Average Error: 7.6 → 1.2
Time: 14.3s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}} \cdot \frac{\sqrt[3]{x}}{t - z}\right)\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}} \cdot \frac{\sqrt[3]{x}}{t - z}\right)
double f(double x, double y, double z, double t) {
        double r628424 = x;
        double r628425 = y;
        double r628426 = z;
        double r628427 = r628425 - r628426;
        double r628428 = t;
        double r628429 = r628428 - r628426;
        double r628430 = r628427 * r628429;
        double r628431 = r628424 / r628430;
        return r628431;
}
↓
double f(double x, double y, double z, double t) {
        double r628432 = x;
        double r628433 = cbrt(r628432);
        double r628434 = y;
        double r628435 = z;
        double r628436 = r628434 - r628435;
        double r628437 = cbrt(r628436);
        double r628438 = r628437 * r628437;
        double r628439 = r628433 / r628438;
        double r628440 = r628433 / r628437;
        double r628441 = t;
        double r628442 = r628441 - r628435;
        double r628443 = r628433 / r628442;
        double r628444 = r628440 * r628443;
        double r628445 = r628439 * r628444;
        return r628445;
}

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

Original7.6
Target8.2
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.6

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

  3. Applied add-cube-cbrt8.1

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

  4. Applied times-frac1.5

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

  6. Applied add-cube-cbrt1.7

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

  7. Applied times-frac1.7

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

  8. Applied associate-*l*1.2

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

  9. Final simplification1.2

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :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))))