Average Error: 2.0 → 2.0
Time: 7.0s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.298520785946563301647513642870177462015 \cdot 10^{-104} \lor \neg \left(y \le 3.224382231478152736415924797172890526842 \cdot 10^{-189}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.298520785946563301647513642870177462015 \cdot 10^{-104} \lor \neg \left(y \le 3.224382231478152736415924797172890526842 \cdot 10^{-189}\right):\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r570579 = x;
        double r570580 = y;
        double r570581 = r570579 - r570580;
        double r570582 = z;
        double r570583 = r570582 - r570580;
        double r570584 = r570581 / r570583;
        double r570585 = t;
        double r570586 = r570584 * r570585;
        return r570586;
}
↓
double f(double x, double y, double z, double t) {
        double r570587 = y;
        double r570588 = -2.2985207859465633e-104;
        bool r570589 = r570587 <= r570588;
        double r570590 = 3.2243822314781527e-189;
        bool r570591 = r570587 <= r570590;
        double r570592 = !r570591;
        bool r570593 = r570589 || r570592;
        double r570594 = x;
        double r570595 = r570594 - r570587;
        double r570596 = z;
        double r570597 = r570596 - r570587;
        double r570598 = r570595 / r570597;
        double r570599 = t;
        double r570600 = r570598 * r570599;
        double r570601 = r570595 * r570599;
        double r570602 = r570601 / r570597;
        double r570603 = r570593 ? r570600 : r570602;
        return r570603;
}

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

Original2.0
Target1.9
Herbie2.0
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.2985207859465633e-104 or 3.2243822314781527e-189 < y

    1. Initial program 0.9

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

    if -2.2985207859465633e-104 < y < 3.2243822314781527e-189

    1. Initial program 5.3

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

    3. Applied associate-*l/5.3

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.298520785946563301647513642870177462015 \cdot 10^{-104} \lor \neg \left(y \le 3.224382231478152736415924797172890526842 \cdot 10^{-189}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(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))