Average Error: 15.2 → 2.0
Time: 10.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(y \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(y \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r306180 = x;
        double r306181 = y;
        double r306182 = z;
        double r306183 = r306181 / r306182;
        double r306184 = t;
        double r306185 = r306183 * r306184;
        double r306186 = r306185 / r306184;
        double r306187 = r306180 * r306186;
        return r306187;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r306188 = y;
        double r306189 = x;
        double r306190 = cbrt(r306189);
        double r306191 = z;
        double r306192 = cbrt(r306191);
        double r306193 = r306190 / r306192;
        double r306194 = r306188 * r306193;
        double r306195 = r306190 * r306190;
        double r306196 = r306192 * r306192;
        double r306197 = r306195 / r306196;
        double r306198 = r306194 * r306197;
        return r306198;
}

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

Original15.2
Target1.6
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Initial program 15.2

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

  2. Simplified6.3

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

  3. Taylor expanded around 0 6.3

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

  4. Simplified6.2

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

  6. Applied add-cube-cbrt7.0

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

  7. Applied add-cube-cbrt7.2

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

  8. Applied times-frac7.2

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

  9. Applied associate-*l*2.0

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

  10. Simplified2.0

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

  11. Final simplification2.0

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

Reproduce

herbie shell --seed 2019196 
(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)))