Details

Time bar (total: 29.8s)

sample67.0ms

Algorithm
intervals
Results
34.0ms259×body80valid
3.0ms5×body640valid
2.0ms3×body1280valid
1.0ms1×body320valid
0.0ms2×body160valid

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (141.0ms)

IterNodesCost
02129
15029
29529
320729
449928
5120928
6480728
done500028

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
30.4b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
42×*-un-lft-identity prod-diff
36×add-cube-cbrt
23×cos-sum
22×times-frac
7×pow1 add-exp-log fma-neg div-inv
6×unpow-prod-down add-cbrt-cube add-log-exp
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×pow-unpow associate-*l* difference-of-squares
2×sub-neg associate-*r/ distribute-lft-out--
1×distribute-rgt-in cos-diff pow-to-exp flip3-- pow-pow distribute-lft-in flip3-+ diff-log pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 124
Calls
4 calls:
25.0ms
(* K (+ m n))
30.0ms
(- (/ (* K (+ m n)) 2.0) M)
84.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
81.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series612.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* K (+ m n))
88.0ms
(- (/ (* K (+ m n)) 2.0) M)
375.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
99.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.7s

Counts
136 → 136
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
03073198
15992557
212492190
338881954
done50001954

prune797.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize37.0ms

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)

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
179×add-sqr-sqrt
148×*-un-lft-identity
129×prod-diff
78×unpow-prod-down
64×add-cube-cbrt
62×distribute-rgt-neg-in
60×distribute-lft-neg-in
51×difference-of-squares
43×distribute-lft-out--
24×fma-neg
13×times-frac sqr-pow
12×add-log-exp
11×associate--r+
6×neg-mul-1 diff-log
3×pow1 add-exp-log pow-unpow
2×expm1-log1p-u sub-neg neg-log add-cbrt-cube log1p-expm1-u
1×associate--l- neg-sub0 pow-to-exp flip3-- pow-pow pow-exp flip-- associate--r-
Counts
2 → 201
Calls
2 calls:
1.8s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
121.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series643.0ms

Counts
2 → 6
Calls
2 calls:
265.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
378.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.4s

Counts
207 → 207
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02749396
15977377
212636047
done50004898

prune692.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
30.4b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite444.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
23×cos-sum
21×prod-diff
20×add-sqr-sqrt add-cube-cbrt
12×cbrt-prod
9×times-frac
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ div-inv distribute-lft-out
1×cos-diff sub-neg
Counts
4 → 81
Calls
4 calls:
7.0ms
(cbrt (+ m n))
7.0ms
(cbrt (+ m n))
4.0ms
(cbrt (+ m n))
419.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series755.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(cbrt (+ m n))
176.0ms
(cbrt (+ m n))
180.0ms
(cbrt (+ m n))
191.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify4.9s

Counts
93 → 93
Iterations

Useful iterations: done (4.9s)

IterNodesCost
02333054
14162628
27641827
318091359
447551215
done50001212

prune760.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.6b
(cbrt (* (cbrt (+ m n)) (cbrt (+ m n))))
30.3b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
24×cbrt-div
23×cos-sum *-un-lft-identity
21×prod-diff
19×add-sqr-sqrt add-cube-cbrt
9×cbrt-prod times-frac
8×flip3-+ flip-+
4×pow1 add-exp-log expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 div-inv
2×associate-*r/ associate-*l/ distribute-lft-out
1×cos-diff sub-neg
Counts
4 → 84
Calls
4 calls:
4.0ms
(cbrt (+ m n))
4.0ms
(cbrt (+ m n))
14.0ms
(cbrt (* (cbrt (+ m n)) (cbrt (+ m n))))
1.0s
(cos (- (/ (* (* K (* (cbrt (+ m n)) (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

series938.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(cbrt (+ m n))
217.0ms
(cbrt (+ m n))
373.0ms
(cbrt (* (cbrt (+ m n)) (cbrt (+ m n))))
156.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

simplify2.3s

Counts
96 → 96
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02934243
15263807
210333363
329662925
done50002907

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

regimes395.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01720
12118
done2118

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.7s8098×body80valid
135.0ms129×body1280valid
118.0ms153×body640valid
54.0ms56×body160valid
53.0ms2×body2560valid
42.0ms94×body320valid