Average Error: 17.5 → 1.6
Time: 25.7s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{t1}{t1 + u} \cdot \frac{\frac{-1}{t1 + u}}{\frac{1}{v}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{t1}{t1 + u} \cdot \frac{\frac{-1}{t1 + u}}{\frac{1}{v}}
double f(double u, double v, double t1) {
        double r559420 = t1;
        double r559421 = -r559420;
        double r559422 = v;
        double r559423 = r559421 * r559422;
        double r559424 = u;
        double r559425 = r559420 + r559424;
        double r559426 = r559425 * r559425;
        double r559427 = r559423 / r559426;
        return r559427;
}
↓
double f(double u, double v, double t1) {
        double r559428 = t1;
        double r559429 = u;
        double r559430 = r559428 + r559429;
        double r559431 = r559428 / r559430;
        double r559432 = -1.0;
        double r559433 = r559432 / r559430;
        double r559434 = 1.0;
        double r559435 = v;
        double r559436 = r559434 / r559435;
        double r559437 = r559433 / r559436;
        double r559438 = r559431 * r559437;
        return r559438;
}

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 17.5

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.4

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

  5. Applied clear-num1.8

    \[\leadsto \frac{-t1}{t1 + u} \cdot \color{blue}{\frac{1}{\frac{t1 + u}{v}}}\]
  6. Using strategy rm

  7. Applied div-inv1.8

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

  8. Applied associate-/r*1.6

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

  9. Final simplification1.6

    \[\leadsto \frac{t1}{t1 + u} \cdot \frac{\frac{-1}{t1 + u}}{\frac{1}{v}}\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))