Details

Time bar (total: 11.1s)

sample69.0ms

Algorithm
intervals
Results
43.0ms258×body80valid
3.0ms4×body1280valid
3.0ms5×body640valid
1.0ms3×body320valid
1.0ms3×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
05016
19516
221116
355315
4197415
5500115

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
42×*-un-lft-identity prod-diff
36×add-cube-cbrt
23×cos-sum
22×times-frac
7×pow1 add-exp-log fma-neg div-inv
6×unpow-prod-down add-cbrt-cube add-log-exp
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×pow-unpow associate-*l* difference-of-squares
2×sub-neg associate-*r/ distribute-lft-out--
1×distribute-rgt-in cos-diff pow-to-exp flip3-- pow-pow distribute-lft-in flip3-+ diff-log pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 124
Calls
4 calls:
11.0ms
(- (/ (* K (+ m n)) 2.0) M)
9.0ms
(* K (+ m n))
33.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series415.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (/ (* K (+ m n)) 2.0) M)
31.0ms
(* K (+ m n))
274.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
54.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify66.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06121660
119071270
250031268

prune492.0ms

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)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
33×add-sqr-sqrt
23×add-cube-cbrt
14×times-frac
12×unpow-prod-down
11×associate-+r+
10×fma-def
9×prod-diff
8×add-log-exp
6×pow-flip
5×pow1 add-exp-log exp-prod add-cbrt-cube
4×exp-sum associate-/r* distribute-lft-out distribute-lft-out-- difference-of-squares
3×expm1-log1p-u pow-unpow log1p-expm1-u associate-/l*
2×associate-+r- div-exp sum-log sqr-pow
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
Counts
3 → 103
Calls
3 calls:
1.0s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
230.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
34.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series628.0ms

Counts
3 → 9
Calls
3 calls:
165.0ms
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
186.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
276.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify52.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04901187
118421061
250011034

prune382.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize22.0ms

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×expm1-log1p-u add-cbrt-cube log1p-expm1-u 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 → 106
Calls
4 calls:
31.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
865.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
865.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
856.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
289.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
270.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
279.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
293.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03651974
111251842
250021820

prune554.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

localize31.0ms

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))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
23×cos-sum
21×prod-diff
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×cbrt-div associate-*r/
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod flip3-+ pow1/3 flip-+ div-inv
1×cos-diff sub-neg
Counts
4 → 72
Calls
4 calls:
3.0ms
(cbrt (* K (+ m n)))
3.0ms
(cbrt (* K (+ m n)))
3.0ms
(cbrt (* K (+ m n)))
32.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series385.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(cbrt (* K (+ m n)))
109.0ms
(cbrt (* K (+ m n)))
109.0ms
(cbrt (* K (+ m n)))
59.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify60.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
04261888
17861586
218781562
350021391

prune404.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

regimes285.0ms

Accuracy

0% (0.3b 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

sample1.9s

Algorithm
intervals
Results
1.4s8108×body80valid
98.0ms126×body1280valid
77.0ms132×body640valid
45.0ms104×body320valid
16.0ms51×body160valid
3.0ms3×body2560valid