Average Error: 0.2 → 0.2
Time: 4.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{{1}^{3} - {m}^{3}} \cdot \left(1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)\right)} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{{1}^{3} - {m}^{3}} \cdot \left(1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)\right)} - 1\right) \cdot m
double f(double m, double v) {
        double r14229 = m;
        double r14230 = 1.0;
        double r14231 = r14230 - r14229;
        double r14232 = r14229 * r14231;
        double r14233 = v;
        double r14234 = r14232 / r14233;
        double r14235 = r14234 - r14230;
        double r14236 = r14235 * r14229;
        return r14236;
}
↓
double f(double m, double v) {
        double r14237 = m;
        double r14238 = v;
        double r14239 = 1.0;
        double r14240 = 3.0;
        double r14241 = pow(r14239, r14240);
        double r14242 = pow(r14237, r14240);
        double r14243 = r14241 - r14242;
        double r14244 = r14238 / r14243;
        double r14245 = r14239 * r14239;
        double r14246 = -r14237;
        double r14247 = r14246 * r14246;
        double r14248 = r14239 * r14246;
        double r14249 = r14247 - r14248;
        double r14250 = r14245 + r14249;
        double r14251 = r14244 * r14250;
        double r14252 = r14237 / r14251;
        double r14253 = r14252 - r14239;
        double r14254 = r14253 * r14237;
        return r14254;
}

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 0.2

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

  3. Applied sub-neg0.2

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

  4. Applied distribute-lft-in0.2

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  8. Applied distribute-rgt-out0.2

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

  9. Applied associate-/l*0.2

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

  11. Applied flip3-+0.2

    \[\leadsto \left(\frac{m}{\frac{v}{\color{blue}{\frac{{1}^{3} + {\left(-m\right)}^{3}}{1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)}}}} - 1\right) \cdot m\]

  12. Applied associate-/r/0.2

    \[\leadsto \left(\frac{m}{\color{blue}{\frac{v}{{1}^{3} + {\left(-m\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)\right)}} - 1\right) \cdot m\]

  13. Simplified0.2

    \[\leadsto \left(\frac{m}{\color{blue}{\frac{v}{{1}^{3} - {m}^{3}}} \cdot \left(1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)\right)} - 1\right) \cdot m\]

  14. Final simplification0.2

    \[\leadsto \left(\frac{m}{\frac{v}{{1}^{3} - {m}^{3}} \cdot \left(1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)\right)} - 1\right) \cdot m\]

Reproduce

herbie shell --seed 2020056 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))