Average Error: 17.9 → 1.3
Time: 2.9s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)
double f(double u, double v, double t1) {
        double r24349 = t1;
        double r24350 = -r24349;
        double r24351 = v;
        double r24352 = r24350 * r24351;
        double r24353 = u;
        double r24354 = r24349 + r24353;
        double r24355 = r24354 * r24354;
        double r24356 = r24352 / r24355;
        return r24356;
}
↓
double f(double u, double v, double t1) {
        double r24357 = t1;
        double r24358 = -r24357;
        double r24359 = u;
        double r24360 = r24357 + r24359;
        double r24361 = r24358 / r24360;
        double r24362 = v;
        double r24363 = 1.0;
        double r24364 = r24363 / r24360;
        double r24365 = r24362 * r24364;
        double r24366 = r24361 * r24365;
        return r24366;
}

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 17.9

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 div-inv1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))