Average Error: 18.1 → 1.3
Time: 18.0s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}
double f(double u, double v, double t1) {
        double r22165 = t1;
        double r22166 = -r22165;
        double r22167 = v;
        double r22168 = r22166 * r22167;
        double r22169 = u;
        double r22170 = r22165 + r22169;
        double r22171 = r22170 * r22170;
        double r22172 = r22168 / r22171;
        return r22172;
}
↓
double f(double u, double v, double t1) {
        double r22173 = v;
        double r22174 = u;
        double r22175 = t1;
        double r22176 = r22174 + r22175;
        double r22177 = r22173 / r22176;
        double r22178 = -r22175;
        double r22179 = r22177 * r22178;
        double r22180 = r22179 / r22176;
        return r22180;
}

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 18.1

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

  2. Simplified1.3

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

  4. Applied pow11.3

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

  5. Applied pow11.3

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

  6. Applied pow-prod-down1.3

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

  7. Simplified1.2

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

  9. Applied div-inv1.3

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

  10. Applied associate-*l*1.4

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

  11. Simplified1.3

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

  12. Final simplification1.3

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

Reproduce

herbie shell --seed 2019179 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))