Average Error: 18.5 → 1.3
Time: 25.3s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{t1}{t1 + u} \cdot v}{-\left(t1 + u\right)}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{t1}{t1 + u} \cdot v}{-\left(t1 + u\right)}
double code(double u, double v, double t1) {
	return ((double) (((double) (((double) -(t1)) * v)) / ((double) (((double) (t1 + u)) * ((double) (t1 + u))))));
}
↓
double code(double u, double v, double t1) {
	return ((double) (((double) (((double) (t1 / ((double) (t1 + u)))) * v)) / ((double) -(((double) (t1 + u))))));
}

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 18.5

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

  3. Applied times-frac1.5

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

  4. Simplified1.5

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

  6. Applied frac-2neg1.5

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

  7. Applied associate-*r/1.3

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

  8. Simplified1.3

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

  9. Final simplification1.3

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

Reproduce

herbie shell --seed 2020113 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))