Average Error: 17.8 → 1.2
Time: 18.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[-\frac{\frac{t1}{t1 + u} \cdot v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
-\frac{\frac{t1}{t1 + u} \cdot v}{t1 + u}
double f(double u, double v, double t1) {
        double r1081588 = t1;
        double r1081589 = -r1081588;
        double r1081590 = v;
        double r1081591 = r1081589 * r1081590;
        double r1081592 = u;
        double r1081593 = r1081588 + r1081592;
        double r1081594 = r1081593 * r1081593;
        double r1081595 = r1081591 / r1081594;
        return r1081595;
}
↓
double f(double u, double v, double t1) {
        double r1081596 = t1;
        double r1081597 = u;
        double r1081598 = r1081596 + r1081597;
        double r1081599 = r1081596 / r1081598;
        double r1081600 = v;
        double r1081601 = r1081599 * r1081600;
        double r1081602 = r1081601 / r1081598;
        double r1081603 = -r1081602;
        return r1081603;
}

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 17.8

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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. Final simplification1.2

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))