Average Error: 7.5 → 2.2
Time: 3.8s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{1 \cdot \frac{x}{y - z}}{t - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{1 \cdot \frac{x}{y - z}}{t - z}
double f(double x, double y, double z, double t) {
        double r904325 = x;
        double r904326 = y;
        double r904327 = z;
        double r904328 = r904326 - r904327;
        double r904329 = t;
        double r904330 = r904329 - r904327;
        double r904331 = r904328 * r904330;
        double r904332 = r904325 / r904331;
        return r904332;
}
↓
double f(double x, double y, double z, double t) {
        double r904333 = 1.0;
        double r904334 = x;
        double r904335 = y;
        double r904336 = z;
        double r904337 = r904335 - r904336;
        double r904338 = r904334 / r904337;
        double r904339 = r904333 * r904338;
        double r904340 = t;
        double r904341 = r904340 - r904336;
        double r904342 = r904339 / r904341;
        return r904342;
}

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
Target8.4
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.5

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

  3. Applied associate-/r*2.2

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

  5. Applied clear-num2.3

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

  7. Applied *-un-lft-identity2.3

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

  8. Applied *-un-lft-identity2.3

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

  9. Applied times-frac2.3

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

  10. Applied add-sqr-sqrt2.3

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

  11. Applied times-frac2.3

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

  12. Simplified2.3

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

  13. Simplified2.2

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

  14. Final simplification2.2

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

Reproduce

herbie shell --seed 2020025 
(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))))