Average Error: 17.9 → 1.3
Time: 44.3s
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 r1217002 = t1;
        double r1217003 = -r1217002;
        double r1217004 = v;
        double r1217005 = r1217003 * r1217004;
        double r1217006 = u;
        double r1217007 = r1217002 + r1217006;
        double r1217008 = r1217007 * r1217007;
        double r1217009 = r1217005 / r1217008;
        return r1217009;
}
↓
double f(double u, double v, double t1) {
        double r1217010 = v;
        double r1217011 = u;
        double r1217012 = t1;
        double r1217013 = r1217011 + r1217012;
        double r1217014 = r1217010 / r1217013;
        double r1217015 = -r1217012;
        double r1217016 = r1217014 * r1217015;
        double r1217017 = r1217016 / r1217013;
        return r1217017;
}

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 17.9

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))