Average Error: 2.4 → 1.4
Time: 3.9s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.477269956526729882709689256541591977713 \cdot 10^{-242}:\\ \;\;\;\;1 \cdot \frac{t}{\frac{z - y}{x - y}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le -0.0:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le -1.477269956526729882709689256541591977713 \cdot 10^{-242}:\\
\;\;\;\;1 \cdot \frac{t}{\frac{z - y}{x - y}}\\

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

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

\end{array}
double f(double x, double y, double z, double t) {
        double r423000 = x;
        double r423001 = y;
        double r423002 = r423000 - r423001;
        double r423003 = z;
        double r423004 = r423003 - r423001;
        double r423005 = r423002 / r423004;
        double r423006 = t;
        double r423007 = r423005 * r423006;
        return r423007;
}
↓
double f(double x, double y, double z, double t) {
        double r423008 = x;
        double r423009 = y;
        double r423010 = r423008 - r423009;
        double r423011 = z;
        double r423012 = r423011 - r423009;
        double r423013 = r423010 / r423012;
        double r423014 = -1.4772699565267299e-242;
        bool r423015 = r423013 <= r423014;
        double r423016 = 1.0;
        double r423017 = t;
        double r423018 = r423012 / r423010;
        double r423019 = r423017 / r423018;
        double r423020 = r423016 * r423019;
        double r423021 = -0.0;
        bool r423022 = r423013 <= r423021;
        double r423023 = r423017 / r423012;
        double r423024 = r423010 * r423023;
        double r423025 = r423013 * r423017;
        double r423026 = r423022 ? r423024 : r423025;
        double r423027 = r423015 ? r423020 : r423026;
        return r423027;
}

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

Derivation

  1. Split input into 3 regimes

  2. if (/ (- x y) (- z y)) < -1.4772699565267299e-242

    1. Initial program 2.7

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

    3. Applied clear-num2.8

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

    5. Applied *-un-lft-identity2.8

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

    6. Applied associate-*l*2.8

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

    7. Simplified2.5

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

    if -1.4772699565267299e-242 < (/ (- x y) (- z y)) < -0.0

    1. Initial program 13.3

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

    3. Applied div-inv13.3

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

    4. Applied associate-*l*0.2

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

    5. Simplified0.2

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

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

    1. Initial program 1.6

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.477269956526729882709689256541591977713 \cdot 10^{-242}:\\ \;\;\;\;1 \cdot \frac{t}{\frac{z - y}{x - y}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le -0.0:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

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

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