Average Error: 7.7 → 1.1
Time: 17.7s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\frac{t - z}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\frac{t - z}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}}
double f(double x, double y, double z, double t) {
        double r36965301 = x;
        double r36965302 = y;
        double r36965303 = z;
        double r36965304 = r36965302 - r36965303;
        double r36965305 = t;
        double r36965306 = r36965305 - r36965303;
        double r36965307 = r36965304 * r36965306;
        double r36965308 = r36965301 / r36965307;
        return r36965308;
}
↓
double f(double x, double y, double z, double t) {
        double r36965309 = x;
        double r36965310 = cbrt(r36965309);
        double r36965311 = r36965310 * r36965310;
        double r36965312 = y;
        double r36965313 = z;
        double r36965314 = r36965312 - r36965313;
        double r36965315 = cbrt(r36965314);
        double r36965316 = r36965315 * r36965315;
        double r36965317 = r36965311 / r36965316;
        double r36965318 = t;
        double r36965319 = r36965318 - r36965313;
        double r36965320 = r36965310 / r36965315;
        double r36965321 = r36965319 / r36965320;
        double r36965322 = r36965317 / r36965321;
        return r36965322;
}

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

Original7.7
Target8.4
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.7

    \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  2. Using strategy rm

  3. Applied associate-/r*2.1

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

  5. Applied add-cube-cbrt2.7

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

  6. Applied add-cube-cbrt2.8

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

  7. Applied times-frac2.8

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

  8. Applied associate-/l*1.1

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

  9. Final simplification1.1

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z)))))

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