Average Error: 7.4 → 0.8
Time: 4.3s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -1.3710723791791016 \cdot 10^{201} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 3.15237795325171946 \cdot 10^{240}\right):\\ \;\;\;\;{\left(\frac{\frac{x}{y - z}}{t - z}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -1.3710723791791016 \cdot 10^{201} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 3.15237795325171946 \cdot 10^{240}\right):\\
\;\;\;\;{\left(\frac{\frac{x}{y - z}}{t - z}\right)}^{1}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r828502 = x;
        double r828503 = y;
        double r828504 = z;
        double r828505 = r828503 - r828504;
        double r828506 = t;
        double r828507 = r828506 - r828504;
        double r828508 = r828505 * r828507;
        double r828509 = r828502 / r828508;
        return r828509;
}
↓
double f(double x, double y, double z, double t) {
        double r828510 = y;
        double r828511 = z;
        double r828512 = r828510 - r828511;
        double r828513 = t;
        double r828514 = r828513 - r828511;
        double r828515 = r828512 * r828514;
        double r828516 = -1.3710723791791016e+201;
        bool r828517 = r828515 <= r828516;
        double r828518 = 3.1523779532517195e+240;
        bool r828519 = r828515 <= r828518;
        double r828520 = !r828519;
        bool r828521 = r828517 || r828520;
        double r828522 = x;
        double r828523 = r828522 / r828512;
        double r828524 = r828523 / r828514;
        double r828525 = 1.0;
        double r828526 = pow(r828524, r828525);
        double r828527 = r828525 / r828515;
        double r828528 = r828522 * r828527;
        double r828529 = r828521 ? r828526 : r828528;
        return r828529;
}

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
Target8.2
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)) < -1.3710723791791016e+201 or 3.1523779532517195e+240 < (* (- y z) (- t z))

    1. Initial program 12.8

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

    3. Applied add-cube-cbrt12.9

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

    4. Applied times-frac0.5

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}}\]
    5. Using strategy rm

    6. Applied pow10.5

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

    7. Applied pow10.5

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

    8. Applied pow-prod-down0.5

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

    9. Simplified0.2

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

    if -1.3710723791791016e+201 < (* (- y z) (- t z)) < 3.1523779532517195e+240

    1. Initial program 1.4

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

    3. Applied div-inv1.5

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -1.3710723791791016 \cdot 10^{201} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 3.15237795325171946 \cdot 10^{240}\right):\\ \;\;\;\;{\left(\frac{\frac{x}{y - z}}{t - z}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(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))))