Average Error: 18.3 → 1.3
Time: 3.2s
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 r27308 = t1;
        double r27309 = -r27308;
        double r27310 = v;
        double r27311 = r27309 * r27310;
        double r27312 = u;
        double r27313 = r27308 + r27312;
        double r27314 = r27313 * r27313;
        double r27315 = r27311 / r27314;
        return r27315;
}
↓
double f(double u, double v, double t1) {
        double r27316 = t1;
        double r27317 = u;
        double r27318 = r27316 + r27317;
        double r27319 = r27316 / r27318;
        double r27320 = v;
        double r27321 = r27319 * r27320;
        double r27322 = r27321 / r27318;
        double r27323 = -r27322;
        return r27323;
}

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 18.3

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

  3. Applied times-frac1.4

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

  5. Applied pow11.4

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

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

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

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

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

  9. Applied distribute-lft-neg-in1.4

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

  10. Applied times-frac1.4

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

  11. Applied unpow-prod-down1.4

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

  12. Applied associate-*l*1.4

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

  13. Simplified1.3

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

  14. Final simplification1.3

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))