Average Error: 2.3 → 1.9
Time: 17.8s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le 2.470328229206232720882843964341106861825 \cdot 10^{-323}:\\ \;\;\;\;\frac{\frac{t}{\sqrt[3]{z - y}} \cdot \frac{x - y}{\sqrt[3]{z - y}}}{\sqrt[3]{z - y}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le 5.779702072575541191674228138407204633316 \cdot 10^{148}:\\ \;\;\;\;\left(\frac{1}{z - y} \cdot \left(x - y\right)\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le 2.470328229206232720882843964341106861825 \cdot 10^{-323}:\\
\;\;\;\;\frac{\frac{t}{\sqrt[3]{z - y}} \cdot \frac{x - y}{\sqrt[3]{z - y}}}{\sqrt[3]{z - y}}\\

\mathbf{elif}\;\frac{x - y}{z - y} \le 5.779702072575541191674228138407204633316 \cdot 10^{148}:\\
\;\;\;\;\left(\frac{1}{z - y} \cdot \left(x - y\right)\right) \cdot t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r413596 = x;
        double r413597 = y;
        double r413598 = r413596 - r413597;
        double r413599 = z;
        double r413600 = r413599 - r413597;
        double r413601 = r413598 / r413600;
        double r413602 = t;
        double r413603 = r413601 * r413602;
        return r413603;
}
↓
double f(double x, double y, double z, double t) {
        double r413604 = x;
        double r413605 = y;
        double r413606 = r413604 - r413605;
        double r413607 = z;
        double r413608 = r413607 - r413605;
        double r413609 = r413606 / r413608;
        double r413610 = 2.4703282292062e-323;
        bool r413611 = r413609 <= r413610;
        double r413612 = t;
        double r413613 = cbrt(r413608);
        double r413614 = r413612 / r413613;
        double r413615 = r413606 / r413613;
        double r413616 = r413614 * r413615;
        double r413617 = r413616 / r413613;
        double r413618 = 5.779702072575541e+148;
        bool r413619 = r413609 <= r413618;
        double r413620 = 1.0;
        double r413621 = r413620 / r413608;
        double r413622 = r413621 * r413606;
        double r413623 = r413622 * r413612;
        double r413624 = r413612 / r413608;
        double r413625 = r413606 * r413624;
        double r413626 = r413619 ? r413623 : r413625;
        double r413627 = r413611 ? r413617 : r413626;
        return r413627;
}

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

Original2.3
Target2.3
Herbie1.9
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (- x y) (- z y)) < 2.4703282292062e-323

    1. Initial program 4.9

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

    3. Applied add-cube-cbrt5.7

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

    4. Applied *-un-lft-identity5.7

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

    5. Applied times-frac5.7

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

    7. Applied associate-*r/5.7

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

    8. Applied associate-*l/4.7

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

    9. Simplified4.8

      \[\leadsto \frac{\color{blue}{\frac{x - y}{\sqrt[3]{z - y}} \cdot \frac{t}{\sqrt[3]{z - y}}}}{\sqrt[3]{z - y}}\]

    if 2.4703282292062e-323 < (/ (- x y) (- z y)) < 5.779702072575541e+148

    1. Initial program 0.1

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

    3. Applied div-inv0.3

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

    if 5.779702072575541e+148 < (/ (- x y) (- z y))

    1. Initial program 12.2

      \[\frac{x - y}{z - y} \cdot t\]

    2. Simplified2.3

      \[\leadsto \color{blue}{\frac{t}{z - y} \cdot \left(x - y\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le 2.470328229206232720882843964341106861825 \cdot 10^{-323}:\\ \;\;\;\;\frac{\frac{t}{\sqrt[3]{z - y}} \cdot \frac{x - y}{\sqrt[3]{z - y}}}{\sqrt[3]{z - y}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le 5.779702072575541191674228138407204633316 \cdot 10^{148}:\\ \;\;\;\;\left(\frac{1}{z - y} \cdot \left(x - y\right)\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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))