Details

Time bar (total: 5.8s)

sample46.0ms

Algorithm
intervals
Results
24.0ms264×body80valid
2.0ms4×body1280valid
1.0ms3×body640valid
1.0ms1×body2560valid
1.0ms2×body320valid
0.0ms3×body160valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
34.3b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite45.0ms

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:
17.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
9.0ms
(* K (+ m n))
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series521.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
28.0ms
(* K (+ m n))
263.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
54.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify41.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0411566
11369528
25001523

prune338.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.2b

localize17.0ms

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)

rewrite48.0ms

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:
19.0ms
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
17.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series603.0ms

Counts
3 → 9
Calls
3 calls:
163.0ms
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
177.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
264.0ms
(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

prune275.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
34.5b
(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:
3.0ms
(cbrt (+ m n))
3.0ms
(cbrt (+ m n))
3.0ms
(cbrt (+ m n))
19.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series483.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(cbrt (+ m n))
128.0ms
(cbrt (+ m n))
126.0ms
(cbrt (+ m n))
102.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify154.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 4 (148.0ms)

IterNodesCost
0186485
1416445
21213439
34532439
45001433

prune367.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.6b
(cbrt (cbrt (+ m n)))
0.6b
(cbrt (* (cbrt (+ m n)) (cbrt (+ m n))))
34.3b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2.0) M))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
26×cbrt-div
16×cbrt-prod
11×*-un-lft-identity
8×flip3-+ flip-+
7×add-sqr-sqrt add-cube-cbrt
4×pow1 add-exp-log frac-times add-cbrt-cube add-log-exp
3×pow1/3
2×cos-sum associate-*r/ associate-*l/ distribute-lft-out
1×cos-diff sub-neg
Counts
4 → 58
Calls
4 calls:
3.0ms
(cbrt (+ m n))
3.0ms
(cbrt (cbrt (+ m n)))
8.0ms
(cbrt (* (cbrt (+ m n)) (cbrt (+ m n))))
21.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2.0) M))

series679.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(cbrt (+ m n))
199.0ms
(cbrt (cbrt (+ m n)))
250.0ms
(cbrt (* (cbrt (+ m n)) (cbrt (+ m n))))
103.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2.0) M))

simplify87.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0355803
1900737
23173731
35001731

prune437.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

regimes237.0ms

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

sample1.1s

Algorithm
intervals
Results
667.0ms8098×body80valid
70.0ms118×body1280valid
57.0ms163×body640valid
25.0ms101×body320valid
14.0ms62×body160valid
5.0ms6×body2560valid