Average Error: 7.8 → 1.1
Time: 2.3s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le 5.91751804643800335 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{1}{t - z}}{\frac{y - z}{x}}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le 1.1045621638475217 \cdot 10^{279}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
\mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le 5.91751804643800335 \cdot 10^{-107}:\\
\;\;\;\;\frac{\frac{1}{t - z}}{\frac{y - z}{x}}\\

\mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le 1.1045621638475217 \cdot 10^{279}:\\
\;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\

\end{array}
double code(double x, double y, double z, double t) {
	return (x / ((y - z) * (t - z)));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((y - z) * (t - z)) <= 5.917518046438003e-107)) {
		VAR = ((1.0 / (t - z)) / ((y - z) / x));
	} else {
		double VAR_1;
		if ((((y - z) * (t - z)) <= 1.1045621638475217e+279)) {
			VAR_1 = (x / ((y - z) * (t - z)));
		} else {
			VAR_1 = ((x / (y - z)) / (t - z));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original7.8
Target8.4
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (- y z) (- t z)) < 5.917518046438003e-107

    1. Initial program 7.5

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

    3. Applied *-commutative7.5

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

    4. Applied associate-/r*3.1

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

    6. Applied clear-num3.3

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

    8. Applied associate-/r/3.1

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

    9. Applied associate-/l*2.6

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

    if 5.917518046438003e-107 < (* (- y z) (- t z)) < 1.1045621638475217e+279

    1. Initial program 0.2

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

    if 1.1045621638475217e+279 < (* (- y z) (- t z))

    1. Initial program 14.9

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

    3. Applied associate-/r*0.1

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le 5.91751804643800335 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{1}{t - z}}{\frac{y - z}{x}}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le 1.1045621638475217 \cdot 10^{279}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(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))))