Average Error: 11.4 → 1.3
Time: 10.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -0.0 \lor \neg \left(\frac{\left(y - z\right) \cdot x}{t - z} \le 4.421158688198110357467490714146095752662 \cdot 10^{222}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -0.0 \lor \neg \left(\frac{\left(y - z\right) \cdot x}{t - z} \le 4.421158688198110357467490714146095752662 \cdot 10^{222}\right):\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r510107 = x;
        double r510108 = y;
        double r510109 = z;
        double r510110 = r510108 - r510109;
        double r510111 = r510107 * r510110;
        double r510112 = t;
        double r510113 = r510112 - r510109;
        double r510114 = r510111 / r510113;
        return r510114;
}
↓
double f(double x, double y, double z, double t) {
        double r510115 = y;
        double r510116 = z;
        double r510117 = r510115 - r510116;
        double r510118 = x;
        double r510119 = r510117 * r510118;
        double r510120 = t;
        double r510121 = r510120 - r510116;
        double r510122 = r510119 / r510121;
        double r510123 = -0.0;
        bool r510124 = r510122 <= r510123;
        double r510125 = 4.4211586881981104e+222;
        bool r510126 = r510122 <= r510125;
        double r510127 = !r510126;
        bool r510128 = r510124 || r510127;
        double r510129 = r510117 / r510121;
        double r510130 = r510118 * r510129;
        double r510131 = r510128 ? r510130 : r510122;
        return r510131;
}

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

Original11.4
Target2.1
Herbie1.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) (- t z)) < -0.0 or 4.4211586881981104e+222 < (/ (* x (- y z)) (- t z))

    1. Initial program 17.4

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

    3. Applied *-un-lft-identity17.4

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

    4. Applied times-frac1.8

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

    5. Simplified1.8

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

    if -0.0 < (/ (* x (- y z)) (- t z)) < 4.4211586881981104e+222

    1. Initial program 0.3

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -0.0 \lor \neg \left(\frac{\left(y - z\right) \cdot x}{t - z} \le 4.421158688198110357467490714146095752662 \cdot 10^{222}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

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

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