Details

Time bar (total: 7.9s)

sample43.0ms

Algorithm
intervals
Results
19.0ms260×body80valid
2.0ms5×body1280valid
2.0ms6×body640valid
1.0ms2×body320valid
0.0ms1×body160valid

simplify48.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.6b

localize25.0ms

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)) 2.0) M)
0.0b
(* K (+ m n))
34.4b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite385.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
11×add-log-exp
10×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
4×associate-*r*
3×sub-neg associate-*l* distribute-lft-out
2×cos-sum associate-+r+ flip3-+ diff-log associate-*r/ sum-log flip-+ distribute-lft-out--
1×+-commutative distribute-rgt-in cos-diff associate-+r- flip3-- distribute-lft-in pow-prod-down prod-exp *-commutative flip-- cbrt-unprod difference-of-squares unswap-sqr
Counts
4 → 64
Calls
4 calls:
320.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
16.0ms
(- (/ (* K (+ m n)) 2.0) M)
21.0ms
(* K (+ m n))
27.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series332.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
58.0ms
(- (/ (* K (+ m n)) 2.0) M)
29.0ms
(* K (+ m n))
61.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify37.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0360530
11201480
25002470

prune289.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.2b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite2.0s

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:
51.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
318.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
1.6s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))

series622.0ms

Counts
3 → 9
Calls
3 calls:
263.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
184.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
175.0ms
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))

simplify50.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04121005
11568934
25001910

prune256.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.2b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite373.0ms

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:
51.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
321.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

series448.0ms

Counts
2 → 6
Calls
2 calls:
266.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
182.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

simplify72.0ms

Algorithm
egg-herbie
Counts
43 → 43
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0253368
1720351
22937346
35002343

prune164.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.2b

localize25.0ms

Local error

Found 4 expressions with local error:

15.0b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
15.0b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
15.0b
(cbrt (- (/ (* K (+ m n)) 2.0) M))
43.5b
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

rewrite92.0ms

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:
11.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
11.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
12.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
56.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

series799.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
243.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
243.0ms
(cbrt (- (/ (* K (+ m n)) 2.0) M))
64.0ms
(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

simplify47.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (39.0ms)

IterNodesCost
0214792
1511722
21517713
35001704

prune358.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.2b

regimes185.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02311
12711
22711

end0.0ms

sample1.2s

Algorithm
intervals
Results
628.0ms8092×body80valid
59.0ms125×body1280valid
42.0ms129×body640valid
24.0ms92×body320valid
11.0ms55×body160valid
1.0ms2×body2560valid