Average Error: 11.5 → 1.5
Time: 5.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} = -\infty:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 5.316577800148401 \cdot 10^{177}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t - z} - \frac{z}{t - z}\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} = -\infty:\\
\;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 5.316577800148401 \cdot 10^{177}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r616496 = x;
        double r616497 = y;
        double r616498 = z;
        double r616499 = r616497 - r616498;
        double r616500 = r616496 * r616499;
        double r616501 = t;
        double r616502 = r616501 - r616498;
        double r616503 = r616500 / r616502;
        return r616503;
}
↓
double f(double x, double y, double z, double t) {
        double r616504 = x;
        double r616505 = y;
        double r616506 = z;
        double r616507 = r616505 - r616506;
        double r616508 = r616504 * r616507;
        double r616509 = t;
        double r616510 = r616509 - r616506;
        double r616511 = r616508 / r616510;
        double r616512 = -inf.0;
        bool r616513 = r616511 <= r616512;
        double r616514 = r616504 / r616510;
        double r616515 = r616514 * r616507;
        double r616516 = 5.316577800148401e+177;
        bool r616517 = r616511 <= r616516;
        double r616518 = r616505 / r616510;
        double r616519 = r616506 / r616510;
        double r616520 = r616518 - r616519;
        double r616521 = r616504 * r616520;
        double r616522 = r616517 ? r616511 : r616521;
        double r616523 = r616513 ? r616515 : r616522;
        return r616523;
}

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

Original11.5
Target2.2
Herbie1.5
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) (- t z)) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity64.0

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    7. Applied div-sub0.1

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

    9. Applied div-inv0.2

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

    10. Applied div-inv0.2

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

    11. Applied distribute-rgt-out--0.2

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

    12. Applied associate-*r*0.4

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

    13. Simplified0.2

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

    if -inf.0 < (/ (* x (- y z)) (- t z)) < 5.316577800148401e+177

    1. Initial program 1.4

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

    if 5.316577800148401e+177 < (/ (* x (- y z)) (- t z))

    1. Initial program 43.7

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

    3. Applied *-un-lft-identity43.7

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

    4. Applied times-frac2.7

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

    5. Simplified2.7

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

    7. Applied div-sub2.7

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} = -\infty:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 5.316577800148401 \cdot 10^{177}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t - z} - \frac{z}{t - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 +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)))