Average Error: 11.1 → 1.3
Time: 13.6s
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 r31756437 = x;
        double r31756438 = y;
        double r31756439 = z;
        double r31756440 = r31756438 - r31756439;
        double r31756441 = r31756437 * r31756440;
        double r31756442 = t;
        double r31756443 = r31756442 - r31756439;
        double r31756444 = r31756441 / r31756443;
        return r31756444;
}
↓
double f(double x, double y, double z, double t) {
        double r31756445 = y;
        double r31756446 = z;
        double r31756447 = r31756445 - r31756446;
        double r31756448 = x;
        double r31756449 = r31756447 * r31756448;
        double r31756450 = t;
        double r31756451 = r31756450 - r31756446;
        double r31756452 = r31756449 / r31756451;
        double r31756453 = 3.016949263831516e-301;
        bool r31756454 = r31756452 <= r31756453;
        double r31756455 = r31756451 / r31756447;
        double r31756456 = r31756448 / r31756455;
        double r31756457 = 5.367760633924734e+261;
        bool r31756458 = r31756452 <= r31756457;
        double r31756459 = r31756447 / r31756451;
        double r31756460 = r31756448 * r31756459;
        double r31756461 = r31756458 ? r31756452 : r31756460;
        double r31756462 = r31756454 ? r31756456 : r31756461;
        return r31756462;
}

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)))