Average Error: 14.0 → 0.7
Time: 25.8s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.009555688743657053093976996432682877192 \cdot 10^{278}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.900141742787772715345890115335440787699 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 4.438182973596565301288302827093808047147 \cdot 10^{-272}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.561199608254915194562496763078682553454 \cdot 10^{97}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.009555688743657053093976996432682877192 \cdot 10^{278}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.900141742787772715345890115335440787699 \cdot 10^{-270}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 4.438182973596565301288302827093808047147 \cdot 10^{-272}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 3.561199608254915194562496763078682553454 \cdot 10^{97}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r65793 = x;
        double r65794 = y;
        double r65795 = z;
        double r65796 = r65794 / r65795;
        double r65797 = t;
        double r65798 = r65796 * r65797;
        double r65799 = r65798 / r65797;
        double r65800 = r65793 * r65799;
        return r65800;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r65801 = y;
        double r65802 = z;
        double r65803 = r65801 / r65802;
        double r65804 = -1.009555688743657e+278;
        bool r65805 = r65803 <= r65804;
        double r65806 = x;
        double r65807 = r65806 / r65802;
        double r65808 = r65801 * r65807;
        double r65809 = -1.9001417427877727e-270;
        bool r65810 = r65803 <= r65809;
        double r65811 = r65802 / r65801;
        double r65812 = r65806 / r65811;
        double r65813 = 4.438182973596565e-272;
        bool r65814 = r65803 <= r65813;
        double r65815 = r65806 * r65801;
        double r65816 = r65815 / r65802;
        double r65817 = 3.561199608254915e+97;
        bool r65818 = r65803 <= r65817;
        double r65819 = 1.0;
        double r65820 = r65819 / r65801;
        double r65821 = r65807 / r65820;
        double r65822 = r65818 ? r65812 : r65821;
        double r65823 = r65814 ? r65816 : r65822;
        double r65824 = r65810 ? r65812 : r65823;
        double r65825 = r65805 ? r65808 : r65824;
        return r65825;
}

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 4 regimes

  2. if (/ y z) < -1.009555688743657e+278

    1. Initial program 54.6

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

    2. Simplified45.9

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

    4. Applied div-inv45.9

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

    5. Applied associate-*l*0.4

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

    6. Simplified0.2

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

    if -1.009555688743657e+278 < (/ y z) < -1.9001417427877727e-270 or 4.438182973596565e-272 < (/ y z) < 3.561199608254915e+97

    1. Initial program 8.2

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

    2. Simplified0.2

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

    4. Applied *-un-lft-identity0.2

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

    5. Applied *-un-lft-identity0.2

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

    6. Applied times-frac0.2

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

    7. Applied associate-*l*0.2

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

    8. Simplified8.7

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

    10. Applied associate-/l*0.2

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

    if -1.9001417427877727e-270 < (/ y z) < 4.438182973596565e-272

    1. Initial program 18.9

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

    2. Simplified15.8

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

    4. Applied *-un-lft-identity15.8

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

    5. Applied *-un-lft-identity15.8

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

    6. Applied times-frac15.8

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

    7. Applied associate-*l*15.8

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

    8. Simplified0.1

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

    if 3.561199608254915e+97 < (/ y z)

    1. Initial program 26.4

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

    2. Simplified12.8

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

    4. Applied *-un-lft-identity12.8

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

    5. Applied *-un-lft-identity12.8

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

    6. Applied times-frac12.8

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

    7. Applied associate-*l*12.8

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

    8. Simplified4.1

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

    10. Applied associate-/l*11.7

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

    12. Applied div-inv11.8

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

    13. Applied associate-/r*4.0

      \[\leadsto \frac{1}{1} \cdot \color{blue}{\frac{\frac{x}{z}}{\frac{1}{y}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.009555688743657053093976996432682877192 \cdot 10^{278}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.900141742787772715345890115335440787699 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 4.438182973596565301288302827093808047147 \cdot 10^{-272}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.561199608254915194562496763078682553454 \cdot 10^{97}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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)))