Average Error: 2.2 → 1.3
Time: 10.5s
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 r362509 = x;
        double r362510 = y;
        double r362511 = r362509 - r362510;
        double r362512 = z;
        double r362513 = r362512 - r362510;
        double r362514 = r362511 / r362513;
        double r362515 = t;
        double r362516 = r362514 * r362515;
        return r362516;
}
↓
double f(double x, double y, double z, double t) {
        double r362517 = x;
        double r362518 = y;
        double r362519 = r362517 - r362518;
        double r362520 = z;
        double r362521 = r362520 - r362518;
        double r362522 = r362519 / r362521;
        double r362523 = -5.448529893679378e-291;
        bool r362524 = r362522 <= r362523;
        double r362525 = t;
        double r362526 = r362521 / r362519;
        double r362527 = r362525 / r362526;
        double r362528 = 4.3600216811328e-313;
        bool r362529 = r362522 <= r362528;
        double r362530 = r362525 / r362521;
        double r362531 = r362519 * r362530;
        double r362532 = r362522 * r362525;
        double r362533 = r362529 ? r362531 : r362532;
        double r362534 = r362524 ? r362527 : r362533;
        return r362534;
}

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 associate-*l/8.5

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

    4. Simplified8.5

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

    6. 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 
(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))