Average Error: 14.8 → 5.8
Time: 25.2s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.699374283935706957857036182841032710783 \cdot 10^{-111}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \le -9.622816168615241516473777822398600547529 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \le 0.02009436619436608117972298259701346978545:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \le 1.676300908348856400628868413342405429055 \cdot 10^{85}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.699374283935706957857036182841032710783 \cdot 10^{-111}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;t \le -9.622816168615241516473777822398600547529 \cdot 10^{-179}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;t \le 0.02009436619436608117972298259701346978545:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;t \le 1.676300908348856400628868413342405429055 \cdot 10^{85}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r57993 = x;
        double r57994 = y;
        double r57995 = z;
        double r57996 = r57994 / r57995;
        double r57997 = t;
        double r57998 = r57996 * r57997;
        double r57999 = r57998 / r57997;
        double r58000 = r57993 * r57999;
        return r58000;
}
↓
double f(double x, double y, double z, double t) {
        double r58001 = t;
        double r58002 = -1.699374283935707e-111;
        bool r58003 = r58001 <= r58002;
        double r58004 = x;
        double r58005 = y;
        double r58006 = r58004 * r58005;
        double r58007 = z;
        double r58008 = r58006 / r58007;
        double r58009 = -9.622816168615242e-179;
        bool r58010 = r58001 <= r58009;
        double r58011 = r58004 / r58007;
        double r58012 = r58005 * r58011;
        double r58013 = 0.02009436619436608;
        bool r58014 = r58001 <= r58013;
        double r58015 = 1.6763009083488564e+85;
        bool r58016 = r58001 <= r58015;
        double r58017 = r58007 / r58005;
        double r58018 = r58004 / r58017;
        double r58019 = r58016 ? r58012 : r58018;
        double r58020 = r58014 ? r58008 : r58019;
        double r58021 = r58010 ? r58012 : r58020;
        double r58022 = r58003 ? r58008 : r58021;
        return r58022;
}

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

Derivation

  1. Split input into 3 regimes

  2. if t < -1.699374283935707e-111 or -9.622816168615242e-179 < t < 0.02009436619436608

    1. Initial program 15.1

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified6.6

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

    4. Applied *-un-lft-identity6.6

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

    5. Applied associate-*l*6.6

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

    6. Simplified5.5

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

    if -1.699374283935707e-111 < t < -9.622816168615242e-179 or 0.02009436619436608 < t < 1.6763009083488564e+85

    1. Initial program 9.9

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified5.8

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

    4. Applied div-inv5.9

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

    5. Applied associate-*l*6.0

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

    6. Simplified6.0

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

    if 1.6763009083488564e+85 < t

    1. Initial program 17.4

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified6.5

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

    4. Applied *-un-lft-identity6.5

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

    5. Applied associate-*l*6.5

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

    6. Simplified6.0

      \[\leadsto 1 \cdot \color{blue}{\frac{x \cdot y}{z}}\]
    7. Using strategy rm

    8. Applied associate-/l*6.7

      \[\leadsto 1 \cdot \color{blue}{\frac{x}{\frac{z}{y}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification5.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.699374283935706957857036182841032710783 \cdot 10^{-111}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \le -9.622816168615241516473777822398600547529 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \le 0.02009436619436608117972298259701346978545:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \le 1.676300908348856400628868413342405429055 \cdot 10^{85}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))