Average Error: 11.7 → 2.4
Time: 2.8s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.7212715542249777 \cdot 10^{41}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \mathbf{elif}\;z \le -7.69254324124208407 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.7212715542249777 \cdot 10^{41}:\\
\;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\

\mathbf{elif}\;z \le -7.69254324124208407 \cdot 10^{-283}:\\
\;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{y - z}{t - 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 ((z <= -3.721271554224978e+41)) {
		VAR = ((double) (x / ((double) (((double) (t / ((double) (y - z)))) - ((double) (z / ((double) (y - z))))))));
	} else {
		double VAR_1;
		if ((z <= -7.692543241242084e-283)) {
			VAR_1 = ((double) (((double) (x / ((double) (t - z)))) * ((double) (y - z))));
		} else {
			VAR_1 = ((double) (x * ((double) (((double) (y - z)) / ((double) (t - 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

Original11.7
Target2.1
Herbie2.4
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -3.7212715542249777e41

    1. Initial program 19.1

      \[\frac{x \cdot \left(y - z\right)}{t - z}\]
    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 div-sub0.1

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

    if -3.7212715542249777e41 < z < -7.69254324124208407e-283

    1. Initial program 5.3

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

    3. Applied associate-/l*3.4

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

    5. Applied associate-/r/4.7

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

    if -7.69254324124208407e-283 < z

    1. Initial program 11.5

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

    3. Applied *-un-lft-identity11.5

      \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{1 \cdot \left(t - z\right)}}\]

    4. Applied times-frac2.4

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

    5. Simplified2.4

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.7212715542249777 \cdot 10^{41}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \mathbf{elif}\;z \le -7.69254324124208407 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020153 
(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)))