Average Error: 17.7 → 1.1
Time: 3.0s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}
double f(double u, double v, double t1) {
        double r22262 = t1;
        double r22263 = -r22262;
        double r22264 = v;
        double r22265 = r22263 * r22264;
        double r22266 = u;
        double r22267 = r22262 + r22266;
        double r22268 = r22267 * r22267;
        double r22269 = r22265 / r22268;
        return r22269;
}
↓
double f(double u, double v, double t1) {
        double r22270 = t1;
        double r22271 = -r22270;
        double r22272 = u;
        double r22273 = r22270 + r22272;
        double r22274 = r22271 / r22273;
        double r22275 = v;
        double r22276 = r22274 * r22275;
        double r22277 = r22276 / r22273;
        return r22277;
}

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 17.7

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 associate-*r/1.1

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

  6. Simplified1.3

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

  8. Applied clear-num1.7

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

  10. Applied associate-/r/1.4

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

  11. Applied associate-*r*1.2

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

  12. Simplified1.1

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

  13. Final simplification1.1

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

Reproduce

herbie shell --seed 2020046 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))