Average Error: 11.1 → 1.3
Time: 14.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.016949263831516 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 5.367760633924734 \cdot 10^{+261}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.016949263831516 \cdot 10^{-301}:\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 5.367760633924734 \cdot 10^{+261}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r15008567 = x;
        double r15008568 = y;
        double r15008569 = z;
        double r15008570 = r15008568 - r15008569;
        double r15008571 = r15008567 * r15008570;
        double r15008572 = t;
        double r15008573 = r15008572 - r15008569;
        double r15008574 = r15008571 / r15008573;
        return r15008574;
}
↓
double f(double x, double y, double z, double t) {
        double r15008575 = y;
        double r15008576 = z;
        double r15008577 = r15008575 - r15008576;
        double r15008578 = x;
        double r15008579 = r15008577 * r15008578;
        double r15008580 = t;
        double r15008581 = r15008580 - r15008576;
        double r15008582 = r15008579 / r15008581;
        double r15008583 = 3.016949263831516e-301;
        bool r15008584 = r15008582 <= r15008583;
        double r15008585 = r15008581 / r15008577;
        double r15008586 = r15008578 / r15008585;
        double r15008587 = 5.367760633924734e+261;
        bool r15008588 = r15008582 <= r15008587;
        double r15008589 = r15008577 / r15008581;
        double r15008590 = r15008578 * r15008589;
        double r15008591 = r15008588 ? r15008582 : r15008590;
        double r15008592 = r15008584 ? r15008586 : r15008591;
        return r15008592;
}

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

Original11.1
Target2.1
Herbie1.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) (- t z)) < 3.016949263831516e-301

    1. Initial program 10.9

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

    3. Applied associate-/l*1.9

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

    if 3.016949263831516e-301 < (/ (* x (- y z)) (- t z)) < 5.367760633924734e+261

    1. Initial program 0.3

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

    3. Applied *-un-lft-identity0.3

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

    4. Applied times-frac2.6

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

    5. Simplified2.6

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

    7. Applied associate-*r/0.3

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

    if 5.367760633924734e+261 < (/ (* x (- y z)) (- t z))

    1. Initial program 53.2

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

    3. Applied *-un-lft-identity53.2

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

    4. Applied times-frac1.4

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

    5. Simplified1.4

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.016949263831516 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 5.367760633924734 \cdot 10^{+261}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))