Average Error: 0.0 → 0.0
Time: 9.8s
Precision: 64
\[\left(1 - Alpha\right) \cdot A + Alpha \cdot B\]
\[1 \cdot A + Alpha \cdot \left(B - A\right)\]
\left(1 - Alpha\right) \cdot A + Alpha \cdot B
1 \cdot A + Alpha \cdot \left(B - A\right)
double f(double Alpha, double A, double B) {
        double r1731013 = 1.0;
        double r1731014 = Alpha;
        double r1731015 = r1731013 - r1731014;
        double r1731016 = A;
        double r1731017 = r1731015 * r1731016;
        double r1731018 = B;
        double r1731019 = r1731014 * r1731018;
        double r1731020 = r1731017 + r1731019;
        return r1731020;
}

double f(double Alpha, double A, double B) {
        double r1731021 = 1.0;
        double r1731022 = A;
        double r1731023 = r1731021 * r1731022;
        double r1731024 = Alpha;
        double r1731025 = B;
        double r1731026 = r1731025 - r1731022;
        double r1731027 = r1731024 * r1731026;
        double r1731028 = r1731023 + r1731027;
        return r1731028;
}

Error

Bits error versus Alpha

Bits error versus A

Bits error versus B

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(1 - Alpha\right) \cdot A + Alpha \cdot B\]
  2. Using strategy rm
  3. Applied flip-+29.7

    \[\leadsto \color{blue}{\frac{\left(\left(1 - Alpha\right) \cdot A\right) \cdot \left(\left(1 - Alpha\right) \cdot A\right) - \left(Alpha \cdot B\right) \cdot \left(Alpha \cdot B\right)}{\left(1 - Alpha\right) \cdot A - Alpha \cdot B}}\]
  4. Taylor expanded around inf 0.0

    \[\leadsto \color{blue}{\left(1 \cdot A + B \cdot Alpha\right) - A \cdot Alpha}\]
  5. Simplified0.0

    \[\leadsto \color{blue}{1 \cdot A + Alpha \cdot \left(B - A\right)}\]
  6. Final simplification0.0

    \[\leadsto 1 \cdot A + Alpha \cdot \left(B - A\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (Alpha A B)
  :name "((1 - Alpha) * A) + (Alpha * B)"
  :precision binary64
  (+ (* (- 1 Alpha) A) (* Alpha B)))