Average Error: 18.4 → 1.3
Time: 20.0s
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 r1086037 = t1;
        double r1086038 = -r1086037;
        double r1086039 = v;
        double r1086040 = r1086038 * r1086039;
        double r1086041 = u;
        double r1086042 = r1086037 + r1086041;
        double r1086043 = r1086042 * r1086042;
        double r1086044 = r1086040 / r1086043;
        return r1086044;
}
↓
double f(double u, double v, double t1) {
        double r1086045 = v;
        double r1086046 = u;
        double r1086047 = t1;
        double r1086048 = r1086046 + r1086047;
        double r1086049 = r1086045 / r1086048;
        double r1086050 = -r1086047;
        double r1086051 = r1086049 * r1086050;
        double r1086052 = r1086051 / r1086048;
        return r1086052;
}

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