Average Error: 18.4 → 1.7
Time: 3.3s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-t1\right) \cdot \frac{1}{\frac{t1 + u}{v}}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-t1\right) \cdot \frac{1}{\frac{t1 + u}{v}}}{t1 + u}
double f(double u, double v, double t1) {
        double r22134 = t1;
        double r22135 = -r22134;
        double r22136 = v;
        double r22137 = r22135 * r22136;
        double r22138 = u;
        double r22139 = r22134 + r22138;
        double r22140 = r22139 * r22139;
        double r22141 = r22137 / r22140;
        return r22141;
}
↓
double f(double u, double v, double t1) {
        double r22142 = t1;
        double r22143 = -r22142;
        double r22144 = 1.0;
        double r22145 = u;
        double r22146 = r22142 + r22145;
        double r22147 = v;
        double r22148 = r22146 / r22147;
        double r22149 = r22144 / r22148;
        double r22150 = r22143 * r22149;
        double r22151 = r22150 / r22146;
        return r22151;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.4

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.5

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied associate-*r/1.3

    \[\leadsto \color{blue}{\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}}\]

  6. Simplified1.4

    \[\leadsto \frac{\color{blue}{\left(-t1\right) \cdot \frac{v}{t1 + u}}}{t1 + u}\]
  7. Using strategy rm

  8. Applied clear-num1.7

    \[\leadsto \frac{\left(-t1\right) \cdot \color{blue}{\frac{1}{\frac{t1 + u}{v}}}}{t1 + u}\]

  9. Final simplification1.7

    \[\leadsto \frac{\left(-t1\right) \cdot \frac{1}{\frac{t1 + u}{v}}}{t1 + u}\]

Reproduce

herbie shell --seed 2020034 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))