Average Error: 14.7 → 0.8
Time: 30.0s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.777824700739059504027072604237357294271 \cdot 10^{-189}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.194701076531514820787324531303599279908 \cdot 10^{-141}:\\ \;\;\;\;\frac{{\left(\sqrt[3]{-1}\right)}^{2} \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.487328446405641062208224523193589026226 \cdot 10^{149}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} = -\infty:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.777824700739059504027072604237357294271 \cdot 10^{-189}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 6.194701076531514820787324531303599279908 \cdot 10^{-141}:\\
\;\;\;\;\frac{{\left(\sqrt[3]{-1}\right)}^{2} \cdot \left(x \cdot y\right)}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 4.487328446405641062208224523193589026226 \cdot 10^{149}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r413671 = x;
        double r413672 = y;
        double r413673 = z;
        double r413674 = r413672 / r413673;
        double r413675 = t;
        double r413676 = r413674 * r413675;
        double r413677 = r413676 / r413675;
        double r413678 = r413671 * r413677;
        return r413678;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r413679 = y;
        double r413680 = z;
        double r413681 = r413679 / r413680;
        double r413682 = -inf.0;
        bool r413683 = r413681 <= r413682;
        double r413684 = x;
        double r413685 = r413684 / r413680;
        double r413686 = r413679 * r413685;
        double r413687 = -1.7778247007390595e-189;
        bool r413688 = r413681 <= r413687;
        double r413689 = r413681 * r413684;
        double r413690 = 6.194701076531515e-141;
        bool r413691 = r413681 <= r413690;
        double r413692 = -1.0;
        double r413693 = cbrt(r413692);
        double r413694 = 2.0;
        double r413695 = pow(r413693, r413694);
        double r413696 = r413684 * r413679;
        double r413697 = r413695 * r413696;
        double r413698 = r413697 / r413680;
        double r413699 = 4.487328446405641e+149;
        bool r413700 = r413681 <= r413699;
        double r413701 = r413700 ? r413689 : r413686;
        double r413702 = r413691 ? r413698 : r413701;
        double r413703 = r413688 ? r413689 : r413702;
        double r413704 = r413683 ? r413686 : r413703;
        return r413704;
}

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
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -inf.0 or 4.487328446405641e+149 < (/ y z)

    1. Initial program 41.5

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

    2. Simplified29.8

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

    4. Applied div-inv29.9

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

    5. Applied associate-*l*1.9

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

    6. Simplified1.8

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

    if -inf.0 < (/ y z) < -1.7778247007390595e-189 or 6.194701076531515e-141 < (/ y z) < 4.487328446405641e+149

    1. Initial program 7.9

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

    2. Simplified0.2

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

    if -1.7778247007390595e-189 < (/ y z) < 6.194701076531515e-141

    1. Initial program 17.3

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

    2. Simplified9.0

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

    4. Applied add-cube-cbrt9.5

      \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right) \cdot \sqrt[3]{\frac{y}{z}}\right)} \cdot x\]

    5. Applied associate-*l*9.5

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right) \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot x\right)}\]
    6. Using strategy rm

    7. Applied div-inv9.4

      \[\leadsto \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right) \cdot \left(\sqrt[3]{\color{blue}{y \cdot \frac{1}{z}}} \cdot x\right)\]

    8. Applied cbrt-prod9.4

      \[\leadsto \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right) \cdot \left(\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{\frac{1}{z}}\right)} \cdot x\right)\]

    9. Taylor expanded around -inf 1.3

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{-1}\right)}^{2} \cdot \left(x \cdot y\right)}{z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.777824700739059504027072604237357294271 \cdot 10^{-189}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.194701076531514820787324531303599279908 \cdot 10^{-141}:\\ \;\;\;\;\frac{{\left(\sqrt[3]{-1}\right)}^{2} \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.487328446405641062208224523193589026226 \cdot 10^{149}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 +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)))