*l* add-log-exp
2×cos-sum associate-*l/
1×pow2 cos-diff sub-neg pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod unswap-sqr
Counts
4 → 93
Calls
4 calls:
55.0ms
(* (sqrt (* K (+ m n))) (sqrt (* K (+ m n))))
7.0ms
(sqrt (* K (+ m n)))
7.0ms
(sqrt (* K (+ m n)))
101.0ms
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

series174.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (sqrt (* K (+ m n))) (sqrt (* K (+ m n))))
50.0ms
(sqrt (* K (+ m n)))
45.0ms
(sqrt (* K (+ m n)))
55.0ms
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

simplify42.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0254656
1959575
25001548

prune383.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.3b

localize34.0ms

Local error

Found 4 expressions with local error:

11.8b
(sqrt (* K (+ m n)))
19.9b
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))
19.9b
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))
19.9b
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×cos-sum
4×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cos-diff sub-neg
2×sqrt-pow1 sqrt-div associate-*r/
1×flip3-+ pow1/2 pow-prod-down sqrt-prod flip-+
Counts
4 → 43
Calls
4 calls:
7.0ms
(sqrt (* K (+ m n)))
96.0ms
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))
97.0ms
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))
100.0ms
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

series206.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(sqrt (* K (+ m n)))
55.0ms
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))
50.0ms
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))
55.0ms
(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

simplify63.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
0175659
1387587
2835582
32178580
45002580

prune351.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.3b

regimes221.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02010
12010

end0.0ms

sample1.2s

Algorithm
intervals
Results
676.0ms8098×body80valid
58.0ms115×body1280valid
53.0ms152×body640valid
35.0ms124×body320valid
12.0ms68×body160valid
2.0ms3×body2560valid