Average Error: 16.6 → 13.3
Time: 16.5s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.282223415085258012742835684889144208601 \cdot 10^{46}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(b \cdot \frac{y}{t} + a\right) + 1}\\ \mathbf{elif}\;t \le 4.427619810627214919217705553013839297329 \cdot 10^{72}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t} + x}{\left(b \cdot \frac{y}{t} + a\right) + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.282223415085258012742835684889144208601 \cdot 10^{46}:\\
\;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(b \cdot \frac{y}{t} + a\right) + 1}\\

\mathbf{elif}\;t \le 4.427619810627214919217705553013839297329 \cdot 10^{72}:\\
\;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r657789 = x;
        double r657790 = y;
        double r657791 = z;
        double r657792 = r657790 * r657791;
        double r657793 = t;
        double r657794 = r657792 / r657793;
        double r657795 = r657789 + r657794;
        double r657796 = a;
        double r657797 = 1.0;
        double r657798 = r657796 + r657797;
        double r657799 = b;
        double r657800 = r657790 * r657799;
        double r657801 = r657800 / r657793;
        double r657802 = r657798 + r657801;
        double r657803 = r657795 / r657802;
        return r657803;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r657804 = t;
        double r657805 = -1.282223415085258e+46;
        bool r657806 = r657804 <= r657805;
        double r657807 = x;
        double r657808 = y;
        double r657809 = r657808 / r657804;
        double r657810 = z;
        double r657811 = r657809 * r657810;
        double r657812 = r657807 + r657811;
        double r657813 = b;
        double r657814 = r657813 * r657809;
        double r657815 = a;
        double r657816 = r657814 + r657815;
        double r657817 = 1.0;
        double r657818 = r657816 + r657817;
        double r657819 = r657812 / r657818;
        double r657820 = 4.427619810627215e+72;
        bool r657821 = r657804 <= r657820;
        double r657822 = r657808 * r657810;
        double r657823 = r657822 / r657804;
        double r657824 = r657807 + r657823;
        double r657825 = r657815 + r657817;
        double r657826 = r657808 * r657813;
        double r657827 = r657826 / r657804;
        double r657828 = r657825 + r657827;
        double r657829 = r657824 / r657828;
        double r657830 = r657810 / r657804;
        double r657831 = r657808 * r657830;
        double r657832 = r657831 + r657807;
        double r657833 = r657832 / r657818;
        double r657834 = r657821 ? r657829 : r657833;
        double r657835 = r657806 ? r657819 : r657834;
        return r657835;
}

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

Original16.6
Target12.8
Herbie13.3
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.282223415085258e+46

    1. Initial program 11.5

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

    2. Simplified3.3

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

    if -1.282223415085258e+46 < t < 4.427619810627215e+72

    1. Initial program 20.4

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

    if 4.427619810627215e+72 < t

    1. Initial program 10.6

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

    2. Simplified3.0

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

    4. Applied div-inv3.0

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

    5. Applied associate-*l*3.0

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

    6. Simplified3.0

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

  4. Final simplification13.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.282223415085258012742835684889144208601 \cdot 10^{46}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(b \cdot \frac{y}{t} + a\right) + 1}\\ \mathbf{elif}\;t \le 4.427619810627214919217705553013839297329 \cdot 10^{72}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t} + x}{\left(b \cdot \frac{y}{t} + a\right) + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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))))