Average Error: 16.0 → 12.2
Time: 9.1s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.93323669588324535 \cdot 10^{36} \lor \neg \left(t \le 62788810252579463200\right):\\ \;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot z}{t} + x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.93323669588324535 \cdot 10^{36} \lor \neg \left(t \le 62788810252579463200\right):\\
\;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r1460811 = x;
        double r1460812 = y;
        double r1460813 = z;
        double r1460814 = r1460812 * r1460813;
        double r1460815 = t;
        double r1460816 = r1460814 / r1460815;
        double r1460817 = r1460811 + r1460816;
        double r1460818 = a;
        double r1460819 = 1.0;
        double r1460820 = r1460818 + r1460819;
        double r1460821 = b;
        double r1460822 = r1460812 * r1460821;
        double r1460823 = r1460822 / r1460815;
        double r1460824 = r1460820 + r1460823;
        double r1460825 = r1460817 / r1460824;
        return r1460825;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1460826 = t;
        double r1460827 = -3.9332366958832453e+36;
        bool r1460828 = r1460826 <= r1460827;
        double r1460829 = 6.278881025257946e+19;
        bool r1460830 = r1460826 <= r1460829;
        double r1460831 = !r1460830;
        bool r1460832 = r1460828 || r1460831;
        double r1460833 = x;
        double r1460834 = y;
        double r1460835 = cbrt(r1460826);
        double r1460836 = r1460835 * r1460835;
        double r1460837 = r1460834 / r1460836;
        double r1460838 = z;
        double r1460839 = r1460838 / r1460835;
        double r1460840 = r1460837 * r1460839;
        double r1460841 = r1460833 + r1460840;
        double r1460842 = a;
        double r1460843 = 1.0;
        double r1460844 = r1460842 + r1460843;
        double r1460845 = b;
        double r1460846 = r1460826 / r1460845;
        double r1460847 = r1460834 / r1460846;
        double r1460848 = r1460844 + r1460847;
        double r1460849 = r1460841 / r1460848;
        double r1460850 = r1460834 * r1460838;
        double r1460851 = r1460850 / r1460826;
        double r1460852 = r1460851 + r1460833;
        double r1460853 = r1460834 * r1460845;
        double r1460854 = r1460853 / r1460826;
        double r1460855 = r1460844 + r1460854;
        double r1460856 = r1460852 / r1460855;
        double r1460857 = r1460832 ? r1460849 : r1460856;
        return r1460857;
}

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

Original16.0
Target12.9
Herbie12.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.9332366958832453e+36 or 6.278881025257946e+19 < t

    1. Initial program 11.5

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

    3. Applied add-cube-cbrt11.7

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

    4. Applied times-frac7.9

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

    6. Applied associate-/l*3.4

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

    if -3.9332366958832453e+36 < t < 6.278881025257946e+19

    1. Initial program 19.9

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

    3. Applied +-commutative19.9

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

  4. Final simplification12.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.93323669588324535 \cdot 10^{36} \lor \neg \left(t \le 62788810252579463200\right):\\ \;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot z}{t} + x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1) (/ (* y b) t))))