Average Error: 2.2 → 1.3
Time: 10.9s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -5.4485298936793777 \cdot 10^{-291}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le 4.3600216811328 \cdot 10^{-313}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le -5.4485298936793777 \cdot 10^{-291}:\\
\;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\

\mathbf{elif}\;\frac{x - y}{z - y} \le 4.3600216811328 \cdot 10^{-313}:\\
\;\;\;\;\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 r280711 = x;
        double r280712 = y;
        double r280713 = r280711 - r280712;
        double r280714 = z;
        double r280715 = r280714 - r280712;
        double r280716 = r280713 / r280715;
        double r280717 = t;
        double r280718 = r280716 * r280717;
        return r280718;
}
↓
double f(double x, double y, double z, double t) {
        double r280719 = x;
        double r280720 = y;
        double r280721 = r280719 - r280720;
        double r280722 = z;
        double r280723 = r280722 - r280720;
        double r280724 = r280721 / r280723;
        double r280725 = -5.448529893679378e-291;
        bool r280726 = r280724 <= r280725;
        double r280727 = t;
        double r280728 = r280723 / r280721;
        double r280729 = r280727 / r280728;
        double r280730 = 4.3600216811328e-313;
        bool r280731 = r280724 <= r280730;
        double r280732 = r280727 / r280723;
        double r280733 = r280721 * r280732;
        double r280734 = r280724 * r280727;
        double r280735 = r280731 ? r280733 : r280734;
        double r280736 = r280726 ? r280729 : r280735;
        return r280736;
}

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
Target2.3
Herbie1.3
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (- x y) (- z y)) < -5.448529893679378e-291

    1. Initial program 2.1

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

    3. Applied div-inv2.2

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

    4. Applied associate-*l*8.2

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

    5. Simplified8.2

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

    7. Applied associate-*r/8.5

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

    8. Simplified8.5

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

    10. Applied associate-/l*1.9

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

    if -5.448529893679378e-291 < (/ (- x y) (- z y)) < 4.3600216811328e-313

    1. Initial program 18.9

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

    3. Applied div-inv18.9

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

    4. Applied associate-*l*0.1

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

    5. Simplified0.1

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

    if 4.3600216811328e-313 < (/ (- x y) (- z y))

    1. Initial program 1.1

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -5.4485298936793777 \cdot 10^{-291}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le 4.3600216811328 \cdot 10^{-313}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 +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))