Average Error: 7.4 → 3.5
Time: 3.8s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -7.1680483536268657 \cdot 10^{54} \lor \neg \left(z \le 6.1309593021235525 \cdot 10^{123}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1 \cdot \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -7.1680483536268657 \cdot 10^{54} \lor \neg \left(z \le 6.1309593021235525 \cdot 10^{123}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((z <= -7.168048353626866e+54) || !(z <= 6.130959302123553e+123))) {
		VAR = ((x + (y / t)) / (x + 1.0));
	} else {
		VAR = ((x + (1.0 * (((y * z) - x) / ((t * z) - x)))) / (x + 1.0));
	}
	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

Original7.4
Target0.4
Herbie3.5
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -7.168048353626866e+54 or 6.130959302123553e+123 < z

    1. Initial program 18.7

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

    2. Taylor expanded around inf 7.7

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

    if -7.168048353626866e+54 < z < 6.130959302123553e+123

    1. Initial program 1.3

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
    2. Using strategy rm

    3. Applied clear-num1.3

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

    5. Applied *-un-lft-identity1.3

      \[\leadsto \frac{x + \frac{1}{\frac{t \cdot z - x}{\color{blue}{1 \cdot \left(y \cdot z - x\right)}}}}{x + 1}\]

    6. Applied *-un-lft-identity1.3

      \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{1 \cdot \left(t \cdot z - x\right)}}{1 \cdot \left(y \cdot z - x\right)}}}{x + 1}\]

    7. Applied times-frac1.3

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

    8. Applied add-cube-cbrt1.3

      \[\leadsto \frac{x + \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{1} \cdot \frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\]

    9. Applied times-frac1.3

      \[\leadsto \frac{x + \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{t \cdot z - x}{y \cdot z - x}}}}{x + 1}\]

    10. Simplified1.3

      \[\leadsto \frac{x + \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\]

    11. Simplified1.3

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.1680483536268657 \cdot 10^{54} \lor \neg \left(z \le 6.1309593021235525 \cdot 10^{123}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1 \cdot \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020075 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))