Average Error: 17.8 → 1.3
Time: 1.1m
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}
double f(double u, double v, double t1) {
        double r2657460 = t1;
        double r2657461 = -r2657460;
        double r2657462 = v;
        double r2657463 = r2657461 * r2657462;
        double r2657464 = u;
        double r2657465 = r2657460 + r2657464;
        double r2657466 = r2657465 * r2657465;
        double r2657467 = r2657463 / r2657466;
        return r2657467;
}
↓
double f(double u, double v, double t1) {
        double r2657468 = v;
        double r2657469 = t1;
        double r2657470 = u;
        double r2657471 = r2657469 + r2657470;
        double r2657472 = r2657468 / r2657471;
        double r2657473 = -r2657469;
        double r2657474 = r2657473 / r2657471;
        double r2657475 = r2657472 * r2657474;
        return r2657475;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

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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. Final simplification1.3

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

Reproduce

herbie shell --seed 2019158 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))