Average Error: 2.2 → 2.1
Time: 17.6s
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 r14612116 = x;
        double r14612117 = y;
        double r14612118 = r14612116 - r14612117;
        double r14612119 = z;
        double r14612120 = r14612119 - r14612117;
        double r14612121 = r14612118 / r14612120;
        double r14612122 = t;
        double r14612123 = r14612121 * r14612122;
        return r14612123;
}
↓
double f(double x, double y, double z, double t) {
        double r14612124 = y;
        double r14612125 = -1.8586745194188488e-190;
        bool r14612126 = r14612124 <= r14612125;
        double r14612127 = t;
        double r14612128 = z;
        double r14612129 = r14612128 - r14612124;
        double r14612130 = x;
        double r14612131 = r14612130 - r14612124;
        double r14612132 = r14612129 / r14612131;
        double r14612133 = r14612127 / r14612132;
        double r14612134 = 6.790926987711054e-54;
        bool r14612135 = r14612124 <= r14612134;
        double r14612136 = r14612127 * r14612131;
        double r14612137 = r14612136 / r14612129;
        double r14612138 = r14612135 ? r14612137 : r14612133;
        double r14612139 = r14612126 ? r14612133 : r14612138;
        return r14612139;
}

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))