Details

Time bar (total: 9.7s)

sample41.0ms

Algorithm
intervals
Results
21.0ms265×body80valid
1.0ms4×body640valid
1.0ms3×body320valid
0.0ms1×body1280valid

simplify50.0ms

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: 12.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(* K (+ m n))
30.7b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×*-un-lft-identity
8×add-cube-cbrt
7×pow1 add-exp-log
6×unpow-prod-down add-cbrt-cube add-log-exp
4×associate-*r*
3×pow-unpow associate-*l* difference-of-squares
2×sub-neg cos-sum associate-*r/ distribute-lft-out--
1×distribute-rgt-in cos-diff pow-to-exp flip3-- pow-pow distribute-lft-in flip3-+ times-frac diff-log pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 67
Calls
4 calls:
32.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
10.0ms
(- (/ (* K (+ m n)) 2.0) M)
10.0ms
(* K (+ m n))
15.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series396.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms
(- (/ (* K (+ m n)) 2.0) M)
25.0ms
(* K (+ m n))
53.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify39.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0378485
11267447
25002443

prune320.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×*-un-lft-identity
6×unpow-prod-down
4×add-cube-cbrt add-log-exp
3×pow1 add-exp-log pow-unpow difference-of-squares
2×add-cbrt-cube distribute-lft-out--
1×pow-to-exp sub-neg flip3-- pow-pow times-frac diff-log pow-exp flip-- sqr-pow
Counts
2 → 34
Calls
2 calls:
3.0ms
(- l (fabs (- m n)))
32.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series273.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(- l (fabs (- m n)))
261.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify51.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0214259
1546247
21696246
35002243

prune136.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

12.2b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
12.2b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
12.2b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
41.7b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×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-- difference-of-squares
Counts
4 → 52
Calls
4 calls:
7.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
7.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
7.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
30.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

series757.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
234.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
232.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
57.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

simplify52.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0214792
1511722
21517713
35001704

prune392.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

12.2b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
12.2b
(cbrt (+ (/ (* K (+ m n)) 2.0) M))
34.7b
(cbrt (- (* (/ (* K (+ m n)) 2.0) (/ (* K (+ m n)) 2.0)) (* M M)))
35.6b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (/ (cbrt (- (* (/ (* K (+ m n)) 2.0) (/ (* K (+ m n)) 2.0)) (* M M))) (cbrt (+ (/ (* K (+ m n)) 2.0) M)))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
13×cbrt-prod
11×*-un-lft-identity
9×add-sqr-sqrt
7×add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
2×flip3-- flip-- difference-of-squares
1×flip3-+ flip-+ distribute-lft-out distribute-lft-out--
Counts
4 → 50
Calls
4 calls:
7.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
7.0ms
(cbrt (+ (/ (* K (+ m n)) 2.0) M))
23.0ms
(cbrt (- (* (/ (* K (+ m n)) 2.0) (/ (* K (+ m n)) 2.0)) (* M M)))
23.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (/ (cbrt (- (* (/ (* K (+ m n)) 2.0) (/ (* K (+ m n)) 2.0)) (* M M))) (cbrt (+ (/ (* K (+ m n)) 2.0) M)))))

series5.1s

Counts
4 → 12
Calls
4 calls:
248.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
231.0ms
(cbrt (+ (/ (* K (+ m n)) 2.0) M))
276.0ms
(cbrt (- (* (/ (* K (+ m n)) 2.0) (/ (* K (+ m n)) 2.0)) (* M M)))
4.3s
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (/ (cbrt (- (* (/ (* K (+ m n)) 2.0) (/ (* K (+ m n)) 2.0)) (* M M))) (cbrt (+ (/ (* K (+ m n)) 2.0) M)))))

simplify46.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04471011
11308905
25001883

prune476.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes111.0ms

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
02110
12310
22310

end0.0ms

sample1.1s

Algorithm
intervals
Results
642.0ms8080×body80valid
56.0ms114×body1280valid
53.0ms154×body640valid
29.0ms113×body320valid
7.0ms42×body160valid
2.0ms3×body2560valid