Average Error: 2.3 → 1.9
Time: 17.7s
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 r446367 = x;
        double r446368 = y;
        double r446369 = r446367 - r446368;
        double r446370 = z;
        double r446371 = r446370 - r446368;
        double r446372 = r446369 / r446371;
        double r446373 = t;
        double r446374 = r446372 * r446373;
        return r446374;
}
↓
double f(double x, double y, double z, double t) {
        double r446375 = x;
        double r446376 = y;
        double r446377 = r446375 - r446376;
        double r446378 = z;
        double r446379 = r446378 - r446376;
        double r446380 = r446377 / r446379;
        double r446381 = 2.4703282292062e-323;
        bool r446382 = r446380 <= r446381;
        double r446383 = t;
        double r446384 = cbrt(r446379);
        double r446385 = r446383 / r446384;
        double r446386 = r446377 / r446384;
        double r446387 = r446385 * r446386;
        double r446388 = r446387 / r446384;
        double r446389 = 5.779702072575541e+148;
        bool r446390 = r446380 <= r446389;
        double r446391 = 1.0;
        double r446392 = r446391 / r446379;
        double r446393 = r446392 * r446377;
        double r446394 = r446393 * r446383;
        double r446395 = r446383 / r446379;
        double r446396 = r446377 * r446395;
        double r446397 = r446390 ? r446394 : r446396;
        double r446398 = r446382 ? r446388 : r446397;
        return r446398;
}

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. Using strategy rm

    3. Applied div-inv12.3

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

    4. Applied associate-*l*2.4

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

    5. Simplified2.3

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