Average Error: 7.5 → 2.2
Time: 4.6s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{x}{y - z}}{t - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{x}{y - z}}{t - z}
double f(double x, double y, double z, double t) {
        double r1343947 = x;
        double r1343948 = y;
        double r1343949 = z;
        double r1343950 = r1343948 - r1343949;
        double r1343951 = t;
        double r1343952 = r1343951 - r1343949;
        double r1343953 = r1343950 * r1343952;
        double r1343954 = r1343947 / r1343953;
        return r1343954;
}
↓
double f(double x, double y, double z, double t) {
        double r1343955 = x;
        double r1343956 = y;
        double r1343957 = z;
        double r1343958 = r1343956 - r1343957;
        double r1343959 = r1343955 / r1343958;
        double r1343960 = t;
        double r1343961 = r1343960 - r1343957;
        double r1343962 = r1343959 / r1343961;
        return r1343962;
}

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

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

  8. Applied associate-/r*2.3

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

  9. Simplified2.2

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

  10. Final simplification2.2

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

Reproduce

herbie shell --seed 2020025 +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))))