Average Error: 17.0 → 13.2
Time: 19.2s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.200885699998733444989436015220153683456 \cdot 10^{-71}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;y \le 6.270483262385894464092382197729043283474 \cdot 10^{-82}:\\ \;\;\;\;\frac{1}{\sqrt[3]{\frac{b \cdot y}{t}} \cdot \left(\sqrt[3]{\frac{b \cdot y}{t}} \cdot \sqrt[3]{\frac{b \cdot y}{t}}\right) + \left(1 + a\right)} \cdot \left(\frac{z \cdot y}{t} + x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.200885699998733444989436015220153683456 \cdot 10^{-71}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\

\mathbf{elif}\;y \le 6.270483262385894464092382197729043283474 \cdot 10^{-82}:\\
\;\;\;\;\frac{1}{\sqrt[3]{\frac{b \cdot y}{t}} \cdot \left(\sqrt[3]{\frac{b \cdot y}{t}} \cdot \sqrt[3]{\frac{b \cdot y}{t}}\right) + \left(1 + a\right)} \cdot \left(\frac{z \cdot y}{t} + x\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r34695731 = x;
        double r34695732 = y;
        double r34695733 = z;
        double r34695734 = r34695732 * r34695733;
        double r34695735 = t;
        double r34695736 = r34695734 / r34695735;
        double r34695737 = r34695731 + r34695736;
        double r34695738 = a;
        double r34695739 = 1.0;
        double r34695740 = r34695738 + r34695739;
        double r34695741 = b;
        double r34695742 = r34695732 * r34695741;
        double r34695743 = r34695742 / r34695735;
        double r34695744 = r34695740 + r34695743;
        double r34695745 = r34695737 / r34695744;
        return r34695745;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r34695746 = y;
        double r34695747 = -5.2008856999987334e-71;
        bool r34695748 = r34695746 <= r34695747;
        double r34695749 = x;
        double r34695750 = t;
        double r34695751 = z;
        double r34695752 = r34695750 / r34695751;
        double r34695753 = r34695746 / r34695752;
        double r34695754 = r34695749 + r34695753;
        double r34695755 = 1.0;
        double r34695756 = a;
        double r34695757 = r34695755 + r34695756;
        double r34695758 = b;
        double r34695759 = r34695750 / r34695758;
        double r34695760 = r34695746 / r34695759;
        double r34695761 = r34695757 + r34695760;
        double r34695762 = r34695754 / r34695761;
        double r34695763 = 6.270483262385894e-82;
        bool r34695764 = r34695746 <= r34695763;
        double r34695765 = 1.0;
        double r34695766 = r34695758 * r34695746;
        double r34695767 = r34695766 / r34695750;
        double r34695768 = cbrt(r34695767);
        double r34695769 = r34695768 * r34695768;
        double r34695770 = r34695768 * r34695769;
        double r34695771 = r34695770 + r34695757;
        double r34695772 = r34695765 / r34695771;
        double r34695773 = r34695751 * r34695746;
        double r34695774 = r34695773 / r34695750;
        double r34695775 = r34695774 + r34695749;
        double r34695776 = r34695772 * r34695775;
        double r34695777 = r34695764 ? r34695776 : r34695762;
        double r34695778 = r34695748 ? r34695762 : r34695777;
        return r34695778;
}

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

Original17.0
Target13.5
Herbie13.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.2008856999987334e-71 or 6.270483262385894e-82 < y

    1. Initial program 25.5

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

    3. Applied div-inv25.5

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

    5. Applied associate-*r/25.5

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

    6. Simplified23.1

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

    8. Applied associate-/l*19.2

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

    if -5.2008856999987334e-71 < y < 6.270483262385894e-82

    1. Initial program 2.9

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

    3. Applied div-inv3.0

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

    5. Applied add-cube-cbrt3.1

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

  4. Final simplification13.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.200885699998733444989436015220153683456 \cdot 10^{-71}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;y \le 6.270483262385894464092382197729043283474 \cdot 10^{-82}:\\ \;\;\;\;\frac{1}{\sqrt[3]{\frac{b \cdot y}{t}} \cdot \left(\sqrt[3]{\frac{b \cdot y}{t}} \cdot \sqrt[3]{\frac{b \cdot y}{t}}\right) + \left(1 + a\right)} \cdot \left(\frac{z \cdot y}{t} + x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"

  :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))))