Average Error: 14.6 → 0.5
Time: 19.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -7.90874680156662538 \cdot 10^{-239} \lor \neg \left(\frac{y}{z} \le 3.9139383207105451 \cdot 10^{-281}\right) \land \frac{y}{z} \le 1.9001415219657884 \cdot 10^{134}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
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 -7.90874680156662538 \cdot 10^{-239} \lor \neg \left(\frac{y}{z} \le 3.9139383207105451 \cdot 10^{-281}\right) \land \frac{y}{z} \le 1.9001415219657884 \cdot 10^{134}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r740970 = x;
        double r740971 = y;
        double r740972 = z;
        double r740973 = r740971 / r740972;
        double r740974 = t;
        double r740975 = r740973 * r740974;
        double r740976 = r740975 / r740974;
        double r740977 = r740970 * r740976;
        return r740977;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r740978 = y;
        double r740979 = z;
        double r740980 = r740978 / r740979;
        double r740981 = -inf.0;
        bool r740982 = r740980 <= r740981;
        double r740983 = 1.0;
        double r740984 = x;
        double r740985 = r740979 / r740984;
        double r740986 = r740985 / r740978;
        double r740987 = r740983 / r740986;
        double r740988 = -7.908746801566625e-239;
        bool r740989 = r740980 <= r740988;
        double r740990 = 3.913938320710545e-281;
        bool r740991 = r740980 <= r740990;
        double r740992 = !r740991;
        double r740993 = 1.9001415219657884e+134;
        bool r740994 = r740980 <= r740993;
        bool r740995 = r740992 && r740994;
        bool r740996 = r740989 || r740995;
        double r740997 = r740979 / r740978;
        double r740998 = r740984 / r740997;
        double r740999 = r740984 * r740978;
        double r741000 = r740999 / r740979;
        double r741001 = r740996 ? r740998 : r741000;
        double r741002 = r740982 ? r740987 : r741001;
        return r741002;
}

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

Original14.6
Target1.5
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045005 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390633 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.65895442315341522 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

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

    1. Initial program 64.0

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

    2. Simplified64.0

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

    4. Applied associate-*r/0.3

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

    6. Applied clear-num0.4

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

    7. Simplified0.4

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

    if -inf.0 < (/ y z) < -7.908746801566625e-239 or 3.913938320710545e-281 < (/ y z) < 1.9001415219657884e+134

    1. Initial program 9.2

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

    2. Simplified0.2

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

    4. Applied associate-*r/8.2

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

    6. Applied associate-/l*0.2

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

    if -7.908746801566625e-239 < (/ y z) < 3.913938320710545e-281 or 1.9001415219657884e+134 < (/ y z)

    1. Initial program 22.7

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

    2. Simplified14.0

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

    4. Applied associate-*r/1.1

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -7.90874680156662538 \cdot 10^{-239} \lor \neg \left(\frac{y}{z} \le 3.9139383207105451 \cdot 10^{-281}\right) \land \frac{y}{z} \le 1.9001415219657884 \cdot 10^{134}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :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)))