Average Error: 7.4 → 2.3
Time: 56.4s
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 r18453231 = x;
        double r18453232 = y;
        double r18453233 = z;
        double r18453234 = r18453232 - r18453233;
        double r18453235 = t;
        double r18453236 = r18453235 - r18453233;
        double r18453237 = r18453234 * r18453236;
        double r18453238 = r18453231 / r18453237;
        return r18453238;
}
↓
double f(double x, double y, double z, double t) {
        double r18453239 = z;
        double r18453240 = -6.926678211265294e-112;
        bool r18453241 = r18453239 <= r18453240;
        double r18453242 = 1.0;
        double r18453243 = y;
        double r18453244 = r18453243 - r18453239;
        double r18453245 = x;
        double r18453246 = r18453244 / r18453245;
        double r18453247 = r18453242 / r18453246;
        double r18453248 = t;
        double r18453249 = r18453248 - r18453239;
        double r18453250 = r18453247 / r18453249;
        double r18453251 = 2.1415659408671625e-142;
        bool r18453252 = r18453239 <= r18453251;
        double r18453253 = r18453242 / r18453244;
        double r18453254 = r18453249 / r18453245;
        double r18453255 = r18453253 / r18453254;
        double r18453256 = r18453252 ? r18453255 : r18453250;
        double r18453257 = r18453241 ? r18453250 : r18453256;
        return r18453257;
}

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))))