Average Error: 11.9 → 1.5
Time: 3.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} = -\infty:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -1.2322421546297341 \cdot 10^{-122}:\\ \;\;\;\;\frac{x \cdot y + x \cdot \left(-z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} = -\infty:\\
\;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -1.2322421546297341 \cdot 10^{-122}:\\
\;\;\;\;\frac{x \cdot y + x \cdot \left(-z\right)}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x * ((double) (y - z)))) / ((double) (t - z))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) (((double) (x * ((double) (y - z)))) / ((double) (t - z)))) <= -inf.0)) {
		VAR = ((double) (((double) (x / ((double) (t - z)))) * ((double) (y - z))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * ((double) (y - z)))) / ((double) (t - z)))) <= -1.232242154629734e-122)) {
			VAR_1 = ((double) (((double) (((double) (x * y)) + ((double) (x * ((double) -(z)))))) / ((double) (t - z))));
		} else {
			VAR_1 = ((double) (x / ((double) (((double) (t - z)) / ((double) (y - z))))));
		}
		VAR = VAR_1;
	}
	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

Original11.9
Target2.0
Herbie1.5
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) (- t z)) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.1

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.2

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \left(y - z\right)}\]

    if -inf.0 < (/ (* x (- y z)) (- t z)) < -1.232242154629734e-122

    1. Initial program 0.3

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

    3. Applied sub-neg0.3

      \[\leadsto \frac{x \cdot \color{blue}{\left(y + \left(-z\right)\right)}}{t - z}\]

    4. Applied distribute-lft-in0.3

      \[\leadsto \frac{\color{blue}{x \cdot y + x \cdot \left(-z\right)}}{t - z}\]

    if -1.232242154629734e-122 < (/ (* x (- y z)) (- t z))

    1. Initial program 9.4

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

    3. Applied associate-/l*2.0

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} = -\infty:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -1.2322421546297341 \cdot 10^{-122}:\\ \;\;\;\;\frac{x \cdot y + x \cdot \left(-z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020120 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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