Average Error: 2.4 → 1.4
Time: 3.9s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.477269956526729882709689256541591977713 \cdot 10^{-242}:\\ \;\;\;\;{\left(\frac{t}{\frac{z - y}{x - y}}\right)}^{1}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le -0.0:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le -1.477269956526729882709689256541591977713 \cdot 10^{-242}:\\
\;\;\;\;{\left(\frac{t}{\frac{z - y}{x - y}}\right)}^{1}\\

\mathbf{elif}\;\frac{x - y}{z - y} \le -0.0:\\
\;\;\;\;\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 r462150 = x;
        double r462151 = y;
        double r462152 = r462150 - r462151;
        double r462153 = z;
        double r462154 = r462153 - r462151;
        double r462155 = r462152 / r462154;
        double r462156 = t;
        double r462157 = r462155 * r462156;
        return r462157;
}
↓
double f(double x, double y, double z, double t) {
        double r462158 = x;
        double r462159 = y;
        double r462160 = r462158 - r462159;
        double r462161 = z;
        double r462162 = r462161 - r462159;
        double r462163 = r462160 / r462162;
        double r462164 = -1.4772699565267299e-242;
        bool r462165 = r462163 <= r462164;
        double r462166 = t;
        double r462167 = r462162 / r462160;
        double r462168 = r462166 / r462167;
        double r462169 = 1.0;
        double r462170 = pow(r462168, r462169);
        double r462171 = -0.0;
        bool r462172 = r462163 <= r462171;
        double r462173 = r462166 / r462162;
        double r462174 = r462160 * r462173;
        double r462175 = r462163 * r462166;
        double r462176 = r462172 ? r462174 : r462175;
        double r462177 = r462165 ? r462170 : r462176;
        return r462177;
}

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

Original2.4
Target2.4
Herbie1.4
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (- x y) (- z y)) < -1.4772699565267299e-242

    1. Initial program 2.7

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

    3. Applied clear-num2.8

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

    5. Applied pow12.8

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

    6. Applied pow12.8

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

    7. Applied pow-prod-down2.8

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

    8. Simplified2.5

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

    if -1.4772699565267299e-242 < (/ (- x y) (- z y)) < -0.0

    1. Initial program 13.3

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

    3. Applied div-inv13.3

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

    4. Applied associate-*l*0.2

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

    5. Simplified0.2

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

    if -0.0 < (/ (- x y) (- z y))

    1. Initial program 1.6

      \[\frac{x - y}{z - y} \cdot t\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.477269956526729882709689256541591977713 \cdot 10^{-242}:\\ \;\;\;\;{\left(\frac{t}{\frac{z - y}{x - y}}\right)}^{1}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le -0.0:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 +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))