Average Error: 18.5 → 1.4
Time: 20.3s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{t1 + u}}{\frac{t1 + u}{-t1}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{t1 + u}}{\frac{t1 + u}{-t1}}
double f(double u, double v, double t1) {
        double r28812 = t1;
        double r28813 = -r28812;
        double r28814 = v;
        double r28815 = r28813 * r28814;
        double r28816 = u;
        double r28817 = r28812 + r28816;
        double r28818 = r28817 * r28817;
        double r28819 = r28815 / r28818;
        return r28819;
}
↓
double f(double u, double v, double t1) {
        double r28820 = v;
        double r28821 = t1;
        double r28822 = u;
        double r28823 = r28821 + r28822;
        double r28824 = r28820 / r28823;
        double r28825 = -r28821;
        double r28826 = r28823 / r28825;
        double r28827 = r28824 / r28826;
        return r28827;
}

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 18.5

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 *-un-lft-identity1.3

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

  6. Applied distribute-lft-neg-in1.3

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

  7. Applied associate-/l*1.4

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

  9. Applied *-un-lft-identity1.4

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

  10. Applied *-un-lft-identity1.4

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

  11. Applied times-frac1.4

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

  12. Applied *-un-lft-identity1.4

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

  13. Applied times-frac1.4

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

  14. Applied associate-*l*1.4

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

  15. Simplified1.4

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

  16. Final simplification1.4

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

Reproduce

herbie shell --seed 2019326 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))