Details

Time bar (total: 5.0s)

sample48.0ms

Algorithm
intervals
Results
25.0ms258×body80valid
3.0ms5×body1280valid
2.0ms5×body640valid
2.0ms5×body320valid
0.0ms2×body160valid

simplify51.0ms

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)

Merged error: 16.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
35.4b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite35.0ms

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:
8.0ms
(- (/ (* K (+ m n)) 2.0) M)
6.0ms
(* K (+ m n))
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series388.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(- (/ (* K (+ m n)) 2.0) M)
24.0ms
(* K (+ m n))
253.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
54.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify39.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0378485
11267447
25002443

prune294.0ms

Filtered
79 candidates to 56 candidates (70.9%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize13.0ms

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)

rewrite29.0ms

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:
17.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
11.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series430.0ms

Counts
2 → 6
Calls
2 calls:
172.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
258.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify74.0ms

Algorithm
egg-herbie
Counts
43 → 43
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0253368
1720351
22937346
35002343

prune141.0ms

Filtered
43 candidates to 31 candidates (72.1%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
35.0b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite27.0ms

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))
17.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series477.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(cbrt (+ m n))
123.0ms
(cbrt (+ m n))
126.0ms
(cbrt (+ m n))
100.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify152.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 4 (147.0ms)

IterNodesCost
0186485
1416445
21213439
34532439
45001433

prune333.0ms

Filtered
64 candidates to 52 candidates (81.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
2.2b
(exp (log (cbrt (+ m n))))
18.9b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (exp (log (cbrt (+ m n))))) 2.0) M))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×cbrt-prod
9×add-sqr-sqrt add-cube-cbrt
7×log-prod exp-sum
6×cbrt-div
5×pow1 exp-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
2×log-div cos-sum exp-diff log-pow
1×cos-diff sub-neg rem-exp-log
Counts
4 → 60
Calls
4 calls:
3.0ms
(cbrt (+ m n))
3.0ms
(cbrt (+ m n))
5.0ms
(exp (log (cbrt (+ m n))))
20.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (exp (log (cbrt (+ m n))))) 2.0) M))

series477.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(cbrt (+ m n))
123.0ms
(cbrt (+ m n))
128.0ms
(exp (log (cbrt (+ m n))))
99.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (exp (log (cbrt (+ m n))))) 2.0) M))

simplify157.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (38.0ms)

IterNodesCost
0231551
1488507
21322497
34858489
45001489

prune385.0ms

Filtered
72 candidates to 59 candidates (81.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

regimes161.0ms

Accuracy

0% (0.1b 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
686.0ms8088×body80valid
71.0ms128×body1280valid
54.0ms154×body640valid
31.0ms118×body320valid
11.0ms57×body160valid
3.0ms4×body2560valid