Average Error: 6.4 → 1.0
Time: 4.9s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -inf.0 \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 8.3049211041063798 \cdot 10^{260}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -inf.0 \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 8.3049211041063798 \cdot 10^{260}\right):\\
\;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t)))) <= -inf.0) || !(((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t)))) <= 8.30492110410638e+260))) {
		VAR = ((double) (x + ((double) (1.0 / ((double) (((double) (t / y)) / ((double) (z - x))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.4
Target2.3
Herbie1.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -inf.0 or 8.3049211041063798e260 < (+ x (/ (* y (- z x)) t))

    1. Initial program 43.0

      \[x + \frac{y \cdot \left(z - x\right)}{t}\]
    2. Using strategy rm

    3. Applied clear-num43.0

      \[\leadsto x + \color{blue}{\frac{1}{\frac{t}{y \cdot \left(z - x\right)}}}\]
    4. Using strategy rm

    5. Applied associate-/r*1.9

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{t}{y}}{z - x}}}\]

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < 8.3049211041063798e260

    1. Initial program 0.8

      \[x + \frac{y \cdot \left(z - x\right)}{t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -inf.0 \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 8.3049211041063798 \cdot 10^{260}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020177 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (neg z) (/ y t))))

  (+ x (/ (* y (- z x)) t)))