Average Error: 16.0 → 12.2
Time: 9.5s
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 r850765 = x;
        double r850766 = y;
        double r850767 = z;
        double r850768 = r850766 * r850767;
        double r850769 = t;
        double r850770 = r850768 / r850769;
        double r850771 = r850765 + r850770;
        double r850772 = a;
        double r850773 = 1.0;
        double r850774 = r850772 + r850773;
        double r850775 = b;
        double r850776 = r850766 * r850775;
        double r850777 = r850776 / r850769;
        double r850778 = r850774 + r850777;
        double r850779 = r850771 / r850778;
        return r850779;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r850780 = t;
        double r850781 = -3.9332366958832453e+36;
        bool r850782 = r850780 <= r850781;
        double r850783 = 6.278881025257946e+19;
        bool r850784 = r850780 <= r850783;
        double r850785 = !r850784;
        bool r850786 = r850782 || r850785;
        double r850787 = x;
        double r850788 = y;
        double r850789 = cbrt(r850780);
        double r850790 = r850789 * r850789;
        double r850791 = r850788 / r850790;
        double r850792 = z;
        double r850793 = r850792 / r850789;
        double r850794 = r850791 * r850793;
        double r850795 = r850787 + r850794;
        double r850796 = a;
        double r850797 = 1.0;
        double r850798 = r850796 + r850797;
        double r850799 = b;
        double r850800 = r850780 / r850799;
        double r850801 = r850788 / r850800;
        double r850802 = r850798 + r850801;
        double r850803 = r850795 / r850802;
        double r850804 = r850788 * r850792;
        double r850805 = r850804 / r850780;
        double r850806 = r850805 + r850787;
        double r850807 = r850788 * r850799;
        double r850808 = r850807 / r850780;
        double r850809 = r850798 + r850808;
        double r850810 = r850806 / r850809;
        double r850811 = r850786 ? r850803 : r850810;
        return r850811;
}

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 pow119.9

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