Average Error: 7.6 → 0.8
Time: 3.4s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -2.51218041477093364 \cdot 10^{209} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 1.6660164360805303 \cdot 10^{161}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]
\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 -2.51218041477093364 \cdot 10^{209} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 1.6660164360805303 \cdot 10^{161}\right):\\
\;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\

\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)) <= -2.5121804147709336e+209) || !(((y - z) * (t - z)) <= 1.6660164360805303e+161))) {
		VAR = ((x / (y - z)) / (t - z));
	} else {
		VAR = (x / ((y - z) * (t - z)));
	}
	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

Original7.6
Target8.4
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- y z) (- t z)) < -2.5121804147709336e+209 or 1.6660164360805303e+161 < (* (- y z) (- t z))

    1. Initial program 11.8

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

    3. Applied associate-/r*0.4

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

    if -2.5121804147709336e+209 < (* (- y z) (- t z)) < 1.6660164360805303e+161

    1. Initial program 1.4

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -2.51218041477093364 \cdot 10^{209} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 1.6660164360805303 \cdot 10^{161}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020102 +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))))