Average Error: 18.8 → 1.3
Time: 1.4m
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 r4535504 = t1;
        double r4535505 = -r4535504;
        double r4535506 = v;
        double r4535507 = r4535505 * r4535506;
        double r4535508 = u;
        double r4535509 = r4535504 + r4535508;
        double r4535510 = r4535509 * r4535509;
        double r4535511 = r4535507 / r4535510;
        return r4535511;
}
↓
double f(double u, double v, double t1) {
        double r4535512 = v;
        double r4535513 = u;
        double r4535514 = t1;
        double r4535515 = r4535513 + r4535514;
        double r4535516 = r4535512 / r4535515;
        double r4535517 = -r4535514;
        double r4535518 = r4535516 * r4535517;
        double r4535519 = r4535518 / r4535515;
        return r4535519;
}

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 18.8

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 associate-*l/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))