Average Error: 11.5 → 1.5
Time: 12.5s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z}} \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{t - z}}\right) \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{t - z}} \cdot \sqrt[3]{x}\right)\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z}} \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{t - z}}\right) \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{t - z}} \cdot \sqrt[3]{x}\right)
double f(double x, double y, double z, double t) {
        double r394202 = x;
        double r394203 = y;
        double r394204 = z;
        double r394205 = r394203 - r394204;
        double r394206 = r394202 * r394205;
        double r394207 = t;
        double r394208 = r394207 - r394204;
        double r394209 = r394206 / r394208;
        return r394209;
}
↓
double f(double x, double y, double z, double t) {
        double r394210 = x;
        double r394211 = cbrt(r394210);
        double r394212 = r394211 * r394211;
        double r394213 = t;
        double r394214 = z;
        double r394215 = r394213 - r394214;
        double r394216 = cbrt(r394215);
        double r394217 = r394212 / r394216;
        double r394218 = y;
        double r394219 = r394218 - r394214;
        double r394220 = cbrt(r394219);
        double r394221 = r394220 * r394220;
        double r394222 = r394221 / r394216;
        double r394223 = r394217 * r394222;
        double r394224 = r394220 / r394216;
        double r394225 = r394224 * r394211;
        double r394226 = r394223 * r394225;
        return r394226;
}

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

Original11.5
Target1.9
Herbie1.5
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.5

    \[\frac{x \cdot \left(y - z\right)}{t - z}\]

  2. Simplified11.7

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

  4. Applied add-cube-cbrt12.5

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

  5. Applied add-cube-cbrt12.7

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

  6. Applied times-frac12.8

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

  7. Applied add-cube-cbrt12.8

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

  8. Applied times-frac3.9

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

  9. Simplified1.5

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

  10. Simplified1.5

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

  11. Final simplification1.5

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))