Average Error: 18.2 → 1.4
Time: 5.3s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v \cdot \left(\frac{-1}{t1 + u} \cdot t1\right)}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v \cdot \left(\frac{-1}{t1 + u} \cdot t1\right)}{t1 + u}
double f(double u, double v, double t1) {
        double r31063 = t1;
        double r31064 = -r31063;
        double r31065 = v;
        double r31066 = r31064 * r31065;
        double r31067 = u;
        double r31068 = r31063 + r31067;
        double r31069 = r31068 * r31068;
        double r31070 = r31066 / r31069;
        return r31070;
}
↓
double f(double u, double v, double t1) {
        double r31071 = v;
        double r31072 = -1.0;
        double r31073 = t1;
        double r31074 = u;
        double r31075 = r31073 + r31074;
        double r31076 = r31072 / r31075;
        double r31077 = r31076 * r31073;
        double r31078 = r31071 * r31077;
        double r31079 = r31078 / r31075;
        return r31079;
}

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 18.2

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 *-un-lft-identity1.5

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

  6. Applied distribute-lft-neg-in1.5

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

  7. Applied associate-/l*1.7

    \[\leadsto \color{blue}{\frac{-1}{\frac{t1 + u}{t1}}} \cdot \frac{v}{t1 + u}\]
  8. Using strategy rm

  9. Applied div-inv1.8

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

  10. Applied associate-/r*1.6

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

  11. Simplified1.6

    \[\leadsto \frac{\color{blue}{\frac{-1}{t1 + u}}}{\frac{1}{t1}} \cdot \frac{v}{t1 + u}\]
  12. Using strategy rm

  13. Applied associate-*r/1.3

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

  14. Simplified1.4

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

  15. Final simplification1.4

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

Reproduce

herbie shell --seed 2020033 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))