Average Error: 14.0 → 0.7
Time: 26.7s
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 r52934 = x;
        double r52935 = y;
        double r52936 = z;
        double r52937 = r52935 / r52936;
        double r52938 = t;
        double r52939 = r52937 * r52938;
        double r52940 = r52939 / r52938;
        double r52941 = r52934 * r52940;
        return r52941;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r52942 = y;
        double r52943 = z;
        double r52944 = r52942 / r52943;
        double r52945 = -1.009555688743657e+278;
        bool r52946 = r52944 <= r52945;
        double r52947 = x;
        double r52948 = r52947 / r52943;
        double r52949 = r52942 * r52948;
        double r52950 = -1.9001417427877727e-270;
        bool r52951 = r52944 <= r52950;
        double r52952 = r52943 / r52942;
        double r52953 = r52947 / r52952;
        double r52954 = 4.438182973596565e-272;
        bool r52955 = r52944 <= r52954;
        double r52956 = r52947 * r52942;
        double r52957 = r52956 / r52943;
        double r52958 = 3.561199608254915e+97;
        bool r52959 = r52944 <= r52958;
        double r52960 = 1.0;
        double r52961 = r52960 / r52942;
        double r52962 = r52948 / r52961;
        double r52963 = r52959 ? r52953 : r52962;
        double r52964 = r52955 ? r52957 : r52963;
        double r52965 = r52951 ? r52953 : r52964;
        double r52966 = r52946 ? r52949 : r52965;
        return r52966;
}

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

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

    5. Applied associate-*l*0.2

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

    6. Simplified8.7

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

    8. Applied associate-/l*0.2

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

    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

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

    5. Applied associate-*l*15.8

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

    6. Simplified0.1

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

    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

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

    5. Applied associate-*l*12.8

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

    6. Simplified4.1

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

    8. Applied associate-/l*11.7

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

    10. Applied div-inv11.8

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

    11. Applied associate-/r*4.0

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