Average Error: 2.2 → 2.2
Time: 13.9s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.912467718582163 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}}\\ \mathbf{elif}\;y \le 8.32421302174108 \cdot 10^{-264}:\\ \;\;\;\;\frac{1}{z - y} \cdot \left(t \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.912467718582163 \cdot 10^{-29}:\\
\;\;\;\;\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}}\\

\mathbf{elif}\;y \le 8.32421302174108 \cdot 10^{-264}:\\
\;\;\;\;\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 r21585107 = x;
        double r21585108 = y;
        double r21585109 = r21585107 - r21585108;
        double r21585110 = z;
        double r21585111 = r21585110 - r21585108;
        double r21585112 = r21585109 / r21585111;
        double r21585113 = t;
        double r21585114 = r21585112 * r21585113;
        return r21585114;
}
↓
double f(double x, double y, double z, double t) {
        double r21585115 = y;
        double r21585116 = -2.912467718582163e-29;
        bool r21585117 = r21585115 <= r21585116;
        double r21585118 = t;
        double r21585119 = z;
        double r21585120 = x;
        double r21585121 = r21585120 - r21585115;
        double r21585122 = r21585119 / r21585121;
        double r21585123 = r21585115 / r21585121;
        double r21585124 = r21585122 - r21585123;
        double r21585125 = r21585118 / r21585124;
        double r21585126 = 8.32421302174108e-264;
        bool r21585127 = r21585115 <= r21585126;
        double r21585128 = 1.0;
        double r21585129 = r21585119 - r21585115;
        double r21585130 = r21585128 / r21585129;
        double r21585131 = r21585118 * r21585121;
        double r21585132 = r21585130 * r21585131;
        double r21585133 = r21585127 ? r21585132 : r21585125;
        double r21585134 = r21585117 ? r21585125 : r21585133;
        return r21585134;
}

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

Original2.2
Target2.1
Herbie2.2
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.912467718582163e-29 or 8.32421302174108e-264 < y

    1. Initial program 1.3

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

    3. Applied clear-num1.4

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

    5. Applied associate-*l/1.3

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

    6. Simplified1.3

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

    8. Applied div-sub1.3

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

    if -2.912467718582163e-29 < y < 8.32421302174108e-264

    1. Initial program 4.7

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

    3. Applied clear-num5.0

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

    5. Applied associate-*l/4.7

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

    6. Simplified4.7

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

    8. Applied div-inv4.8

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

    9. Applied *-un-lft-identity4.8

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

    10. Applied times-frac5.2

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

    11. Simplified5.1

      \[\leadsto \frac{1}{z - y} \cdot \color{blue}{\left(t \cdot \left(x - y\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.912467718582163 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}}\\ \mathbf{elif}\;y \le 8.32421302174108 \cdot 10^{-264}:\\ \;\;\;\;\frac{1}{z - y} \cdot \left(t \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(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))