Average Error: 18.4 → 1.6
Time: 15.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-1}{t1 + u} \cdot \left(t1 \cdot \frac{v}{t1 + u}\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-1}{t1 + u} \cdot \left(t1 \cdot \frac{v}{t1 + u}\right)
double f(double u, double v, double t1) {
        double r21120 = t1;
        double r21121 = -r21120;
        double r21122 = v;
        double r21123 = r21121 * r21122;
        double r21124 = u;
        double r21125 = r21120 + r21124;
        double r21126 = r21125 * r21125;
        double r21127 = r21123 / r21126;
        return r21127;
}
↓
double f(double u, double v, double t1) {
        double r21128 = -1.0;
        double r21129 = t1;
        double r21130 = u;
        double r21131 = r21129 + r21130;
        double r21132 = r21128 / r21131;
        double r21133 = v;
        double r21134 = r21133 / r21131;
        double r21135 = r21129 * r21134;
        double r21136 = r21132 * r21135;
        return r21136;
}

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 18.4

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.5

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

  5. Applied div-inv1.7

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

  6. Applied associate-*r*1.3

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

  7. Simplified1.6

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

  8. Final simplification1.6

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

Reproduce

herbie shell --seed 2019195 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))