Details

Time bar (total: 35.3s)

sample95.0ms

Algorithm
intervals
Results
53.0ms261×body80valid
3.0ms4×body1280valid
3.0ms6×body640valid
1.0ms2×body320valid

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (145.0ms)

IterNodesCost
02129
15029
29529
320729
449928
5120928
6480728
done500028

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ 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
(pow (- (/ (+ m n) 2.0) M) 2.0)
32.2b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite9.5s

Algorithm
rewrite-expression-head
Rules
179×add-sqr-sqrt
144×*-un-lft-identity
141×prod-diff
130×associate-*r*
123×exp-sum
72×add-cube-cbrt
66×unpow-prod-down
50×distribute-lft-neg-in distribute-rgt-neg-in
46×difference-of-squares
35×distribute-lft-out--
23×cos-sum
20×times-frac
11×sqr-pow
9×pow1
8×add-exp-log add-cbrt-cube
6×associate-*l*
5×neg-mul-1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r/ div-inv
2×sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in cos-diff pow-to-exp pow-pow distribute-lft-in flip3-+ exp-diff pow-exp flip-+ distribute-lft-out associate--r-
Counts
4 → 224
Calls
4 calls:
25.0ms
(* K (+ m n))
9.2s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
97.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
72.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series1.2s

Counts
4 → 12
Calls
4 calls:
49.0ms
(* K (+ m n))
595.0ms
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
405.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
104.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.9s

Counts
236 → 236
Iterations

Useful iterations: done (1.9s)

IterNodesCost
06299112
111877956
224767241
done50006804

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity
11×add-cube-cbrt
9×prod-diff
6×unpow-prod-down
4×add-log-exp
3×pow1 add-exp-log pow-unpow fma-neg difference-of-squares
2×expm1-log1p-u add-cbrt-cube log1p-expm1-u distribute-lft-out--
1×pow-to-exp sub-neg flip3-- pow-pow times-frac diff-log pow-exp flip-- sqr-pow
Counts
2 → 50
Calls
2 calls:
14.0ms
(- l (fabs (- m n)))
107.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series411.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(- l (fabs (- m n)))
394.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.4s

Counts
56 → 56
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0132935
1273747
2574641
31649581
done5000564

prune242.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize82.0ms

Local error

Found 4 expressions with local error:

14.9b
(cbrt (/ (* K (+ m n)) 2.0))
14.9b
(cbrt (/ (* K (+ m n)) 2.0))
32.1b
(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
32.8b
(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

rewrite315.0ms

Algorithm
rewrite-expression-head
Rules
156×prod-diff
102×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
98×cbrt-prod
80×cos-sum sin-sum
60×unpow-prod-down cube-prod
42×times-frac
14×div-inv
6×cube-mult unpow3 sqr-pow
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×sub-neg cbrt-div pow1/3
1×cos-diff sin-diff
Counts
4 → 216
Calls
4 calls:
13.0ms
(cbrt (/ (* K (+ m n)) 2.0))
8.0ms
(cbrt (/ (* K (+ m n)) 2.0))
132.0ms
(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
129.0ms
(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

series789.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(cbrt (/ (* K (+ m n)) 2.0))
231.0ms
(cbrt (/ (* K (+ m n)) 2.0))
159.0ms
(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
195.0ms
(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

simplify3.0s

Counts
228 → 228
Iterations

Useful iterations: done (2.9s)

IterNodesCost
049314384
17938056
211866156
326115792
done50015152

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
14.9b
(cbrt (/ (* K (+ m n)) 2.0))
32.2b
(cos (- (/ (* K (+ m n)) 2.0) M))
32.8b
(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
99×prod-diff
80×sin-sum
69×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
49×cbrt-prod
33×unpow-prod-down cube-prod
30×times-frac
23×cos-sum
10×div-inv
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow
2×sub-neg
1×cos-diff pow-to-exp cbrt-div pow-pow pow1/3 pow-exp sin-diff rem-cube-cbrt
Counts
4 → 166
Calls
4 calls:
15.0ms
(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
9.0ms
(cbrt (/ (* K (+ m n)) 2.0))
53.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))
137.0ms
(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

series569.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
166.0ms
(cbrt (/ (* K (+ m n)) 2.0))
66.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))
146.0ms
(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

simplify3.7s

Counts
178 → 178
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
05199368
18795614
214624408
346224172
done50004172

prune760.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.0b

regimes269.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01720
12118
done2118

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.7s8086×body80valid
108.0ms142×body640valid
89.0ms124×body1280valid
40.0ms106×body320valid
12.0ms47×body160valid
1.0ms1×body2560valid