Average Error: 11.4 → 1.5
Time: 12.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -1.353657953588875008584498903337160668689 \cdot 10^{306}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.37755421982307784760864075070745739156 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -1.353657953588875008584498903337160668689 \cdot 10^{306}:\\
\;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.37755421982307784760864075070745739156 \cdot 10^{-299}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r419457 = x;
        double r419458 = y;
        double r419459 = z;
        double r419460 = r419458 - r419459;
        double r419461 = r419457 * r419460;
        double r419462 = t;
        double r419463 = r419462 - r419459;
        double r419464 = r419461 / r419463;
        return r419464;
}
↓
double f(double x, double y, double z, double t) {
        double r419465 = x;
        double r419466 = y;
        double r419467 = z;
        double r419468 = r419466 - r419467;
        double r419469 = r419465 * r419468;
        double r419470 = t;
        double r419471 = r419470 - r419467;
        double r419472 = r419469 / r419471;
        double r419473 = -1.353657953588875e+306;
        bool r419474 = r419472 <= r419473;
        double r419475 = r419471 / r419468;
        double r419476 = r419465 / r419475;
        double r419477 = -3.377554219823078e-299;
        bool r419478 = r419472 <= r419477;
        double r419479 = r419468 / r419471;
        double r419480 = r419465 * r419479;
        double r419481 = r419478 ? r419472 : r419480;
        double r419482 = r419474 ? r419476 : r419481;
        return r419482;
}

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

Original11.4
Target2.3
Herbie1.5
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) (- t z)) < -1.353657953588875e+306

    1. Initial program 63.7

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

    3. Applied associate-/l*0.1

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

    if -1.353657953588875e+306 < (/ (* x (- y z)) (- t z)) < -3.377554219823078e-299

    1. Initial program 0.3

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

    if -3.377554219823078e-299 < (/ (* x (- y z)) (- t z))

    1. Initial program 11.0

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

    3. Applied *-un-lft-identity11.0

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

    4. Applied times-frac2.5

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

    5. Simplified2.5

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -1.353657953588875008584498903337160668689 \cdot 10^{306}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.37755421982307784760864075070745739156 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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