Average Error: 7.1 → 0.8
Time: 17.0s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \le -2.342968553224854 \cdot 10^{+280}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{elif}\;\left(t - z\right) \cdot \left(y - z\right) \le 3.071620186460857 \cdot 10^{+194}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \le -2.342968553224854 \cdot 10^{+280}:\\
\;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\

\mathbf{elif}\;\left(t - z\right) \cdot \left(y - z\right) \le 3.071620186460857 \cdot 10^{+194}:\\
\;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r36803814 = x;
        double r36803815 = y;
        double r36803816 = z;
        double r36803817 = r36803815 - r36803816;
        double r36803818 = t;
        double r36803819 = r36803818 - r36803816;
        double r36803820 = r36803817 * r36803819;
        double r36803821 = r36803814 / r36803820;
        return r36803821;
}
↓
double f(double x, double y, double z, double t) {
        double r36803822 = t;
        double r36803823 = z;
        double r36803824 = r36803822 - r36803823;
        double r36803825 = y;
        double r36803826 = r36803825 - r36803823;
        double r36803827 = r36803824 * r36803826;
        double r36803828 = -2.342968553224854e+280;
        bool r36803829 = r36803827 <= r36803828;
        double r36803830 = x;
        double r36803831 = r36803830 / r36803826;
        double r36803832 = r36803831 / r36803824;
        double r36803833 = 3.071620186460857e+194;
        bool r36803834 = r36803827 <= r36803833;
        double r36803835 = r36803830 / r36803827;
        double r36803836 = r36803834 ? r36803835 : r36803832;
        double r36803837 = r36803829 ? r36803832 : r36803836;
        return r36803837;
}

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

Original7.1
Target7.9
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- y z) (- t z)) < -2.342968553224854e+280 or 3.071620186460857e+194 < (* (- y z) (- t z))

    1. Initial program 12.2

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

    3. Applied associate-/r*0.2

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

    if -2.342968553224854e+280 < (* (- y z) (- t z)) < 3.071620186460857e+194

    1. Initial program 1.4

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \le -2.342968553224854 \cdot 10^{+280}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{elif}\;\left(t - z\right) \cdot \left(y - z\right) \le 3.071620186460857 \cdot 10^{+194}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 +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 (* (- y z) (- t z)))))

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