Average Error: 10.9 → 1.6
Time: 7.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -1.4853878379412445 \cdot 10^{+262}:\\ \;\;\;\;\frac{x}{\frac{1}{y - z} \cdot \left(t - z\right)}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -3.3843796556327705 \cdot 10^{-136}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -1.4853878379412445 \cdot 10^{+262}:\\
\;\;\;\;\frac{x}{\frac{1}{y - z} \cdot \left(t - z\right)}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -3.3843796556327705 \cdot 10^{-136}:\\
\;\;\;\;\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 r12475488 = x;
        double r12475489 = y;
        double r12475490 = z;
        double r12475491 = r12475489 - r12475490;
        double r12475492 = r12475488 * r12475491;
        double r12475493 = t;
        double r12475494 = r12475493 - r12475490;
        double r12475495 = r12475492 / r12475494;
        return r12475495;
}
↓
double f(double x, double y, double z, double t) {
        double r12475496 = y;
        double r12475497 = z;
        double r12475498 = r12475496 - r12475497;
        double r12475499 = x;
        double r12475500 = r12475498 * r12475499;
        double r12475501 = t;
        double r12475502 = r12475501 - r12475497;
        double r12475503 = r12475500 / r12475502;
        double r12475504 = -1.4853878379412445e+262;
        bool r12475505 = r12475503 <= r12475504;
        double r12475506 = 1.0;
        double r12475507 = r12475506 / r12475498;
        double r12475508 = r12475507 * r12475502;
        double r12475509 = r12475499 / r12475508;
        double r12475510 = -3.3843796556327705e-136;
        bool r12475511 = r12475503 <= r12475510;
        double r12475512 = r12475498 / r12475502;
        double r12475513 = r12475499 * r12475512;
        double r12475514 = r12475511 ? r12475503 : r12475513;
        double r12475515 = r12475505 ? r12475509 : r12475514;
        return r12475515;
}

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

Original10.9
Target2.2
Herbie1.6
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) (- t z)) < -1.4853878379412445e+262

    1. Initial program 53.6

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

    3. Applied associate-/l*0.9

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

    5. Applied div-inv1.0

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

    if -1.4853878379412445e+262 < (/ (* x (- y z)) (- t z)) < -3.3843796556327705e-136

    1. Initial program 0.3

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

    if -3.3843796556327705e-136 < (/ (* x (- y z)) (- t z))

    1. Initial program 9.2

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

    3. Applied *-un-lft-identity9.2

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

    4. Applied times-frac2.1

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

    5. Simplified2.1

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -1.4853878379412445 \cdot 10^{+262}:\\ \;\;\;\;\frac{x}{\frac{1}{y - z} \cdot \left(t - z\right)}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le -3.3843796556327705 \cdot 10^{-136}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(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)))