Average Error: 2.2 → 2.2
Time: 16.0s
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 r23916198 = x;
        double r23916199 = y;
        double r23916200 = r23916198 - r23916199;
        double r23916201 = z;
        double r23916202 = r23916201 - r23916199;
        double r23916203 = r23916200 / r23916202;
        double r23916204 = t;
        double r23916205 = r23916203 * r23916204;
        return r23916205;
}
↓
double f(double x, double y, double z, double t) {
        double r23916206 = y;
        double r23916207 = -2.912467718582163e-29;
        bool r23916208 = r23916206 <= r23916207;
        double r23916209 = t;
        double r23916210 = z;
        double r23916211 = x;
        double r23916212 = r23916211 - r23916206;
        double r23916213 = r23916210 / r23916212;
        double r23916214 = r23916206 / r23916212;
        double r23916215 = r23916213 - r23916214;
        double r23916216 = r23916209 / r23916215;
        double r23916217 = 8.32421302174108e-264;
        bool r23916218 = r23916206 <= r23916217;
        double r23916219 = 1.0;
        double r23916220 = r23916210 - r23916206;
        double r23916221 = r23916219 / r23916220;
        double r23916222 = r23916209 * r23916212;
        double r23916223 = r23916221 * r23916222;
        double r23916224 = r23916218 ? r23916223 : r23916216;
        double r23916225 = r23916208 ? r23916216 : r23916224;
        return r23916225;
}

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 div-inv5.1

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

    6. Applied *-un-lft-identity5.1

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

    7. Applied times-frac4.8

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

    8. Applied associate-*l*5.2

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

    9. Simplified5.1

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