Average Error: 17.7 → 1.2
Time: 28.6s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[-\frac{\frac{v}{\frac{t1 + u}{t1}}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
-\frac{\frac{v}{\frac{t1 + u}{t1}}}{t1 + u}
double f(double u, double v, double t1) {
        double r1633385 = t1;
        double r1633386 = -r1633385;
        double r1633387 = v;
        double r1633388 = r1633386 * r1633387;
        double r1633389 = u;
        double r1633390 = r1633385 + r1633389;
        double r1633391 = r1633390 * r1633390;
        double r1633392 = r1633388 / r1633391;
        return r1633392;
}
↓
double f(double u, double v, double t1) {
        double r1633393 = v;
        double r1633394 = t1;
        double r1633395 = u;
        double r1633396 = r1633394 + r1633395;
        double r1633397 = r1633396 / r1633394;
        double r1633398 = r1633393 / r1633397;
        double r1633399 = r1633398 / r1633396;
        double r1633400 = -r1633399;
        return r1633400;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Try it out

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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-frac1.2

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

  5. Applied div-inv1.3

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

  6. Applied associate-*r*1.2

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

  8. Applied distribute-frac-neg1.2

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

  9. Applied distribute-lft-neg-out1.2

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

  10. Applied distribute-lft-neg-out1.2

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

  11. Simplified1.2

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

  12. Final simplification1.2

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

Reproduce

herbie shell --seed 2019139 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))