Average Error: 11.9 → 2.4
Time: 3.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.30440867097708453 \cdot 10^{-106} \lor \neg \left(z \le 4.5683127974833349 \cdot 10^{-53}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.30440867097708453 \cdot 10^{-106} \lor \neg \left(z \le 4.5683127974833349 \cdot 10^{-53}\right):\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r618363 = x;
        double r618364 = y;
        double r618365 = z;
        double r618366 = r618364 - r618365;
        double r618367 = r618363 * r618366;
        double r618368 = t;
        double r618369 = r618368 - r618365;
        double r618370 = r618367 / r618369;
        return r618370;
}
↓
double f(double x, double y, double z, double t) {
        double r618371 = z;
        double r618372 = -4.3044086709770845e-106;
        bool r618373 = r618371 <= r618372;
        double r618374 = 4.568312797483335e-53;
        bool r618375 = r618371 <= r618374;
        double r618376 = !r618375;
        bool r618377 = r618373 || r618376;
        double r618378 = x;
        double r618379 = y;
        double r618380 = r618379 - r618371;
        double r618381 = t;
        double r618382 = r618381 - r618371;
        double r618383 = r618380 / r618382;
        double r618384 = r618378 * r618383;
        double r618385 = r618378 / r618382;
        double r618386 = r618385 * r618380;
        double r618387 = r618377 ? r618384 : r618386;
        return r618387;
}

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

Original11.9
Target2.2
Herbie2.4
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.3044086709770845e-106 or 4.568312797483335e-53 < z

    1. Initial program 15.3

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

    3. Applied *-un-lft-identity15.3

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

    4. Applied times-frac0.5

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

    5. Simplified0.5

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

    if -4.3044086709770845e-106 < z < 4.568312797483335e-53

    1. Initial program 5.6

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

    3. Applied associate-/l*5.3

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

    5. Applied associate-/r/6.0

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \left(y - z\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.30440867097708453 \cdot 10^{-106} \lor \neg \left(z \le 4.5683127974833349 \cdot 10^{-53}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +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)))