Average Error: 7.5 → 2.7
Time: 7.5s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{1}{1}}{\frac{y - z}{\frac{x}{t - z}}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{1}{1}}{\frac{y - z}{\frac{x}{t - z}}}
double f(double x, double y, double z, double t) {
        double r2271669 = x;
        double r2271670 = y;
        double r2271671 = z;
        double r2271672 = r2271670 - r2271671;
        double r2271673 = t;
        double r2271674 = r2271673 - r2271671;
        double r2271675 = r2271672 * r2271674;
        double r2271676 = r2271669 / r2271675;
        return r2271676;
}
↓
double f(double x, double y, double z, double t) {
        double r2271677 = 1.0;
        double r2271678 = r2271677 / r2271677;
        double r2271679 = y;
        double r2271680 = z;
        double r2271681 = r2271679 - r2271680;
        double r2271682 = x;
        double r2271683 = t;
        double r2271684 = r2271683 - r2271680;
        double r2271685 = r2271682 / r2271684;
        double r2271686 = r2271681 / r2271685;
        double r2271687 = r2271678 / r2271686;
        return r2271687;
}

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

Original7.5
Target8.5
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.5

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

  3. Applied *-un-lft-identity7.5

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

  4. Applied times-frac2.2

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

  6. Applied *-un-lft-identity2.2

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

  7. Applied associate-*l*2.2

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

  8. Simplified2.2

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

  10. Applied *-un-lft-identity2.2

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

  11. Applied *-un-lft-identity2.2

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

  12. Applied times-frac2.2

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

  13. Applied associate-/l*2.7

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

  14. Final simplification2.7

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

Reproduce

herbie shell --seed 2020018 +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))))