Average Error: 2.2 → 2.1
Time: 19.9s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.8586745194188488 \cdot 10^{-190}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \mathbf{elif}\;y \le 6.790926987711054 \cdot 10^{-54}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.8586745194188488 \cdot 10^{-190}:\\
\;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\

\mathbf{elif}\;y \le 6.790926987711054 \cdot 10^{-54}:\\
\;\;\;\;\frac{t \cdot \left(x - y\right)}{z - y}\\

\mathbf{else}:\\
\;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r22815200 = x;
        double r22815201 = y;
        double r22815202 = r22815200 - r22815201;
        double r22815203 = z;
        double r22815204 = r22815203 - r22815201;
        double r22815205 = r22815202 / r22815204;
        double r22815206 = t;
        double r22815207 = r22815205 * r22815206;
        return r22815207;
}
↓
double f(double x, double y, double z, double t) {
        double r22815208 = y;
        double r22815209 = -1.8586745194188488e-190;
        bool r22815210 = r22815208 <= r22815209;
        double r22815211 = t;
        double r22815212 = z;
        double r22815213 = r22815212 - r22815208;
        double r22815214 = x;
        double r22815215 = r22815214 - r22815208;
        double r22815216 = r22815213 / r22815215;
        double r22815217 = r22815211 / r22815216;
        double r22815218 = 6.790926987711054e-54;
        bool r22815219 = r22815208 <= r22815218;
        double r22815220 = r22815211 * r22815215;
        double r22815221 = r22815220 / r22815213;
        double r22815222 = r22815219 ? r22815221 : r22815217;
        double r22815223 = r22815210 ? r22815217 : r22815222;
        return r22815223;
}

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
Target2.2
Herbie2.1
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.8586745194188488e-190 or 6.790926987711054e-54 < y

    1. Initial program 0.8

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

    3. Applied clear-num0.9

      \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \cdot t\]
    4. Using strategy rm

    5. Applied associate-*l/0.8

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

    6. Simplified0.8

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

    if -1.8586745194188488e-190 < y < 6.790926987711054e-54

    1. Initial program 5.6

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

    3. Applied associate-*l/5.5

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.8586745194188488 \cdot 10^{-190}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \mathbf{elif}\;y \le 6.790926987711054 \cdot 10^{-54}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +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))