Average Error: 18.1 → 1.2
Time: 4.7s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \leq 0 \lor \neg \left(\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \leq 1.288430744239899 \cdot 10^{+248}\right):\\ \;\;\;\;\frac{v}{t1 + u} \cdot \frac{1}{-1 - \frac{u}{t1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \end{array}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \leq 0 \lor \neg \left(\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \leq 1.288430744239899 \cdot 10^{+248}\right):\\
\;\;\;\;\frac{v}{t1 + u} \cdot \frac{1}{-1 - \frac{u}{t1}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\\

\end{array}
(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))
↓
(FPCore (u v t1)
 :precision binary64
 (if (or (<= (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))) 0.0)
         (not
          (<= (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))) 1.288430744239899e+248)))
   (* (/ v (+ t1 u)) (/ 1.0 (- -1.0 (/ u t1))))
   (/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))))
double code(double u, double v, double t1) {
	return (-t1 * v) / ((t1 + u) * (t1 + u));
}
↓
double code(double u, double v, double t1) {
	double tmp;
	if ((((-t1 * v) / ((t1 + u) * (t1 + u))) <= 0.0) || !(((-t1 * v) / ((t1 + u) * (t1 + u))) <= 1.288430744239899e+248)) {
		tmp = (v / (t1 + u)) * (1.0 / (-1.0 - (u / t1)));
	} else {
		tmp = (-t1 * v) / ((t1 + u) * (t1 + u));
	}
	return tmp;
}

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. Split input into 2 regimes

  2. if (/.f64 (*.f64 (neg.f64 t1) v) (*.f64 (+.f64 t1 u) (+.f64 t1 u))) < -0.0 or 1.28843074423989897e248 < (/.f64 (*.f64 (neg.f64 t1) v) (*.f64 (+.f64 t1 u) (+.f64 t1 u)))

    1. Initial program 21.6

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

    2. Simplified1.3

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

    4. Applied div-inv_binary641.3

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

    if -0.0 < (/.f64 (*.f64 (neg.f64 t1) v) (*.f64 (+.f64 t1 u) (+.f64 t1 u))) < 1.28843074423989897e248

    1. Initial program 0.8

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \leq 0 \lor \neg \left(\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \leq 1.288430744239899 \cdot 10^{+248}\right):\\ \;\;\;\;\frac{v}{t1 + u} \cdot \frac{1}{-1 - \frac{u}{t1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020253 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))