Details

Time bar (total: 25.4s)

sample83.0ms

Algorithm
intervals
Results
39.0ms258×body80valid
8.0ms8×body1280valid
3.0ms5×body320valid
2.0ms3×body640valid
1.0ms3×body160valid

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (130.0ms)

IterNodesCost
02129
15029
29329
319729
446528
5114128
6470928
done500028

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
36.2b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite438.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
17×*-un-lft-identity
9×add-log-exp
8×add-cube-cbrt
7×pow1 add-exp-log unpow-prod-down
6×add-cbrt-cube
5×difference-of-squares
4×associate-*r* distribute-lft-out--
3×sub-neg pow-unpow diff-log associate-*l*
2×cos-sum associate-*r/ associate--l+ sqr-pow
1×associate--l- 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 unswap-sqr
Counts
4 → 74
Calls
4 calls:
259.0ms
(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
39.0ms
(* K (+ m n))
86.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
51.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series755.0ms

Counts
4 → 12
Calls
4 calls:
263.0ms
(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
28.0ms
(* K (+ m n))
375.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
90.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.0s

Counts
86 → 86
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01871305
14181230
29961151
329821145
done50001137

prune535.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite415.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
7×unpow-prod-down add-log-exp
5×difference-of-squares
4×add-cube-cbrt distribute-lft-out--
3×pow1 add-exp-log pow-unpow diff-log
2×sub-neg associate--l+ add-cbrt-cube sqr-pow
1×associate--l- pow-to-exp flip3-- pow-pow times-frac pow-exp flip--
Counts
2 → 41
Calls
2 calls:
314.0ms
(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
98.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series694.0ms

Counts
2 → 6
Calls
2 calls:
264.0ms
(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
430.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.5s

Counts
47 → 47
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0120902
1261848
2556809
31585803
done5001791

prune197.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize74.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.5b
(* (cbrt (+ m n)) (cbrt (+ m n)))
36.1b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite481.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod *-un-lft-identity
22×add-sqr-sqrt
16×cbrt-div
14×add-cube-cbrt
11×pow1
9×swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×cos-sum associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 cos-diff sub-neg pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 91
Calls
4 calls:
4.0ms
(cbrt (+ m n))
4.0ms
(cbrt (+ m n))
65.0ms
(* (cbrt (+ m n)) (cbrt (+ m n)))
404.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series808.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt (+ m n))
200.0ms
(cbrt (+ m n))
224.0ms
(* (cbrt (+ m n)) (cbrt (+ m n)))
201.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify3.9s

Counts
103 → 103
Iterations

Useful iterations: done (3.9s)

IterNodesCost
01501490
13091374
27191166
316721060
448081048
done50001014

prune680.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

localize72.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (cbrt (cbrt (+ m n))) 2)
0.6b
(cbrt (cbrt (+ m n)))
0.6b
(cbrt (cbrt (+ m n)))
35.9b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (pow (cbrt (cbrt (+ m n))) 2) (cbrt (cbrt (+ m n))))) 2.0) M))

rewrite615.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod
18×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt
10×unpow-prod-down
8×cbrt-div
5×pow1 add-exp-log
4×add-cbrt-cube add-log-exp
3×pow-unpow pow1/3 distribute-lft-out
2×cos-sum pow-pow flip3-+ flip-+
1×cos-diff pow-to-exp sub-neg pow-exp unpow2 sqr-pow
Counts
4 → 70
Calls
4 calls:
20.0ms
(pow (cbrt (cbrt (+ m n))) 2)
10.0ms
(cbrt (cbrt (+ m n)))
10.0ms
(cbrt (cbrt (+ m n)))
573.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (pow (cbrt (cbrt (+ m n))) 2) (cbrt (cbrt (+ m n))))) 2.0) M))

series1.1s

Counts
4 → 12
Calls
4 calls:
357.0ms
(pow (cbrt (cbrt (+ m n))) 2)
289.0ms
(cbrt (cbrt (+ m n)))
262.0ms
(cbrt (cbrt (+ m n)))
147.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (pow (cbrt (cbrt (+ m n))) 2) (cbrt (cbrt (+ m n))))) 2.0) M))

simplify1.9s

Counts
82 → 82
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01571324
13441114
2731996
32043873
done5000825

prune650.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.8b

regimes346.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01619
12017
done2017

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.0s8099×body80valid
171.0ms111×body1280valid
103.0ms123×body320valid
99.0ms136×body640valid
15.0ms49×body160valid
3.0ms2×body2560valid