Average Error: 18.1 → 1.2
Time: 3.7s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\left(-t1\right) \cdot \frac{1}{t1 + u}\right) \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\left(-t1\right) \cdot \frac{1}{t1 + u}\right) \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r32085 = t1;
        double r32086 = -r32085;
        double r32087 = v;
        double r32088 = r32086 * r32087;
        double r32089 = u;
        double r32090 = r32085 + r32089;
        double r32091 = r32090 * r32090;
        double r32092 = r32088 / r32091;
        return r32092;
}
↓
double f(double u, double v, double t1) {
        double r32093 = t1;
        double r32094 = -r32093;
        double r32095 = 1.0;
        double r32096 = u;
        double r32097 = r32093 + r32096;
        double r32098 = r32095 / r32097;
        double r32099 = r32094 * r32098;
        double r32100 = v;
        double r32101 = r32100 / r32097;
        double r32102 = r32099 * r32101;
        return r32102;
}

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-frac1.2

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

  5. Applied div-inv1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))