Average Error: 14.2 → 2.8
Time: 20.7s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 1.4005708519536854 \cdot 10^{-298}:\\ \;\;\;\;\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \left(\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}} \cdot \frac{x}{\sqrt[3]{z}}\right)\\ \mathbf{elif}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 5.155399044473928 \cdot 10^{+268}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 1.4005708519536854 \cdot 10^{-298}:\\
\;\;\;\;\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \left(\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}} \cdot \frac{x}{\sqrt[3]{z}}\right)\\

\mathbf{elif}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 5.155399044473928 \cdot 10^{+268}:\\
\;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r1879091 = x;
        double r1879092 = y;
        double r1879093 = z;
        double r1879094 = r1879092 / r1879093;
        double r1879095 = t;
        double r1879096 = r1879094 * r1879095;
        double r1879097 = r1879096 / r1879095;
        double r1879098 = r1879091 * r1879097;
        return r1879098;
}
↓
double f(double x, double y, double z, double t) {
        double r1879099 = x;
        double r1879100 = y;
        double r1879101 = z;
        double r1879102 = r1879100 / r1879101;
        double r1879103 = t;
        double r1879104 = r1879102 * r1879103;
        double r1879105 = r1879104 / r1879103;
        double r1879106 = r1879099 * r1879105;
        double r1879107 = 1.4005708519536854e-298;
        bool r1879108 = r1879106 <= r1879107;
        double r1879109 = cbrt(r1879101);
        double r1879110 = r1879100 / r1879109;
        double r1879111 = cbrt(r1879110);
        double r1879112 = r1879111 * r1879111;
        double r1879113 = r1879109 * r1879109;
        double r1879114 = cbrt(r1879113);
        double r1879115 = r1879112 / r1879114;
        double r1879116 = cbrt(r1879109);
        double r1879117 = r1879111 / r1879116;
        double r1879118 = r1879099 / r1879109;
        double r1879119 = r1879117 * r1879118;
        double r1879120 = r1879115 * r1879119;
        double r1879121 = 5.155399044473928e+268;
        bool r1879122 = r1879106 <= r1879121;
        double r1879123 = r1879099 * r1879100;
        double r1879124 = r1879123 / r1879101;
        double r1879125 = r1879122 ? r1879106 : r1879124;
        double r1879126 = r1879108 ? r1879120 : r1879125;
        return r1879126;
}

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 3 regimes

  2. if (* x (/ (* (/ y z) t) t)) < 1.4005708519536854e-298

    1. Initial program 16.0

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

    2. Simplified4.8

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

    4. Applied add-cube-cbrt5.5

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

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

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

    6. Applied times-frac5.5

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

    7. Applied associate-*r*5.0

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

    8. Simplified5.0

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

    10. Applied add-cube-cbrt5.0

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

    11. Applied cbrt-prod5.1

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

    12. Applied add-cube-cbrt5.3

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

    13. Applied times-frac5.3

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

    14. Applied associate-*l*3.3

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

    if 1.4005708519536854e-298 < (* x (/ (* (/ y z) t) t)) < 5.155399044473928e+268

    1. Initial program 0.9

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

    if 5.155399044473928e+268 < (* x (/ (* (/ y z) t) t))

    1. Initial program 49.2

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

    2. Simplified6.1

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

    3. Taylor expanded around 0 5.6

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

  4. Final simplification2.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 1.4005708519536854 \cdot 10^{-298}:\\ \;\;\;\;\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \left(\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}} \cdot \frac{x}{\sqrt[3]{z}}\right)\\ \mathbf{elif}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 5.155399044473928 \cdot 10^{+268}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019154 +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)))