Average Error: 7.4 → 2.3
Time: 1.1m
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.926678211265294330642012033135922586379 \cdot 10^{-112}:\\ \;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\ \mathbf{elif}\;z \le 2.141565940867162526513329699771167619696 \cdot 10^{-142}:\\ \;\;\;\;\frac{\frac{1}{y - z}}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.926678211265294330642012033135922586379 \cdot 10^{-112}:\\
\;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\

\mathbf{elif}\;z \le 2.141565940867162526513329699771167619696 \cdot 10^{-142}:\\
\;\;\;\;\frac{\frac{1}{y - z}}{\frac{t - z}{x}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r29214748 = x;
        double r29214749 = y;
        double r29214750 = z;
        double r29214751 = r29214749 - r29214750;
        double r29214752 = t;
        double r29214753 = r29214752 - r29214750;
        double r29214754 = r29214751 * r29214753;
        double r29214755 = r29214748 / r29214754;
        return r29214755;
}
↓
double f(double x, double y, double z, double t) {
        double r29214756 = z;
        double r29214757 = -6.926678211265294e-112;
        bool r29214758 = r29214756 <= r29214757;
        double r29214759 = 1.0;
        double r29214760 = y;
        double r29214761 = r29214760 - r29214756;
        double r29214762 = x;
        double r29214763 = r29214761 / r29214762;
        double r29214764 = r29214759 / r29214763;
        double r29214765 = t;
        double r29214766 = r29214765 - r29214756;
        double r29214767 = r29214764 / r29214766;
        double r29214768 = 2.1415659408671625e-142;
        bool r29214769 = r29214756 <= r29214768;
        double r29214770 = r29214759 / r29214761;
        double r29214771 = r29214766 / r29214762;
        double r29214772 = r29214770 / r29214771;
        double r29214773 = r29214769 ? r29214772 : r29214767;
        double r29214774 = r29214758 ? r29214767 : r29214773;
        return r29214774;
}

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

Original7.4
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 2 regimes

  2. if z < -6.926678211265294e-112 or 2.1415659408671625e-142 < z

    1. Initial program 8.0

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

    3. Applied associate-/r*0.9

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

    5. Applied clear-num1.0

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

    if -6.926678211265294e-112 < z < 2.1415659408671625e-142

    1. Initial program 5.7

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

    3. Applied associate-/r*5.6

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

    5. Applied clear-num5.9

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

    7. Applied div-inv5.9

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

    8. Applied *-un-lft-identity5.9

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

    9. Applied times-frac5.7

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

    10. Applied associate-/l*5.9

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

    11. Simplified5.8

      \[\leadsto \frac{\frac{1}{y - z}}{\color{blue}{\frac{t - z}{x}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.926678211265294330642012033135922586379 \cdot 10^{-112}:\\ \;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\ \mathbf{elif}\;z \le 2.141565940867162526513329699771167619696 \cdot 10^{-142}:\\ \;\;\;\;\frac{\frac{1}{y - z}}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(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))))