Average Error: 7.3 → 1.4
Time: 14.0s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -8.812482183219169527609542821052580809101 \cdot 10^{214} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 21364.92791914778717909939587116241455078\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]
\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 -8.812482183219169527609542821052580809101 \cdot 10^{214} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 21364.92791914778717909939587116241455078\right):\\
\;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\

\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 r1012548 = x;
        double r1012549 = y;
        double r1012550 = z;
        double r1012551 = r1012549 - r1012550;
        double r1012552 = t;
        double r1012553 = r1012552 - r1012550;
        double r1012554 = r1012551 * r1012553;
        double r1012555 = r1012548 / r1012554;
        return r1012555;
}
↓
double f(double x, double y, double z, double t) {
        double r1012556 = y;
        double r1012557 = z;
        double r1012558 = r1012556 - r1012557;
        double r1012559 = t;
        double r1012560 = r1012559 - r1012557;
        double r1012561 = r1012558 * r1012560;
        double r1012562 = -8.81248218321917e+214;
        bool r1012563 = r1012561 <= r1012562;
        double r1012564 = 21364.927919147787;
        bool r1012565 = r1012561 <= r1012564;
        double r1012566 = !r1012565;
        bool r1012567 = r1012563 || r1012566;
        double r1012568 = x;
        double r1012569 = r1012568 / r1012558;
        double r1012570 = r1012569 / r1012560;
        double r1012571 = 1.0;
        double r1012572 = r1012571 / r1012561;
        double r1012573 = r1012568 * r1012572;
        double r1012574 = r1012567 ? r1012570 : r1012573;
        return r1012574;
}

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

Original7.3
Target8.1
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- y z) (- t z)) < -8.81248218321917e+214 or 21364.927919147787 < (* (- y z) (- t z))

    1. Initial program 9.5

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

    3. Applied associate-/r*1.1

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

    5. Applied clear-num1.7

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

    7. Applied *-un-lft-identity1.7

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

    8. Applied *-un-lft-identity1.7

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

    9. Applied times-frac1.7

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

    10. Applied *-un-lft-identity1.7

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

    11. Applied times-frac1.7

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

    12. Applied add-cube-cbrt1.7

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

    13. Applied times-frac1.7

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

    14. Simplified1.7

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

    15. Simplified1.1

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

    if -8.81248218321917e+214 < (* (- y z) (- t z)) < 21364.927919147787

    1. Initial program 1.9

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

    3. Applied div-inv2.3

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -8.812482183219169527609542821052580809101 \cdot 10^{214} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 21364.92791914778717909939587116241455078\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019350 +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))))