Details

Time bar (total: 5.1s)

sample38.0ms

Algorithm
intervals
Results
19.0ms255×body80valid
2.0ms5×body640valid
1.0ms4×body320valid
0.0ms1×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize22.0ms

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)
34.1b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
17×add-sqr-sqrt
14×add-log-exp
8×add-cube-cbrt
7×pow1 add-exp-log distribute-lft-out--
6×unpow-prod-down diff-log add-cbrt-cube
4×associate-*r*
3×sub-neg pow-unpow associate-*l* difference-of-squares
2×cos-sum distribute-rgt-neg-in associate-*r/ neg-log associate--r+
1×associate--l- neg-sub0 distribute-rgt-in cos-diff pow-to-exp flip3-- pow-pow distribute-lft-in flip3-+ times-frac pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out associate--r- unswap-sqr sqr-pow
Counts
4 → 77
Calls
4 calls:
21.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
6.0ms
(* K (+ m n))
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series518.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
24.0ms
(* K (+ m n))
258.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
56.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify47.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0435667
11447621
25001620

prune341.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×add-log-exp
11×add-sqr-sqrt
7×distribute-lft-out--
6×unpow-prod-down diff-log
4×add-cube-cbrt
3×pow1 add-exp-log pow-unpow difference-of-squares
2×sub-neg distribute-rgt-neg-in neg-log add-cbrt-cube associate--r+
1×associate--l- neg-sub0 pow-to-exp flip3-- pow-pow times-frac pow-exp flip-- associate--r- sqr-pow
Counts
2 → 44
Calls
2 calls:
21.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
11.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series441.0ms

Counts
2 → 6
Calls
2 calls:
182.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
260.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify85.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0277469
1798444
23368435
35001432

prune167.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

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))
18.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series481.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(cbrt (+ m n))
129.0ms
(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

prune356.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
8×cbrt-prod add-sqr-sqrt add-cube-cbrt
5×pow1
4×add-exp-log cbrt-div cos-sum log-prod log-pow add-cbrt-cube add-log-exp
3×exp-prod
2×cos-diff sub-neg log-div flip3-+ exp-diff pow1/3 flip-+ distribute-lft-out
1×rem-log-exp exp-sum
Counts
4 → 56
Calls
4 calls:
3.0ms
(cbrt (+ m n))
3.0ms
(cbrt (+ m n))
17.0ms
(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
17.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series451.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(cbrt (+ m n))
127.0ms
(cbrt (+ m n))
100.0ms
(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
100.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify49.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0226762
1488687
21374683
35001683

prune392.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.0b

regimes182.0ms

Accuracy

0% (0.2b remaining)

Error of 1.1b against oracle of 0.9b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12310
22310

end0.0ms

sample1.0s

Algorithm
intervals
Results
621.0ms8142×body80valid
63.0ms120×body1280valid
46.0ms140×body640valid
20.0ms85×body320valid
8.0ms49×body160valid
5.0ms7×body2560valid