Average Error: 2.4 → 1.0
Time: 37.5s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \cdot t = -\infty:\\ \;\;\;\;\frac{1}{z - y} \cdot \left(t \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \cdot t \le -2.640233754742454971582408319579857218009 \cdot 10^{-299}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \cdot t \le 0.0:\\ \;\;\;\;\frac{1}{z - y} \cdot \left(t \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \cdot t = -\infty:\\
\;\;\;\;\frac{1}{z - y} \cdot \left(t \cdot \left(x - y\right)\right)\\

\mathbf{elif}\;\frac{x - y}{z - y} \cdot t \le -2.640233754742454971582408319579857218009 \cdot 10^{-299}:\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

\mathbf{elif}\;\frac{x - y}{z - y} \cdot t \le 0.0:\\
\;\;\;\;\frac{1}{z - y} \cdot \left(t \cdot \left(x - y\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r21730124 = x;
        double r21730125 = y;
        double r21730126 = r21730124 - r21730125;
        double r21730127 = z;
        double r21730128 = r21730127 - r21730125;
        double r21730129 = r21730126 / r21730128;
        double r21730130 = t;
        double r21730131 = r21730129 * r21730130;
        return r21730131;
}
↓
double f(double x, double y, double z, double t) {
        double r21730132 = x;
        double r21730133 = y;
        double r21730134 = r21730132 - r21730133;
        double r21730135 = z;
        double r21730136 = r21730135 - r21730133;
        double r21730137 = r21730134 / r21730136;
        double r21730138 = t;
        double r21730139 = r21730137 * r21730138;
        double r21730140 = -inf.0;
        bool r21730141 = r21730139 <= r21730140;
        double r21730142 = 1.0;
        double r21730143 = r21730142 / r21730136;
        double r21730144 = r21730138 * r21730134;
        double r21730145 = r21730143 * r21730144;
        double r21730146 = -2.640233754742455e-299;
        bool r21730147 = r21730139 <= r21730146;
        double r21730148 = 0.0;
        bool r21730149 = r21730139 <= r21730148;
        double r21730150 = r21730135 / r21730134;
        double r21730151 = r21730133 / r21730134;
        double r21730152 = r21730150 - r21730151;
        double r21730153 = r21730138 / r21730152;
        double r21730154 = r21730149 ? r21730145 : r21730153;
        double r21730155 = r21730147 ? r21730139 : r21730154;
        double r21730156 = r21730141 ? r21730145 : r21730155;
        return r21730156;
}

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

Original2.4
Target2.4
Herbie1.0
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (/ (- x y) (- z y)) t) < -inf.0 or -2.640233754742455e-299 < (* (/ (- x y) (- z y)) t) < 0.0

    1. Initial program 12.4

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

    3. Applied clear-num12.4

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

    5. Applied associate-*l/12.0

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

    6. Simplified12.0

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

    8. Applied div-inv12.0

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

    9. Applied *-un-lft-identity12.0

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

    10. Applied times-frac0.5

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

    11. Simplified0.5

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

    if -inf.0 < (* (/ (- x y) (- z y)) t) < -2.640233754742455e-299

    1. Initial program 0.3

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

    if 0.0 < (* (/ (- x y) (- z y)) t)

    1. Initial program 1.9

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

    3. Applied clear-num2.1

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

    5. Applied associate-*l/1.9

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

    6. Simplified1.9

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

    8. Applied div-sub1.9

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \cdot t = -\infty:\\ \;\;\;\;\frac{1}{z - y} \cdot \left(t \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \cdot t \le -2.640233754742454971582408319579857218009 \cdot 10^{-299}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \cdot t \le 0.0:\\ \;\;\;\;\frac{1}{z - y} \cdot \left(t \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"

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

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