Average Error: 16.4 → 12.9
Time: 6.0s
Precision: binary64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8.9774741475485463 \cdot 10^{-72} \lor \neg \left(y \le 3.150062354636128 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(\sqrt[3]{\frac{y \cdot z}{t}} \cdot \sqrt[3]{\frac{y \cdot z}{t}}\right) \cdot \sqrt[3]{\frac{y \cdot z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -8.9774741475485463 \cdot 10^{-72} \lor \neg \left(y \le 3.150062354636128 \cdot 10^{-37}\right):\\
\;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \left(\sqrt[3]{\frac{y \cdot z}{t}} \cdot \sqrt[3]{\frac{y \cdot z}{t}}\right) \cdot \sqrt[3]{\frac{y \cdot z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{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 <= -8.977474147548546e-72) || !(y <= 3.150062354636128e-37))) {
		VAR = ((double) (((double) (x + ((double) (y * ((double) (z / t)))))) / ((double) (((double) (a + 1.0)) + ((double) (y * ((double) (b / t))))))));
	} else {
		VAR = ((double) (((double) (x + ((double) (((double) (((double) cbrt(((double) (((double) (y * z)) / t)))) * ((double) cbrt(((double) (((double) (y * z)) / t)))))) * ((double) cbrt(((double) (((double) (y * z)) / t)))))))) / ((double) (((double) (a + 1.0)) + ((double) (((double) (y * b)) / 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

Original16.4
Target13.3
Herbie12.9
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -8.9774741475485463e-72 or 3.150062354636128e-37 < y

    1. Initial program 26.3

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

    3. Applied *-un-lft-identity26.3

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

    4. Applied times-frac23.9

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

    5. Simplified23.9

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

    7. Applied *-un-lft-identity23.9

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

    8. Applied times-frac20.1

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

    9. Simplified20.1

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

    if -8.9774741475485463e-72 < y < 3.150062354636128e-37

    1. Initial program 2.7

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

    3. Applied add-cube-cbrt3.0

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

  4. Final simplification12.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.9774741475485463 \cdot 10^{-72} \lor \neg \left(y \le 3.150062354636128 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(\sqrt[3]{\frac{y \cdot z}{t}} \cdot \sqrt[3]{\frac{y \cdot z}{t}}\right) \cdot \sqrt[3]{\frac{y \cdot z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020155 
(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))))