Average Error: 18.4 → 1.3
Time: 4.5s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[-\frac{\frac{t1}{t1 + u} \cdot v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
-\frac{\frac{t1}{t1 + u} \cdot v}{t1 + u}
double f(double u, double v, double t1) {
        double r34107 = t1;
        double r34108 = -r34107;
        double r34109 = v;
        double r34110 = r34108 * r34109;
        double r34111 = u;
        double r34112 = r34107 + r34111;
        double r34113 = r34112 * r34112;
        double r34114 = r34110 / r34113;
        return r34114;
}
↓
double f(double u, double v, double t1) {
        double r34115 = t1;
        double r34116 = u;
        double r34117 = r34115 + r34116;
        double r34118 = r34115 / r34117;
        double r34119 = v;
        double r34120 = r34118 * r34119;
        double r34121 = r34120 / r34117;
        double r34122 = -r34121;
        return r34122;
}

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-frac1.6

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

  5. Applied add-cube-cbrt1.9

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{-t1}{t1 + u}} \cdot \sqrt[3]{\frac{-t1}{t1 + u}}\right) \cdot \sqrt[3]{\frac{-t1}{t1 + u}}\right)} \cdot \frac{v}{t1 + u}\]
  6. Using strategy rm

  7. Applied associate-*r/1.6

    \[\leadsto \color{blue}{\frac{\left(\left(\sqrt[3]{\frac{-t1}{t1 + u}} \cdot \sqrt[3]{\frac{-t1}{t1 + u}}\right) \cdot \sqrt[3]{\frac{-t1}{t1 + u}}\right) \cdot v}{t1 + u}}\]

  8. Simplified1.3

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

  9. Final simplification1.3

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

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))