Details

Time bar (total: 13.5s)

sample41.0ms

Algorithm
intervals
Results
21.0ms268×body80valid
1.0ms4×body640valid
1.0ms5×body320valid
1.0ms2×body1280valid
0.0ms1×body160valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (62.0ms)

IterNodesCost
02129
15029
29229
319529
442828
5122828
6459228
done500028

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
31.7b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite624.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
17×add-sqr-sqrt
14×add-log-exp
8×add-cube-cbrt
7×pow1 add-exp-log distribute-lft-out--
6×unpow-prod-down diff-log add-cbrt-cube
4×associate-*r*
3×sub-neg pow-unpow associate-*l* difference-of-squares
2×cos-sum distribute-rgt-neg-in associate-*r/ neg-log associate--r+
1×associate--l- neg-sub0 distribute-rgt-in cos-diff pow-to-exp flip3-- pow-pow distribute-lft-in flip3-+ times-frac pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out associate--r- unswap-sqr sqr-pow
Counts
4 → 77
Calls
4 calls:
11.0ms
(* K (+ m n))
31.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
564.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
15.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series506.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* K (+ m n))
255.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
175.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
52.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.1s

Counts
89 → 89
Iterations

Useful iterations: 3 (411.0ms)

IterNodesCost
01891340
14331261
210161168
328041149
done50011149

prune347.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

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))))

rewrite602.0ms

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:
33.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
567.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series438.0ms

Counts
2 → 6
Calls
2 calls:
261.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
177.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify820.0ms

Counts
50 → 50
Iterations

Useful iterations: 3 (231.0ms)

IterNodesCost
0122937
1277879
2628826
31880807
done5001807

prune169.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt K)
0.6b
(cbrt K)
0.6b
(cbrt K)
31.7b
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite47.0ms

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:
0.0ms
(cbrt K)
0.0ms
(cbrt K)
0.0ms
(cbrt K)
45.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series642.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(cbrt K)
180.0ms
(cbrt K)
185.0ms
(cbrt K)
99.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify1.7s

Counts
55 → 55
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
060516
1113498
2235386
3564335
41858335
done5000335

prune268.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.8b

localize34.0ms

Local error

Found 4 expressions with local error:

3.2b
(* K (+ (pow m 3) (pow n 3)))
4.8b
(+ (pow m 3) (pow n 3))
31.7b
(cos (- (/ (/ (* K (+ (pow m 3) (pow n 3))) (+ (* m m) (- (* n n) (* m n)))) 2.0) M))
35.5b
(/ (* K (+ (pow m 3) (pow n 3))) (+ (* m m) (- (* n n) (* m n))))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
11×add-exp-log add-cbrt-cube
10×add-sqr-sqrt distribute-lft-out
9×associate-*r*
8×add-cube-cbrt unpow-prod-down cube-prod
6×pow1 add-log-exp
4×flip3-+ associate-*r/ flip-+
3×times-frac associate-*l* associate-/r*
2×cbrt-undiv cos-sum div-exp prod-exp associate-/r/ sum-cubes cbrt-unprod associate-/l/
1×+-commutative distribute-rgt-in cos-diff sub-neg frac-2neg distribute-lft-in pow-prod-down clear-num sum-log *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 80
Calls
4 calls:
51.0ms
(* K (+ (pow m 3) (pow n 3)))
14.0ms
(+ (pow m 3) (pow n 3))
118.0ms
(cos (- (/ (/ (* K (+ (pow m 3) (pow n 3))) (+ (* m m) (- (* n n) (* m n)))) 2.0) M))
31.0ms
(/ (* K (+ (pow m 3) (pow n 3))) (+ (* m m) (- (* n n) (* m n))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* K (+ (pow m 3) (pow n 3)))
52.0ms
(+ (pow m 3) (pow n 3))
184.0ms
(cos (- (/ (/ (* K (+ (pow m 3) (pow n 3))) (+ (* m m) (- (* n n) (* m n)))) 2.0) M))
131.0ms
(/ (* K (+ (pow m 3) (pow n 3))) (+ (* m m) (- (* n n) (* m n))))

simplify669.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
01491853
13911662
215921442
done50011442

prune477.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

regimes181.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01720
12118
done2118

end0.0ms

sample1.1s

Algorithm
intervals
Results
630.0ms8117×body80valid
57.0ms160×body640valid
52.0ms102×body1280valid
26.0ms109×body320valid
8.0ms50×body160valid
4.0ms6×body2560valid