Average Error: 2.7 → 2.1
Time: 3.8s
Precision: binary64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y - z \cdot t} \le -1.86727 \cdot 10^{-319} \lor \neg \left(\frac{x}{y - z \cdot t} \le -0.0\right):\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - z \cdot \frac{t}{x}}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{y - z \cdot t} \le -1.86727 \cdot 10^{-319} \lor \neg \left(\frac{x}{y - z \cdot t} \le -0.0\right):\\
\;\;\;\;\frac{x}{y - z \cdot t}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{y}{x} - z \cdot \frac{t}{x}}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x / ((double) (y - ((double) (z * t))))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (x / ((double) (y - ((double) (z * t)))))) <= -1.8672717018924e-319) || !(((double) (x / ((double) (y - ((double) (z * t)))))) <= -0.0))) {
		VAR = ((double) (x / ((double) (y - ((double) (z * t))))));
	} else {
		VAR = ((double) (1.0 / ((double) (((double) (y / x)) - ((double) (z * ((double) (t / x))))))));
	}
	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

Original2.7
Target1.8
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ x (- y (* z t))) < -1.86727e-319 or -0.0 < (/ x (- y (* z t)))

    1. Initial program 0.1

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

    if -1.86727e-319 < (/ x (- y (* z t))) < -0.0

    1. Initial program 9.1

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

    3. Applied clear-num9.2

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

    5. Applied div-sub14.3

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

    6. Simplified7.0

      \[\leadsto \frac{1}{\frac{y}{x} - \color{blue}{z \cdot \frac{t}{x}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y - z \cdot t} \le -1.86727 \cdot 10^{-319} \lor \neg \left(\frac{x}{y - z \cdot t} \le -0.0\right):\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - z \cdot \frac{t}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

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