Average Error: 14.7 → 0.7
Time: 15.0s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.1673826862143979 \cdot 10^{+231}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.8275878233556424 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.0532503690597818 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.1115659814397386 \cdot 10^{+232}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.1673826862143979 \cdot 10^{+231}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.8275878233556424 \cdot 10^{-156}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 1.0532503690597818 \cdot 10^{-123}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;\frac{y}{z} \le 1.1115659814397386 \cdot 10^{+232}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r32581699 = x;
        double r32581700 = y;
        double r32581701 = z;
        double r32581702 = r32581700 / r32581701;
        double r32581703 = t;
        double r32581704 = r32581702 * r32581703;
        double r32581705 = r32581704 / r32581703;
        double r32581706 = r32581699 * r32581705;
        return r32581706;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r32581707 = y;
        double r32581708 = z;
        double r32581709 = r32581707 / r32581708;
        double r32581710 = -1.1673826862143979e+231;
        bool r32581711 = r32581709 <= r32581710;
        double r32581712 = x;
        double r32581713 = r32581712 * r32581707;
        double r32581714 = r32581713 / r32581708;
        double r32581715 = -1.8275878233556424e-156;
        bool r32581716 = r32581709 <= r32581715;
        double r32581717 = r32581709 * r32581712;
        double r32581718 = 1.0532503690597818e-123;
        bool r32581719 = r32581709 <= r32581718;
        double r32581720 = r32581712 / r32581708;
        double r32581721 = r32581720 * r32581707;
        double r32581722 = 1.1115659814397386e+232;
        bool r32581723 = r32581709 <= r32581722;
        double r32581724 = r32581723 ? r32581717 : r32581721;
        double r32581725 = r32581719 ? r32581721 : r32581724;
        double r32581726 = r32581716 ? r32581717 : r32581725;
        double r32581727 = r32581711 ? r32581714 : r32581726;
        return r32581727;
}

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

Original14.7
Target1.4
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -1.1673826862143979e+231

    1. Initial program 47.5

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

    2. Simplified0.7

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

    3. Taylor expanded around 0 0.7

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

    if -1.1673826862143979e+231 < (/ y z) < -1.8275878233556424e-156 or 1.0532503690597818e-123 < (/ y z) < 1.1115659814397386e+232

    1. Initial program 7.9

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

    2. Simplified10.8

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

    3. Taylor expanded around 0 9.3

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

    5. Applied *-un-lft-identity9.3

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

    6. Applied times-frac0.3

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

    7. Simplified0.3

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

    if -1.8275878233556424e-156 < (/ y z) < 1.0532503690597818e-123 or 1.1115659814397386e+232 < (/ y z)

    1. Initial program 19.8

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

    2. Simplified1.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.1673826862143979 \cdot 10^{+231}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.8275878233556424 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.0532503690597818 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.1115659814397386 \cdot 10^{+232}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 +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)))