Average Error: 7.5 → 1.1
Time: 10.6s
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 r14846316 = x;
        double r14846317 = y;
        double r14846318 = z;
        double r14846319 = r14846317 - r14846318;
        double r14846320 = t;
        double r14846321 = r14846320 - r14846318;
        double r14846322 = r14846319 * r14846321;
        double r14846323 = r14846316 / r14846322;
        return r14846323;
}
↓
double f(double x, double y, double z, double t) {
        double r14846324 = x;
        double r14846325 = cbrt(r14846324);
        double r14846326 = r14846325 * r14846325;
        double r14846327 = y;
        double r14846328 = z;
        double r14846329 = r14846327 - r14846328;
        double r14846330 = cbrt(r14846329);
        double r14846331 = r14846330 * r14846330;
        double r14846332 = r14846326 / r14846331;
        double r14846333 = t;
        double r14846334 = r14846333 - r14846328;
        double r14846335 = r14846325 / r14846330;
        double r14846336 = r14846334 / r14846335;
        double r14846337 = r14846332 / r14846336;
        return r14846337;
}

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

Original7.5
Target8.2
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 7.5

    \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  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-cbrt2.9

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

  7. Applied times-frac2.9

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

  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 2019156 +o rules:numerics
(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))))