Average Error: 18.1 → 1.4
Time: 19.2s
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 r906564 = t1;
        double r906565 = -r906564;
        double r906566 = v;
        double r906567 = r906565 * r906566;
        double r906568 = u;
        double r906569 = r906564 + r906568;
        double r906570 = r906569 * r906569;
        double r906571 = r906567 / r906570;
        return r906571;
}
↓
double f(double u, double v, double t1) {
        double r906572 = v;
        double r906573 = u;
        double r906574 = t1;
        double r906575 = r906573 + r906574;
        double r906576 = r906572 / r906575;
        double r906577 = -r906574;
        double r906578 = r906576 * r906577;
        double r906579 = r906578 / r906575;
        return r906579;
}

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. Using strategy rm

  3. Applied times-frac1.5

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

  5. Applied associate-*l/1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))