Average Error: 17.7 → 1.2
Time: 38.1s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}
double f(double u, double v, double t1) {
        double r1500938 = t1;
        double r1500939 = -r1500938;
        double r1500940 = v;
        double r1500941 = r1500939 * r1500940;
        double r1500942 = u;
        double r1500943 = r1500938 + r1500942;
        double r1500944 = r1500943 * r1500943;
        double r1500945 = r1500941 / r1500944;
        return r1500945;
}
↓
double f(double u, double v, double t1) {
        double r1500946 = v;
        double r1500947 = u;
        double r1500948 = t1;
        double r1500949 = r1500947 + r1500948;
        double r1500950 = r1500946 / r1500949;
        double r1500951 = -r1500948;
        double r1500952 = r1500950 * r1500951;
        double r1500953 = r1500952 / r1500949;
        return r1500953;
}

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 17.7

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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-*l/1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019149 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))