Average Error: 7.7 → 1.9
Time: 6.5s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{1}{y - z}}{\frac{t - z}{x}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{1}{y - z}}{\frac{t - z}{x}}
double f(double x, double y, double z, double t) {
        double r710409 = x;
        double r710410 = y;
        double r710411 = z;
        double r710412 = r710410 - r710411;
        double r710413 = t;
        double r710414 = r710413 - r710411;
        double r710415 = r710412 * r710414;
        double r710416 = r710409 / r710415;
        return r710416;
}
↓
double f(double x, double y, double z, double t) {
        double r710417 = 1.0;
        double r710418 = y;
        double r710419 = z;
        double r710420 = r710418 - r710419;
        double r710421 = r710417 / r710420;
        double r710422 = t;
        double r710423 = r710422 - r710419;
        double r710424 = x;
        double r710425 = r710423 / r710424;
        double r710426 = r710421 / r710425;
        return r710426;
}

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

Original7.7
Target8.5
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.7

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

  3. Applied *-un-lft-identity7.7

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

  4. Applied times-frac1.9

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

  6. Applied clear-num2.1

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

  8. Applied pow12.1

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

  9. Applied pow12.1

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

  10. Applied pow-prod-down2.1

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

  11. Simplified1.9

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

  12. Final simplification1.9

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

Reproduce

herbie shell --seed 2019322 
(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))))