Average Error: 7.1 → 2.2
Time: 3.7s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{x}{t - z}}{y - z} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right)\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{x}{t - z}}{y - z} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right)
double f(double x, double y, double z, double t) {
        double r738286 = x;
        double r738287 = y;
        double r738288 = z;
        double r738289 = r738287 - r738288;
        double r738290 = t;
        double r738291 = r738290 - r738288;
        double r738292 = r738289 * r738291;
        double r738293 = r738286 / r738292;
        return r738293;
}
↓
double f(double x, double y, double z, double t) {
        double r738294 = x;
        double r738295 = t;
        double r738296 = z;
        double r738297 = r738295 - r738296;
        double r738298 = r738294 / r738297;
        double r738299 = y;
        double r738300 = r738299 - r738296;
        double r738301 = r738298 / r738300;
        double r738302 = 1.0;
        double r738303 = cbrt(r738302);
        double r738304 = r738303 * r738303;
        double r738305 = r738301 * r738304;
        return r738305;
}

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

Original7.1
Target7.9
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 7.1

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

  3. Applied *-un-lft-identity7.1

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

  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

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

  7. Applied add-cube-cbrt2.2

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

  8. Applied times-frac2.2

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

  9. Applied associate-*l*2.2

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

  10. Simplified2.2

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

  11. Final simplification2.2

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

Reproduce

herbie shell --seed 2020001 +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))))