Average Error: 2.2 → 1.6
Time: 4.5s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} = -\infty:\\ \;\;\;\;{\left(\frac{\left(x - y\right) \cdot t}{z - y}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} = -\infty:\\
\;\;\;\;{\left(\frac{\left(x - y\right) \cdot t}{z - y}\right)}^{1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r552582 = x;
        double r552583 = y;
        double r552584 = r552582 - r552583;
        double r552585 = z;
        double r552586 = r552585 - r552583;
        double r552587 = r552584 / r552586;
        double r552588 = t;
        double r552589 = r552587 * r552588;
        return r552589;
}
↓
double f(double x, double y, double z, double t) {
        double r552590 = x;
        double r552591 = y;
        double r552592 = r552590 - r552591;
        double r552593 = z;
        double r552594 = r552593 - r552591;
        double r552595 = r552592 / r552594;
        double r552596 = -inf.0;
        bool r552597 = r552595 <= r552596;
        double r552598 = t;
        double r552599 = r552592 * r552598;
        double r552600 = r552599 / r552594;
        double r552601 = 1.0;
        double r552602 = pow(r552600, r552601);
        double r552603 = r552595 * r552598;
        double r552604 = r552597 ? r552602 : r552603;
        return r552604;
}

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 pow18.2

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

    9. Applied pow18.2

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

    10. Applied pow-prod-down8.2

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

    11. Applied pow18.2

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

    12. Applied pow-prod-down8.2

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

    13. Simplified0.3

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

    15. Applied associate-*r/0.3

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

    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

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

Reproduce

herbie shell --seed 2020021 
(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))