Average Error: 7.5 → 2.3
Time: 9.1s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 4.0510841144545337 \cdot 10^{-255}:\\ \;\;\;\;\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\left(t - z\right) \cdot \frac{y - z}{x}}\\ \mathbf{elif}\;z \le 1.5692981510658075 \cdot 10^{-125}:\\ \;\;\;\;\frac{1}{y - z} \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;z \le 4.0510841144545337 \cdot 10^{-255}:\\
\;\;\;\;\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\left(t - z\right) \cdot \frac{y - z}{x}}\\

\mathbf{elif}\;z \le 1.5692981510658075 \cdot 10^{-125}:\\
\;\;\;\;\frac{1}{y - z} \cdot \frac{x}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r936655 = x;
        double r936656 = y;
        double r936657 = z;
        double r936658 = r936656 - r936657;
        double r936659 = t;
        double r936660 = r936659 - r936657;
        double r936661 = r936658 * r936660;
        double r936662 = r936655 / r936661;
        return r936662;
}
↓
double f(double x, double y, double z, double t) {
        double r936663 = z;
        double r936664 = 4.0510841144545337e-255;
        bool r936665 = r936663 <= r936664;
        double r936666 = 1.0;
        double r936667 = cbrt(r936666);
        double r936668 = r936667 * r936667;
        double r936669 = t;
        double r936670 = r936669 - r936663;
        double r936671 = y;
        double r936672 = r936671 - r936663;
        double r936673 = x;
        double r936674 = r936672 / r936673;
        double r936675 = r936670 * r936674;
        double r936676 = r936668 / r936675;
        double r936677 = 1.5692981510658075e-125;
        bool r936678 = r936663 <= r936677;
        double r936679 = r936666 / r936672;
        double r936680 = r936673 / r936670;
        double r936681 = r936679 * r936680;
        double r936682 = r936673 / r936672;
        double r936683 = r936682 / r936670;
        double r936684 = r936678 ? r936681 : r936683;
        double r936685 = r936665 ? r936676 : r936684;
        return r936685;
}

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

Derivation

  1. Split input into 3 regimes

  2. if z < 4.0510841144545337e-255

    1. Initial program 7.5

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

    3. Applied associate-/r*2.5

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

    5. Applied clear-num2.8

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

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

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

    8. Applied add-cube-cbrt2.8

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

    9. Applied times-frac2.8

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

    10. Applied associate-/l*3.3

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

    11. Simplified3.0

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

    if 4.0510841144545337e-255 < z < 1.5692981510658075e-125

    1. Initial program 5.3

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

    3. Applied *-un-lft-identity5.3

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

    4. Applied times-frac3.9

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

    if 1.5692981510658075e-125 < z

    1. Initial program 8.1

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

    3. Applied associate-/r*0.7

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 4.0510841144545337 \cdot 10^{-255}:\\ \;\;\;\;\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\left(t - z\right) \cdot \frac{y - z}{x}}\\ \mathbf{elif}\;z \le 1.5692981510658075 \cdot 10^{-125}:\\ \;\;\;\;\frac{1}{y - z} \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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))))