Average Error: 17.8 → 1.3
Time: 1.4m
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[-\frac{\frac{t1}{t1 + u} \cdot v}{t1 + u}\]
\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 r4170425 = t1;
        double r4170426 = -r4170425;
        double r4170427 = v;
        double r4170428 = r4170426 * r4170427;
        double r4170429 = u;
        double r4170430 = r4170425 + r4170429;
        double r4170431 = r4170430 * r4170430;
        double r4170432 = r4170428 / r4170431;
        return r4170432;
}
↓
double f(double u, double v, double t1) {
        double r4170433 = t1;
        double r4170434 = u;
        double r4170435 = r4170433 + r4170434;
        double r4170436 = r4170433 / r4170435;
        double r4170437 = v;
        double r4170438 = r4170436 * r4170437;
        double r4170439 = r4170438 / r4170435;
        double r4170440 = -r4170439;
        return r4170440;
}

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-frac1.2

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

  5. Applied associate-*r/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019125 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))