Average Error: 18.8 → 1.1
Time: 15.6s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[-\frac{v \cdot \frac{t1}{t1 + u}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
-\frac{v \cdot \frac{t1}{t1 + u}}{t1 + u}
double f(double u, double v, double t1) {
        double r25331 = t1;
        double r25332 = -r25331;
        double r25333 = v;
        double r25334 = r25332 * r25333;
        double r25335 = u;
        double r25336 = r25331 + r25335;
        double r25337 = r25336 * r25336;
        double r25338 = r25334 / r25337;
        return r25338;
}
↓
double f(double u, double v, double t1) {
        double r25339 = v;
        double r25340 = t1;
        double r25341 = u;
        double r25342 = r25340 + r25341;
        double r25343 = r25340 / r25342;
        double r25344 = r25339 * r25343;
        double r25345 = r25344 / r25342;
        double r25346 = -r25345;
        return r25346;
}

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 18.8

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

  2. Simplified1.3

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

  4. Applied *-un-lft-identity1.3

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

  5. Applied *-un-lft-identity1.3

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

  6. Applied distribute-lft-neg-in1.3

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

  7. Applied times-frac1.3

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

  8. Applied associate-*l*1.3

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

  9. Simplified1.1

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

  10. Final simplification1.1

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

Reproduce

herbie shell --seed 2019196 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))