Average Error: 2.2 → 1.6
Time: 4.4s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} = -\infty:\\ \;\;\;\;\frac{\frac{\left(x - y\right) \cdot t}{z - y}}{1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} = -\infty:\\
\;\;\;\;\frac{\frac{\left(x - y\right) \cdot t}{z - y}}{1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r419317 = x;
        double r419318 = y;
        double r419319 = r419317 - r419318;
        double r419320 = z;
        double r419321 = r419320 - r419318;
        double r419322 = r419319 / r419321;
        double r419323 = t;
        double r419324 = r419322 * r419323;
        return r419324;
}
↓
double f(double x, double y, double z, double t) {
        double r419325 = x;
        double r419326 = y;
        double r419327 = r419325 - r419326;
        double r419328 = z;
        double r419329 = r419328 - r419326;
        double r419330 = r419327 / r419329;
        double r419331 = -inf.0;
        bool r419332 = r419330 <= r419331;
        double r419333 = t;
        double r419334 = r419327 * r419333;
        double r419335 = r419334 / r419329;
        double r419336 = 1.0;
        double r419337 = r419335 / r419336;
        double r419338 = r419330 * r419333;
        double r419339 = r419332 ? r419337 : r419338;
        return r419339;
}

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
Target2.2
Herbie1.6
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- x y) (- z y)) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity64.0

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

    4. Applied add-cube-cbrt64.0

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}{1 \cdot \left(z - y\right)} \cdot t\]

    5. Applied times-frac64.0

      \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{1} \cdot \frac{\sqrt[3]{x - y}}{z - y}\right)} \cdot t\]

    6. Applied associate-*l*8.2

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{1} \cdot \left(\frac{\sqrt[3]{x - y}}{z - y} \cdot t\right)}\]
    7. Using strategy rm

    8. Applied associate-*l/8.2

      \[\leadsto \color{blue}{\frac{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \left(\frac{\sqrt[3]{x - y}}{z - y} \cdot t\right)}{1}}\]

    9. Simplified0.3

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

    11. Applied associate-*r/0.3

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

    if -inf.0 < (/ (- x y) (- z y))

    1. Initial program 1.6

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

  4. Final simplification1.6

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

Reproduce

herbie shell --seed 2020021 +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))