Average Error: 18.4 → 1.3
Time: 16.6s
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 r1203461 = t1;
        double r1203462 = -r1203461;
        double r1203463 = v;
        double r1203464 = r1203462 * r1203463;
        double r1203465 = u;
        double r1203466 = r1203461 + r1203465;
        double r1203467 = r1203466 * r1203466;
        double r1203468 = r1203464 / r1203467;
        return r1203468;
}
↓
double f(double u, double v, double t1) {
        double r1203469 = v;
        double r1203470 = u;
        double r1203471 = t1;
        double r1203472 = r1203470 + r1203471;
        double r1203473 = r1203469 / r1203472;
        double r1203474 = -r1203471;
        double r1203475 = r1203473 * r1203474;
        double r1203476 = r1203475 / r1203472;
        return r1203476;
}

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 18.4

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2019170 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))