Details

Time bar (total: 5.4s)

sample44.0ms

Algorithm
intervals
Results
21.0ms259×body80valid
3.0ms10×body640valid
2.0ms4×body1280valid
0.0ms3×body160valid
0.0ms2×body320valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
33.9b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
14×*-un-lft-identity
10×add-cube-cbrt associate-*r*
9×pow1
8×add-exp-log add-cbrt-cube
6×unpow-prod-down associate-*l*
4×add-log-exp
3×pow-unpow associate-*r/ exp-sum
2×sub-neg cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
1×distribute-rgt-in cos-diff pow-to-exp pow-pow distribute-lft-in flip3-+ times-frac exp-diff pow-exp flip-+ distribute-lft-out distribute-lft-out-- associate--r- sqr-pow
Counts
4 → 75
Calls
4 calls:
6.0ms
(* K (+ m n))
27.0ms
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
11.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series709.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* K (+ m n))
357.0ms
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
271.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
56.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify48.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0489871
11795780
25001777

prune354.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize15.0ms

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)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×add-log-exp
11×add-sqr-sqrt
7×distribute-lft-out--
6×unpow-prod-down diff-log
4×add-cube-cbrt
3×pow1 add-exp-log pow-unpow difference-of-squares
2×sub-neg distribute-rgt-neg-in neg-log add-cbrt-cube associate--r+
1×associate--l- neg-sub0 pow-to-exp flip3-- pow-pow times-frac pow-exp flip-- associate--r- sqr-pow
Counts
2 → 44
Calls
2 calls:
21.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
11.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series450.0ms

Counts
2 → 6
Calls
2 calls:
182.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
268.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify79.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0277469
1798444
23368435
35001432

prune162.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
34.1b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite28.0ms

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))

series488.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(cbrt (+ m n))
126.0ms
(cbrt (+ m n))
134.0ms
(cbrt (+ m n))
103.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify151.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 4 (141.0ms)

IterNodesCost
0186485
1416445
21213439
34532439
45001433

prune355.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.6b
(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
34.1b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
8×cbrt-prod add-sqr-sqrt add-cube-cbrt
5×pow1
4×add-exp-log cbrt-div cos-sum log-prod log-pow add-cbrt-cube add-log-exp
3×exp-prod
2×cos-diff sub-neg log-div flip3-+ exp-diff pow1/3 flip-+ distribute-lft-out
1×rem-log-exp exp-sum
Counts
4 → 56
Calls
4 calls:
3.0ms
(cbrt (+ m n))
3.0ms
(cbrt (+ m n))
17.0ms
(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
17.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series464.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(cbrt (+ m n))
128.0ms
(cbrt (+ m n))
107.0ms
(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
101.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify53.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0226762
1488687
21374683
35001683

prune406.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

regimes227.0ms

Accuracy

0% (0.3b remaining)

Error of 1.6b against oracle of 1.3b and baseline of 1.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12310
22310

end0.0ms

sample1.1s

Algorithm
intervals
Results
664.0ms8091×body80valid
60.0ms122×body1280valid
59.0ms174×body640valid
28.0ms113×body320valid
11.0ms67×body160valid
1.0ms1×body2560valid