Average Error: 18.1 → 1.4
Time: 4.5s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r37088 = t1;
        double r37089 = -r37088;
        double r37090 = v;
        double r37091 = r37089 * r37090;
        double r37092 = u;
        double r37093 = r37088 + r37092;
        double r37094 = r37093 * r37093;
        double r37095 = r37091 / r37094;
        return r37095;
}
↓
double f(double u, double v, double t1) {
        double r37096 = t1;
        double r37097 = -r37096;
        double r37098 = u;
        double r37099 = r37096 + r37098;
        double r37100 = r37097 / r37099;
        double r37101 = v;
        double r37102 = r37101 / r37099;
        double r37103 = r37100 * r37102;
        return r37103;
}

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-frac1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))