Average Error: 7.6 → 1.3
Time: 17.6s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x}}{y - z}}{\sqrt[3]{t - z}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}\right)\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{\sqrt[3]{x}}{y - z}}{\sqrt[3]{t - z}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}\right)
double f(double x, double y, double z, double t) {
        double r22491409 = x;
        double r22491410 = y;
        double r22491411 = z;
        double r22491412 = r22491410 - r22491411;
        double r22491413 = t;
        double r22491414 = r22491413 - r22491411;
        double r22491415 = r22491412 * r22491414;
        double r22491416 = r22491409 / r22491415;
        return r22491416;
}
↓
double f(double x, double y, double z, double t) {
        double r22491417 = x;
        double r22491418 = cbrt(r22491417);
        double r22491419 = y;
        double r22491420 = z;
        double r22491421 = r22491419 - r22491420;
        double r22491422 = r22491418 / r22491421;
        double r22491423 = t;
        double r22491424 = r22491423 - r22491420;
        double r22491425 = cbrt(r22491424);
        double r22491426 = r22491422 / r22491425;
        double r22491427 = r22491418 / r22491425;
        double r22491428 = r22491427 * r22491427;
        double r22491429 = r22491426 * r22491428;
        return r22491429;
}

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
Target8.3
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.6

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

  3. Applied associate-/r*2.1

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

  5. Applied add-cube-cbrt2.7

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

  6. Applied *-un-lft-identity2.7

    \[\leadsto \frac{\frac{x}{\color{blue}{1 \cdot \left(y - z\right)}}}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}\]

  7. Applied add-cube-cbrt2.8

    \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{1 \cdot \left(y - z\right)}}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}\]

  8. Applied times-frac2.8

    \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{1} \cdot \frac{\sqrt[3]{x}}{y - z}}}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}\]

  9. Applied times-frac1.2

    \[\leadsto \color{blue}{\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{1}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{y - z}}{\sqrt[3]{t - z}}}\]

  10. Simplified1.3

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

  11. Final simplification1.3

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

Reproduce

herbie shell --seed 2019171 
(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 (/ 1.0 (* (- y z) (- t z)))))

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