Average Error: 12.4 → 2.2
Time: 2.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.005580395321849346630996821746555203942 \cdot 10^{-59} \lor \neg \left(z \le 1.294868886508425312995381834557730708192 \cdot 10^{-182}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.005580395321849346630996821746555203942 \cdot 10^{-59} \lor \neg \left(z \le 1.294868886508425312995381834557730708192 \cdot 10^{-182}\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 r544219 = x;
        double r544220 = y;
        double r544221 = z;
        double r544222 = r544220 - r544221;
        double r544223 = r544219 * r544222;
        double r544224 = t;
        double r544225 = r544224 - r544221;
        double r544226 = r544223 / r544225;
        return r544226;
}
↓
double f(double x, double y, double z, double t) {
        double r544227 = z;
        double r544228 = -1.0055803953218493e-59;
        bool r544229 = r544227 <= r544228;
        double r544230 = 1.2948688865084253e-182;
        bool r544231 = r544227 <= r544230;
        double r544232 = !r544231;
        bool r544233 = r544229 || r544232;
        double r544234 = x;
        double r544235 = y;
        double r544236 = r544235 - r544227;
        double r544237 = t;
        double r544238 = r544237 - r544227;
        double r544239 = r544236 / r544238;
        double r544240 = r544234 * r544239;
        double r544241 = r544234 / r544238;
        double r544242 = r544241 * r544236;
        double r544243 = r544233 ? r544240 : r544242;
        return r544243;
}

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

Original12.4
Target2.4
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.0055803953218493e-59 or 1.2948688865084253e-182 < z

    1. Initial program 14.8

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

    3. Applied *-un-lft-identity14.8

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

    4. Applied times-frac0.8

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

    5. Simplified0.8

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

    if -1.0055803953218493e-59 < z < 1.2948688865084253e-182

    1. Initial program 6.4

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

    3. Applied associate-/l*6.3

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

    5. Applied associate-/r/5.6

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.005580395321849346630996821746555203942 \cdot 10^{-59} \lor \neg \left(z \le 1.294868886508425312995381834557730708192 \cdot 10^{-182}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020002 +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)))