Average Error: 12.1 → 2.1
Time: 5.2s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.42187688089345209 \cdot 10^{-242} \lor \neg \left(z \le 1.3626492206831902 \cdot 10^{-72}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.42187688089345209 \cdot 10^{-242} \lor \neg \left(z \le 1.3626492206831902 \cdot 10^{-72}\right):\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return (((double) (x * ((double) (y - z)))) / ((double) (t - z)));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((z <= -2.421876880893452e-242) || !(z <= 1.3626492206831902e-72))) {
		VAR = ((double) (x * (((double) (y - z)) / ((double) (t - z)))));
	} else {
		VAR = ((double) ((x / ((double) (t - z))) * ((double) (y - z))));
	}
	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

Original12.1
Target2.0
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.42187688089345209e-242 or 1.3626492206831902e-72 < z

    1. Initial program 13.9

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

    3. Applied *-un-lft-identity13.9

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

    4. Applied times-frac1.0

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

    5. Simplified1.0

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

    if -2.42187688089345209e-242 < z < 1.3626492206831902e-72

    1. Initial program 6.0

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

    3. Applied associate-/l*5.3

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

    5. Applied associate-/r/5.8

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.42187688089345209 \cdot 10^{-242} \lor \neg \left(z \le 1.3626492206831902 \cdot 10^{-72}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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)))