Details

Time bar (total: 19.4s)

sample43.0ms

Algorithm
intervals
Results
20.0ms255×body80valid
3.0ms8×body640valid
2.0ms5×body1280valid
1.0ms3×body320valid
0.0ms2×body160valid

simplify4.4s

Counts
1 → 1
Iterations

Useful iterations: 4 (65.0ms)

IterNodesCost
02129
15029
29229
319529
443128
5126128
6478528
done500028

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
0.0b
(* K (+ m n))
32.6b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite4.0s

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
14×add-sqr-sqrt add-log-exp
10×associate-*r*
8×pow1 add-cube-cbrt add-cbrt-cube
7×add-exp-log
6×diff-log associate-*l* distribute-lft-out--
4×sub-neg
3×associate-*r/ exp-sum
2×cos-sum distribute-rgt-neg-in pow-prod-down neg-log prod-exp *-commutative cbrt-unprod associate--r+ associate--r- unswap-sqr
1×associate--l- neg-sub0 distribute-rgt-in cos-diff flip3-- distribute-lft-in flip3-+ exp-diff flip-- flip-+ distribute-lft-out difference-of-squares
Counts
4 → 79
Calls
4 calls:
578.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
3.4s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
9.0ms
(* K (+ m n))
15.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series632.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
361.0ms
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
28.0ms
(* K (+ m n))
55.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify745.0ms

Counts
91 → 91
Iterations

Useful iterations: done (742.0ms)

IterNodesCost
01821920
14501860
213501620
done50001595

prune395.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.4b

localize15.0ms

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))))

rewrite619.0ms

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:
34.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
583.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series460.0ms

Counts
2 → 6
Calls
2 calls:
272.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
188.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify1.1s

Counts
50 → 50
Iterations

Useful iterations: 3 (252.0ms)

IterNodesCost
0122937
1277879
2628826
31900807
done5000807

prune184.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
32.6b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite161.0ms

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:
2.0ms
(cbrt (+ m n))
2.0ms
(cbrt (+ m n))
2.0ms
(cbrt (+ m n))
152.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series498.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(cbrt (+ m n))
134.0ms
(cbrt (+ m n))
130.0ms
(cbrt (+ m n))
103.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify1.8s

Counts
64 → 64
Iterations

Useful iterations: 4 (629.0ms)

IterNodesCost
091868
1190835
2395653
3863602
42578596
done5000596

prune395.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.6b
(cbrt (- m))
0.7b
(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
29.7b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2.0) M))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1 add-exp-log
15×pow-prod-down prod-exp add-cbrt-cube cbrt-unprod
14×cbrt-prod cbrt-div
10×*-un-lft-identity associate-*r/ associate-*l/
8×add-sqr-sqrt add-cube-cbrt
7×flip3-+ flip-+
4×frac-times add-log-exp
3×distribute-lft-neg-in distribute-rgt-neg-in
2×cos-sum pow1/3
1×cos-diff neg-mul-1 sub-neg associate-*r* associate-*l* *-commutative distribute-lft-out
Counts
4 → 78
Calls
4 calls:
2.0ms
(cbrt (+ m n))
1.0ms
(cbrt (- m))
94.0ms
(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
167.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2.0) M))

series837.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(cbrt (+ m n))
202.0ms
(cbrt (- m))
162.0ms
(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
342.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2.0) M))

simplify756.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (214.0ms)

IterNodesCost
02181669
15321624
217201385
done50011385

prune507.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.4b

regimes317.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01720
12118
done2118

end0.0ms

sample1.1s

Algorithm
intervals
Results
647.0ms8075×body80valid
69.0ms136×body1280valid
58.0ms161×body640valid
24.0ms100×body320valid
11.0ms68×body160valid
2.0ms3×body2560valid