Average Error: 17.9 → 1.2
Time: 5.1s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
↓
\[\frac{v}{t1 + u} \cdot \frac{-1}{1 + \frac{u}{t1}} \]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v}{t1 + u} \cdot \frac{-1}{1 + \frac{u}{t1}}

(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))
↓
(FPCore (u v t1)
 :precision binary64
 (* (/ v (+ t1 u)) (/ -1.0 (+ 1.0 (/ u t1)))))
double code(double u, double v, double t1) {
	return (-t1 * v) / ((t1 + u) * (t1 + u));
}
↓
double code(double u, double v, double t1) {
	return (v / (t1 + u)) * (-1.0 / (1.0 + (u / t1)));
}

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 17.9

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

  2. Simplified1.2

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

  4. Applied div-inv_binary641.2

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

  5. Simplified1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2021205 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))