Average Error: 14.6 → 1.8
Time: 23.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.537949709390907 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 5.382487776465567 \cdot 10^{+233}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -5.537949709390907 \cdot 10^{-146}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le -0.0:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\mathbf{elif}\;\frac{y}{z} \le 5.382487776465567 \cdot 10^{+233}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r3173410 = x;
        double r3173411 = y;
        double r3173412 = z;
        double r3173413 = r3173411 / r3173412;
        double r3173414 = t;
        double r3173415 = r3173413 * r3173414;
        double r3173416 = r3173415 / r3173414;
        double r3173417 = r3173410 * r3173416;
        return r3173417;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3173418 = y;
        double r3173419 = z;
        double r3173420 = r3173418 / r3173419;
        double r3173421 = -5.537949709390907e-146;
        bool r3173422 = r3173420 <= r3173421;
        double r3173423 = x;
        double r3173424 = r3173419 / r3173418;
        double r3173425 = r3173423 / r3173424;
        double r3173426 = -0.0;
        bool r3173427 = r3173420 <= r3173426;
        double r3173428 = r3173419 / r3173423;
        double r3173429 = r3173418 / r3173428;
        double r3173430 = 5.382487776465567e+233;
        bool r3173431 = r3173420 <= r3173430;
        double r3173432 = r3173420 * r3173423;
        double r3173433 = r3173423 * r3173418;
        double r3173434 = r3173433 / r3173419;
        double r3173435 = r3173431 ? r3173432 : r3173434;
        double r3173436 = r3173427 ? r3173429 : r3173435;
        double r3173437 = r3173422 ? r3173425 : r3173436;
        return r3173437;
}

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) < -5.537949709390907e-146

    1. Initial program 13.1

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

    2. Simplified4.6

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

    4. Applied add-cube-cbrt5.6

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

    5. Applied *-un-lft-identity5.6

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

    6. Applied times-frac5.6

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

    7. Applied associate-*l*7.1

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

    9. Applied associate-*l/9.6

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

    10. Applied frac-times9.6

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

    11. Simplified9.6

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

    12. Simplified8.6

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

    14. Applied associate-/l*4.2

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

    if -5.537949709390907e-146 < (/ y z) < -0.0

    1. Initial program 17.2

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

    2. Simplified11.9

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

    4. Applied add-cube-cbrt12.2

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

    5. Applied *-un-lft-identity12.2

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

    6. Applied times-frac12.2

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

    7. Applied associate-*l*3.1

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

    9. Applied div-inv3.1

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

    10. Applied associate-*l*3.1

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

    11. Simplified1.1

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

    if -0.0 < (/ y z) < 5.382487776465567e+233

    1. Initial program 10.5

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

    2. Simplified0.5

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

    if 5.382487776465567e+233 < (/ y z)

    1. Initial program 42.4

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

    2. Simplified31.8

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

    4. Applied add-cube-cbrt32.3

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

    5. Applied *-un-lft-identity32.3

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

    6. Applied times-frac32.3

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

    7. Applied associate-*l*8.4

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

    9. Applied associate-*l/2.2

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

    10. Applied frac-times2.2

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

    11. Simplified2.2

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

    12. Simplified0.9

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.537949709390907 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 5.382487776465567 \cdot 10^{+233}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019139 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))