Average Error: 2.7 → 1.7
Time: 3.4s
Precision: binary64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -7.598287989168853 \cdot 10^{+57} \lor \neg \left(x \leq 1.0663212078845744 \cdot 10^{+46}\right) \land x \leq 7.2338309609106325 \cdot 10^{+196}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -7.598287989168853 \cdot 10^{+57} \lor \neg \left(x \leq 1.0663212078845744 \cdot 10^{+46}\right) \land x \leq 7.2338309609106325 \cdot 10^{+196}:\\
\;\;\;\;\frac{1}{\frac{y}{x} - z \cdot \frac{t}{x}}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return (x / ((double) (y - ((double) (z * t)))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((x <= -7.598287989168853e+57) || (!(x <= 1.0663212078845744e+46) && (x <= 7.2338309609106325e+196)))) {
		VAR = (1.0 / ((double) ((y / x) - ((double) (z * (t / x))))));
	} else {
		VAR = (x / ((double) (y - ((double) (z * t)))));
	}
	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
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -7.5982879891688527e57 or 1.06632120788457444e46 < x < 7.23383096091063247e196

    1. Initial program Error: 6.4 bits

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

    3. Applied clear-numError: 6.5 bits

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

    5. Applied div-subError: 6.5 bits

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

    6. SimplifiedError: 3.1 bits

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

    if -7.5982879891688527e57 < x < 1.06632120788457444e46 or 7.23383096091063247e196 < x

    1. Initial program Error: 1.1 bits

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

  4. Final simplificationError: 1.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.598287989168853 \cdot 10^{+57} \lor \neg \left(x \leq 1.0663212078845744 \cdot 10^{+46}\right) \land x \leq 7.2338309609106325 \cdot 10^{+196}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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))))