Average Error: 17.8 → 1.2
Time: 22.3s
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 r1240480 = t1;
        double r1240481 = -r1240480;
        double r1240482 = v;
        double r1240483 = r1240481 * r1240482;
        double r1240484 = u;
        double r1240485 = r1240480 + r1240484;
        double r1240486 = r1240485 * r1240485;
        double r1240487 = r1240483 / r1240486;
        return r1240487;
}
↓
double f(double u, double v, double t1) {
        double r1240488 = t1;
        double r1240489 = -r1240488;
        double r1240490 = u;
        double r1240491 = r1240488 + r1240490;
        double r1240492 = r1240489 / r1240491;
        double r1240493 = v;
        double r1240494 = r1240492 * r1240493;
        double r1240495 = r1240494 / r1240491;
        return r1240495;
}

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 17.8

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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/1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019172 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))