Average Error: 7.5 → 2.2
Time: 18.5s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{1}{t - z}}{\frac{\sqrt[3]{y - z}}{x}} \cdot \frac{\frac{1}{\sqrt[3]{y - z}}}{\sqrt[3]{y - z}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{1}{t - z}}{\frac{\sqrt[3]{y - z}}{x}} \cdot \frac{\frac{1}{\sqrt[3]{y - z}}}{\sqrt[3]{y - z}}
double f(double x, double y, double z, double t) {
        double r670118 = x;
        double r670119 = y;
        double r670120 = z;
        double r670121 = r670119 - r670120;
        double r670122 = t;
        double r670123 = r670122 - r670120;
        double r670124 = r670121 * r670123;
        double r670125 = r670118 / r670124;
        return r670125;
}
↓
double f(double x, double y, double z, double t) {
        double r670126 = 1.0;
        double r670127 = t;
        double r670128 = z;
        double r670129 = r670127 - r670128;
        double r670130 = r670126 / r670129;
        double r670131 = y;
        double r670132 = r670131 - r670128;
        double r670133 = cbrt(r670132);
        double r670134 = x;
        double r670135 = r670133 / r670134;
        double r670136 = r670130 / r670135;
        double r670137 = r670126 / r670133;
        double r670138 = r670137 / r670133;
        double r670139 = r670136 * r670138;
        return r670139;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.5
Target8.3
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.5

    \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  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 clear-num2.3

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

  7. Applied *-un-lft-identity2.3

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

  8. Applied *-un-lft-identity2.3

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

  9. Applied add-cube-cbrt2.9

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

  10. Applied times-frac2.9

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

  11. Applied add-cube-cbrt2.9

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

  12. Applied times-frac2.8

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

  13. Applied times-frac2.3

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

  14. Simplified2.3

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

  15. Simplified2.2

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

  16. Final simplification2.2

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

Reproduce

herbie shell --seed 2019196 
(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))))