Average Error: 15.3 → 0.6
Time: 11.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -4.271360513759333161781280648465473250074 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -0.0 \lor \neg \left(\frac{y}{z} \le 9.193416187857939378229423416553993724805 \cdot 10^{231}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} = -\infty:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le -4.271360513759333161781280648465473250074 \cdot 10^{-161}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -0.0 \lor \neg \left(\frac{y}{z} \le 9.193416187857939378229423416553993724805 \cdot 10^{231}\right):\\
\;\;\;\;\frac{y \cdot x}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r444052 = x;
        double r444053 = y;
        double r444054 = z;
        double r444055 = r444053 / r444054;
        double r444056 = t;
        double r444057 = r444055 * r444056;
        double r444058 = r444057 / r444056;
        double r444059 = r444052 * r444058;
        return r444059;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r444060 = y;
        double r444061 = z;
        double r444062 = r444060 / r444061;
        double r444063 = -inf.0;
        bool r444064 = r444062 <= r444063;
        double r444065 = 1.0;
        double r444066 = x;
        double r444067 = r444061 / r444066;
        double r444068 = r444067 / r444060;
        double r444069 = r444065 / r444068;
        double r444070 = -4.271360513759333e-161;
        bool r444071 = r444062 <= r444070;
        double r444072 = r444066 * r444062;
        double r444073 = -0.0;
        bool r444074 = r444062 <= r444073;
        double r444075 = 9.19341618785794e+231;
        bool r444076 = r444062 <= r444075;
        double r444077 = !r444076;
        bool r444078 = r444074 || r444077;
        double r444079 = r444060 * r444066;
        double r444080 = r444079 / r444061;
        double r444081 = r444061 / r444060;
        double r444082 = r444066 / r444081;
        double r444083 = r444078 ? r444080 : r444082;
        double r444084 = r444071 ? r444072 : r444083;
        double r444085 = r444064 ? r444069 : r444084;
        return r444085;
}

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

Original15.3
Target1.6
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

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

    1. Initial program 64.0

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

    2. Simplified0.3

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

    4. Applied clear-num0.4

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

    5. Simplified0.4

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

    if -inf.0 < (/ y z) < -4.271360513759333e-161

    1. Initial program 10.6

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

    2. Simplified9.4

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

    4. Applied *-un-lft-identity9.4

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

    5. Applied times-frac0.3

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

    6. Simplified0.3

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

    if -4.271360513759333e-161 < (/ y z) < -0.0 or 9.19341618785794e+231 < (/ y z)

    1. Initial program 22.3

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

    2. Simplified0.8

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

    if -0.0 < (/ y z) < 9.19341618785794e+231

    1. Initial program 10.8

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

    2. Simplified7.4

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

    4. Applied associate-/l*0.7

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -4.271360513759333161781280648465473250074 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -0.0 \lor \neg \left(\frac{y}{z} \le 9.193416187857939378229423416553993724805 \cdot 10^{231}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))