Average Error: 7.9 → 1.2
Time: 3.9s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{y - z}} \cdot \frac{\frac{\sqrt[3]{x}}{t - z}}{\sqrt[3]{y - z}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{y - z}} \cdot \frac{\frac{\sqrt[3]{x}}{t - z}}{\sqrt[3]{y - z}}
double f(double x, double y, double z, double t) {
        double r731717 = x;
        double r731718 = y;
        double r731719 = z;
        double r731720 = r731718 - r731719;
        double r731721 = t;
        double r731722 = r731721 - r731719;
        double r731723 = r731720 * r731722;
        double r731724 = r731717 / r731723;
        return r731724;
}
↓
double f(double x, double y, double z, double t) {
        double r731725 = x;
        double r731726 = cbrt(r731725);
        double r731727 = r731726 * r731726;
        double r731728 = y;
        double r731729 = z;
        double r731730 = r731728 - r731729;
        double r731731 = cbrt(r731730);
        double r731732 = r731727 / r731731;
        double r731733 = r731732 / r731731;
        double r731734 = t;
        double r731735 = r731734 - r731729;
        double r731736 = r731726 / r731735;
        double r731737 = r731736 / r731731;
        double r731738 = r731733 * r731737;
        return r731738;
}

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

Original7.9
Target8.8
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 7.9

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

  3. Applied *-un-lft-identity7.9

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

  4. Applied times-frac2.2

    \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity2.2

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

  7. Applied *-un-lft-identity2.2

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

  8. Applied times-frac2.2

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

  9. Applied associate-*l*2.2

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

  10. Simplified2.1

    \[\leadsto \frac{1}{1} \cdot \color{blue}{\frac{\frac{x}{t - z}}{y - z}}\]
  11. Using strategy rm

  12. Applied add-cube-cbrt2.7

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

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

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

  14. Applied add-cube-cbrt2.9

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

  15. Applied times-frac2.9

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

  16. Applied times-frac1.2

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

  17. Simplified1.2

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

  18. Final simplification1.2

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

Reproduce

herbie shell --seed 2020081 
(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))))