Average Error: 0.1 → 0.1
Time: 3.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{1}{\frac{v}{m \cdot m}}\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(1 \cdot \frac{m}{v} - \frac{1}{\frac{v}{m \cdot m}}\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r9407 = m;
        double r9408 = 1.0;
        double r9409 = r9408 - r9407;
        double r9410 = r9407 * r9409;
        double r9411 = v;
        double r9412 = r9410 / r9411;
        double r9413 = r9412 - r9408;
        double r9414 = r9413 * r9409;
        return r9414;
}
↓
double f(double m, double v) {
        double r9415 = 1.0;
        double r9416 = m;
        double r9417 = v;
        double r9418 = r9416 / r9417;
        double r9419 = r9415 * r9418;
        double r9420 = 1.0;
        double r9421 = r9416 * r9416;
        double r9422 = r9417 / r9421;
        double r9423 = r9420 / r9422;
        double r9424 = r9419 - r9423;
        double r9425 = r9424 - r9415;
        double r9426 = r9415 - r9416;
        double r9427 = r9425 * r9426;
        return r9427;
}

Error

Bits error versus m

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

    \[\leadsto \left(\frac{m \cdot \color{blue}{\left(1 + \left(-m\right)\right)}}{v} - 1\right) \cdot \left(1 - m\right)\]

  4. Applied distribute-lft-in0.1

    \[\leadsto \left(\frac{\color{blue}{m \cdot 1 + m \cdot \left(-m\right)}}{v} - 1\right) \cdot \left(1 - m\right)\]

  5. Simplified0.1

    \[\leadsto \left(\frac{\color{blue}{1 \cdot m} + m \cdot \left(-m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]

  6. Simplified0.1

    \[\leadsto \left(\frac{1 \cdot m + \color{blue}{\left(-m\right) \cdot m}}{v} - 1\right) \cdot \left(1 - m\right)\]
  7. Using strategy rm

  8. Applied distribute-lft-neg-out0.1

    \[\leadsto \left(\frac{1 \cdot m + \color{blue}{\left(-m \cdot m\right)}}{v} - 1\right) \cdot \left(1 - m\right)\]

  9. Applied unsub-neg0.1

    \[\leadsto \left(\frac{\color{blue}{1 \cdot m - m \cdot m}}{v} - 1\right) \cdot \left(1 - m\right)\]

  10. Applied div-sub0.1

    \[\leadsto \left(\color{blue}{\left(\frac{1 \cdot m}{v} - \frac{m \cdot m}{v}\right)} - 1\right) \cdot \left(1 - m\right)\]

  11. Simplified0.1

    \[\leadsto \left(\left(\color{blue}{1 \cdot \frac{m}{v}} - \frac{m \cdot m}{v}\right) - 1\right) \cdot \left(1 - m\right)\]
  12. Using strategy rm

  13. Applied clear-num0.1

    \[\leadsto \left(\left(1 \cdot \frac{m}{v} - \color{blue}{\frac{1}{\frac{v}{m \cdot m}}}\right) - 1\right) \cdot \left(1 - m\right)\]

  14. Final simplification0.1

    \[\leadsto \left(\left(1 \cdot \frac{m}{v} - \frac{1}{\frac{v}{m \cdot m}}\right) - 1\right) \cdot \left(1 - m\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))