Details

Time bar (total: 10.4s)

sample72.0ms

Algorithm
intervals
Results
47.0ms258×body80valid
3.0ms4×body1280valid
3.0ms5×body640valid
1.0ms3×body320valid
1.0ms3×body160valid

simplify48.0ms

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: 15.1b

localize22.0ms

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)
37.1b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite68.0ms

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:
9.0ms
(- (/ (* K (+ m n)) 2.0) M)
9.0ms
(* K (+ m n))
31.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
17.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series403.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (/ (* K (+ m n)) 2.0) M)
24.0ms
(* K (+ m n))
264.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
56.0ms
(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

prune325.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize14.0ms

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)

rewrite1.2s

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:
1.0s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
199.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
31.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series598.0ms

Counts
3 → 9
Calls
3 calls:
158.0ms
(/ 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))))
263.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify46.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04121005
11568934
25001910

prune272.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.2b
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
0.2b
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
0.2b
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
51×cbrt-prod
37×times-frac
35×add-sqr-sqrt
32×*-un-lft-identity
30×add-cube-cbrt
9×exp-sum
6×unpow-prod-down
5×pow1 add-exp-log
4×add-cbrt-cube add-log-exp
3×associate-+r- pow-unpow cbrt-div exp-diff pow1/3 associate-/r/ div-inv
2×difference-of-squares
1×pow-to-exp pow-pow pow-exp distribute-lft-out-- sqr-pow
Counts
4 → 98
Calls
4 calls:
30.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
848.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
843.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
846.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
264.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
279.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
273.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
276.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))

simplify45.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03541892
110751785
250011763

prune502.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

localize26.0ms

Local error

Found 4 expressions with local error:

14.3b
(cbrt (* K (+ m n)))
14.3b
(cbrt (* K (+ m n)))
14.3b
(cbrt (* K (+ m n)))
37.3b
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-div associate-*r/
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cbrt-prod flip3-+ pow1/3 flip-+
2×cos-sum
1×cos-diff sub-neg
Counts
4 → 43
Calls
4 calls:
3.0ms
(cbrt (* K (+ m n)))
6.0ms
(cbrt (* K (+ m n)))
3.0ms
(cbrt (* K (+ m n)))
26.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series373.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(cbrt (* K (+ m n)))
105.0ms
(cbrt (* K (+ m n)))
105.0ms
(cbrt (* K (+ m n)))
54.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify52.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 4 (47.0ms)

IterNodesCost
0186496
1357446
2740422
31608419
45001407

prune280.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

regimes263.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02435
12435

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.4s8108×body80valid
103.0ms126×body1280valid
78.0ms132×body640valid
49.0ms104×body320valid
16.0ms51×body160valid
3.0ms3×body2560valid