Average Error: 0.2 → 0.2
Time: 3.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{\frac{m}{\sqrt{1}}}{\frac{v}{1 - m}} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{\frac{m}{\sqrt{1}}}{\frac{v}{1 - m}} - 1\right) \cdot m
double f(double m, double v) {
        double r11094 = m;
        double r11095 = 1.0;
        double r11096 = r11095 - r11094;
        double r11097 = r11094 * r11096;
        double r11098 = v;
        double r11099 = r11097 / r11098;
        double r11100 = r11099 - r11095;
        double r11101 = r11100 * r11094;
        return r11101;
}
↓
double f(double m, double v) {
        double r11102 = m;
        double r11103 = 1.0;
        double r11104 = sqrt(r11103);
        double r11105 = r11102 / r11104;
        double r11106 = v;
        double r11107 = 1.0;
        double r11108 = r11107 - r11102;
        double r11109 = r11106 / r11108;
        double r11110 = r11105 / r11109;
        double r11111 = r11110 - r11107;
        double r11112 = r11111 * r11102;
        return r11112;
}

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 add-sqr-sqrt0.4

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

  4. Applied associate-/r*0.3

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

  6. Applied *-un-lft-identity0.3

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

  7. Applied sqrt-prod0.3

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

  8. Applied times-frac0.4

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

  9. Applied associate-/l*0.4

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(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))