Average Error: 16.6 → 12.8
Time: 10.7s
Precision: binary64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.31173273275306726 \cdot 10^{39} \lor \neg \left(y \le 3.575521334595492 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}}{1} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\right)\right)}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.31173273275306726 \cdot 10^{39} \lor \neg \left(y \le 3.575521334595492 \cdot 10^{-93}\right):\\
\;\;\;\;\frac{x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}}{1} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\right)\right)}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (x + ((double) (((double) (y * z)) / t)))) / ((double) (((double) (a + 1.0)) + ((double) (((double) (y * b)) / t))))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double VAR;
	if (((y <= -1.3117327327530673e+39) || !(y <= 3.575521334595492e-93))) {
		VAR = ((double) (((double) (x + ((double) (((double) (((double) (((double) cbrt(y)) * ((double) cbrt(y)))) / ((double) cbrt(t)))) * ((double) (((double) (((double) (((double) cbrt(((double) cbrt(y)))) * ((double) cbrt(((double) cbrt(y)))))) / 1.0)) * ((double) (((double) (((double) cbrt(((double) cbrt(y)))) / ((double) cbrt(t)))) * ((double) (z / ((double) cbrt(t)))))))))))) / ((double) (((double) (a + 1.0)) + ((double) (y * ((double) (b / t))))))));
	} else {
		VAR = ((double) (((double) (x + ((double) (((double) (y * z)) / t)))) / ((double) (((double) (a + 1.0)) + ((double) (((double) (y * b)) * ((double) (1.0 / t))))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.6
Target13.4
Herbie12.8
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.3117327327530673e+39 or 3.575521334595492e-93 < y

    1. Initial program 28.0

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt28.2

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

    4. Applied times-frac26.5

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
    5. Using strategy rm

    6. Applied *-un-lft-identity26.5

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

    7. Applied times-frac22.4

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

    8. Simplified22.4

      \[\leadsto \frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \color{blue}{y} \cdot \frac{b}{t}}\]
    9. Using strategy rm

    10. Applied add-cube-cbrt22.5

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

    11. Applied times-frac22.5

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

    12. Applied associate-*l*20.7

      \[\leadsto \frac{x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\right)}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\]
    13. Using strategy rm

    14. Applied *-un-lft-identity20.7

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

    15. Applied add-cube-cbrt20.7

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

    16. Applied times-frac20.7

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

    17. Applied associate-*l*20.8

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

    if -1.3117327327530673e+39 < y < 3.575521334595492e-93

    1. Initial program 4.1

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
    2. Using strategy rm

    3. Applied div-inv4.1

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\left(y \cdot b\right) \cdot \frac{1}{t}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification12.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.31173273275306726 \cdot 10^{39} \lor \neg \left(y \le 3.575521334595492 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}}{1} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\right)\right)}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020148 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))