Average Error: 18.0 → 1.4
Time: 3.3s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{1}{\frac{t1 + u}{-t1}} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{1}{\frac{t1 + u}{-t1}} \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r23108 = t1;
        double r23109 = -r23108;
        double r23110 = v;
        double r23111 = r23109 * r23110;
        double r23112 = u;
        double r23113 = r23108 + r23112;
        double r23114 = r23113 * r23113;
        double r23115 = r23111 / r23114;
        return r23115;
}
↓
double f(double u, double v, double t1) {
        double r23116 = 1.0;
        double r23117 = t1;
        double r23118 = u;
        double r23119 = r23117 + r23118;
        double r23120 = -r23117;
        double r23121 = r23119 / r23120;
        double r23122 = r23116 / r23121;
        double r23123 = v;
        double r23124 = r23123 / r23119;
        double r23125 = r23122 * r23124;
        return r23125;
}

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 18.0

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 clear-num1.4

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

  6. Final simplification1.4

    \[\leadsto \frac{1}{\frac{t1 + u}{-t1}} \cdot \frac{v}{t1 + u}\]

Reproduce

herbie shell --seed 2020049 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))