Average Error: 18.1 → 1.8
Time: 18.8s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{1}{\frac{t1 + u}{\left(-v\right) \cdot \frac{t1}{t1 + u}}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{1}{\frac{t1 + u}{\left(-v\right) \cdot \frac{t1}{t1 + u}}}
double f(double u, double v, double t1) {
        double r993022 = t1;
        double r993023 = -r993022;
        double r993024 = v;
        double r993025 = r993023 * r993024;
        double r993026 = u;
        double r993027 = r993022 + r993026;
        double r993028 = r993027 * r993027;
        double r993029 = r993025 / r993028;
        return r993029;
}
↓
double f(double u, double v, double t1) {
        double r993030 = 1.0;
        double r993031 = t1;
        double r993032 = u;
        double r993033 = r993031 + r993032;
        double r993034 = v;
        double r993035 = -r993034;
        double r993036 = r993031 / r993033;
        double r993037 = r993035 * r993036;
        double r993038 = r993033 / r993037;
        double r993039 = r993030 / r993038;
        return r993039;
}

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 18.1

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

  3. Applied times-frac1.3

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

  5. Applied associate-*r/1.2

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

  7. Applied clear-num1.8

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

  8. Final simplification1.8

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))