Details

Time bar (total: 5.1s)

sample43.0ms

Algorithm
intervals
Results
22.0ms262×body80valid
2.0ms3×body1280valid
1.0ms3×body320valid
1.0ms2×body640valid
0.0ms1×body160valid

simplify49.0ms

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: 15.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(* K (+ m n))
34.6b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite38.0ms

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)
11.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms
(* K (+ m n))
12.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series394.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (/ (* K (+ m n)) 2.0) M)
258.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
28.0ms
(* K (+ m n))
54.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify38.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0378485
11267447
25002443

prune320.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(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)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
24×add-log-exp
15×add-sqr-sqrt
13×distribute-lft-out--
12×diff-log
8×exp-prod
6×add-cube-cbrt unpow-prod-down
5×rem-exp-log
4×pow1 add-exp-log distribute-rgt-neg-in neg-log difference-of-squares
3×sub-neg pow-unpow exp-sum add-cbrt-cube
2×associate--r+ associate--r-
1×associate--l- neg-sub0 pow-to-exp flip3-- pow-pow times-frac exp-diff pow-exp flip-- sqr-pow
Counts
3 → 68
Calls
3 calls:
21.0ms
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
20.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
12.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series561.0ms

Counts
3 → 9
Calls
3 calls:
123.0ms
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
180.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
258.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify36.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0356720
11112675
25002670

prune248.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize29.0ms

Local error

Found 4 expressions with local error:

15.6b
(cbrt (* K (+ m n)))
15.6b
(cbrt (* K (+ m n)))
15.6b
(cbrt (* K (+ m n)))
34.8b
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite24.0ms

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:
4.0ms
(cbrt (* K (+ m n)))
4.0ms
(cbrt (* K (+ m n)))
4.0ms
(cbrt (* K (+ m n)))
10.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series371.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(cbrt (* K (+ m n)))
104.0ms
(cbrt (* K (+ m n)))
108.0ms
(cbrt (* K (+ m n)))
53.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify53.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 4 (48.0ms)

IterNodesCost
0186496
1357446
2740422
31608419
45001407

prune301.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt K)
0.5b
(cbrt K)
0.5b
(cbrt K)
34.5b
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
2×cos-sum
1×cos-diff sub-neg
Counts
4 → 43
Calls
4 calls:
1.0ms
(cbrt K)
1.0ms
(cbrt K)
1.0ms
(cbrt K)
13.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series630.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt K)
172.0ms
(cbrt K)
173.0ms
(cbrt K)
102.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify95.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
0111309
1265279
2681273
33070273
45001273

prune406.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

regimes202.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12310
22310

end0.0ms

sample1.1s

Algorithm
intervals
Results
685.0ms8074×body80valid
70.0ms133×body1280valid
53.0ms139×body640valid
23.0ms88×body320valid
14.0ms78×body160valid
1.0ms2×body2560valid