Average Error: 16.7 → 13.3
Time: 5.0s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.57154151277953785 \cdot 10^{-112} \lor \neg \left(t \le 2.57219527487254833 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.57154151277953785 \cdot 10^{-112} \lor \neg \left(t \le 2.57219527487254833 \cdot 10^{-31}\right):\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r576677 = x;
        double r576678 = y;
        double r576679 = z;
        double r576680 = r576678 * r576679;
        double r576681 = t;
        double r576682 = r576680 / r576681;
        double r576683 = r576677 + r576682;
        double r576684 = a;
        double r576685 = 1.0;
        double r576686 = r576684 + r576685;
        double r576687 = b;
        double r576688 = r576678 * r576687;
        double r576689 = r576688 / r576681;
        double r576690 = r576686 + r576689;
        double r576691 = r576683 / r576690;
        return r576691;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r576692 = t;
        double r576693 = -3.571541512779538e-112;
        bool r576694 = r576692 <= r576693;
        double r576695 = 2.5721952748725483e-31;
        bool r576696 = r576692 <= r576695;
        double r576697 = !r576696;
        bool r576698 = r576694 || r576697;
        double r576699 = x;
        double r576700 = y;
        double r576701 = z;
        double r576702 = r576692 / r576701;
        double r576703 = r576700 / r576702;
        double r576704 = r576699 + r576703;
        double r576705 = a;
        double r576706 = 1.0;
        double r576707 = r576705 + r576706;
        double r576708 = b;
        double r576709 = r576708 / r576692;
        double r576710 = r576700 * r576709;
        double r576711 = r576707 + r576710;
        double r576712 = r576704 / r576711;
        double r576713 = r576700 * r576701;
        double r576714 = 1.0;
        double r576715 = r576714 / r576692;
        double r576716 = r576713 * r576715;
        double r576717 = r576699 + r576716;
        double r576718 = r576700 * r576708;
        double r576719 = r576718 * r576715;
        double r576720 = r576707 + r576719;
        double r576721 = r576717 / r576720;
        double r576722 = r576698 ? r576712 : r576721;
        return r576722;
}

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

Original16.7
Target13.8
Herbie13.3
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.571541512779538e-112 or 2.5721952748725483e-31 < t

    1. Initial program 11.4

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

    3. Applied div-inv11.4

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

    5. Applied associate-/l*9.1

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

    7. Applied associate-*l*5.9

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

    8. Simplified5.9

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

    if -3.571541512779538e-112 < t < 2.5721952748725483e-31

    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

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

    5. Applied div-inv25.5

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

  4. Final simplification13.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.57154151277953785 \cdot 10^{-112} \lor \neg \left(t \le 2.57219527487254833 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(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))))