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 r28596 = t1;
        double r28597 = -r28596;
        double r28598 = v;
        double r28599 = r28597 * r28598;
        double r28600 = u;
        double r28601 = r28596 + r28600;
        double r28602 = r28601 * r28601;
        double r28603 = r28599 / r28602;
        return r28603;
}
↓
double f(double u, double v, double t1) {
        double r28604 = v;
        double r28605 = t1;
        double r28606 = u;
        double r28607 = r28605 + r28606;
        double r28608 = r28604 / r28607;
        double r28609 = -r28605;
        double r28610 = r28607 / r28609;
        double r28611 = r28608 / r28610;
        return r28611;
}

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 clear-num1.4

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

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

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

  8. Applied add-sqr-sqrt1.4

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

  9. Applied times-frac1.4

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

  10. Applied associate-*l*1.4

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

  11. Simplified1.4

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

  12. 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))))