Average Error: 7.2 → 2.1
Time: 5.7s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{x \cdot \frac{1}{y - z}}{t - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{x \cdot \frac{1}{y - z}}{t - z}
double code(double x, double y, double z, double t) {
	return ((double) (x / ((double) (((double) (y - z)) * ((double) (t - z))))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x * ((double) (1.0 / ((double) (y - z)))))) / ((double) (t - z))));
}

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

Original7.2
Target8.0
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.2

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

  3. Applied associate-/r*2.1

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

  5. Applied div-inv2.1

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

  6. Final simplification2.1

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

Reproduce

herbie shell --seed 2020163 
(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 (/ 1.0 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))