Average Error: 16.4 → 15.6
Time: 4.4s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -2.465408554466323141555913071584577674662 \cdot 10^{-188} \lor \neg \left(b \le 7.053515903621808556448055808879062426153 \cdot 10^{176}\right):\\ \;\;\;\;\left(x + \left(y \cdot z\right) \cdot \frac{1}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{y}}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;b \le -2.465408554466323141555913071584577674662 \cdot 10^{-188} \lor \neg \left(b \le 7.053515903621808556448055808879062426153 \cdot 10^{176}\right):\\
\;\;\;\;\left(x + \left(y \cdot z\right) \cdot \frac{1}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{y}}{z}}}{\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 r742627 = x;
        double r742628 = y;
        double r742629 = z;
        double r742630 = r742628 * r742629;
        double r742631 = t;
        double r742632 = r742630 / r742631;
        double r742633 = r742627 + r742632;
        double r742634 = a;
        double r742635 = 1.0;
        double r742636 = r742634 + r742635;
        double r742637 = b;
        double r742638 = r742628 * r742637;
        double r742639 = r742638 / r742631;
        double r742640 = r742636 + r742639;
        double r742641 = r742633 / r742640;
        return r742641;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r742642 = b;
        double r742643 = -2.465408554466323e-188;
        bool r742644 = r742642 <= r742643;
        double r742645 = 7.053515903621809e+176;
        bool r742646 = r742642 <= r742645;
        double r742647 = !r742646;
        bool r742648 = r742644 || r742647;
        double r742649 = x;
        double r742650 = y;
        double r742651 = z;
        double r742652 = r742650 * r742651;
        double r742653 = 1.0;
        double r742654 = t;
        double r742655 = r742653 / r742654;
        double r742656 = r742652 * r742655;
        double r742657 = r742649 + r742656;
        double r742658 = a;
        double r742659 = 1.0;
        double r742660 = r742658 + r742659;
        double r742661 = cbrt(r742654);
        double r742662 = r742661 * r742661;
        double r742663 = r742650 / r742662;
        double r742664 = r742642 / r742661;
        double r742665 = r742663 * r742664;
        double r742666 = r742660 + r742665;
        double r742667 = r742653 / r742666;
        double r742668 = r742657 * r742667;
        double r742669 = r742654 / r742650;
        double r742670 = r742669 / r742651;
        double r742671 = r742653 / r742670;
        double r742672 = r742649 + r742671;
        double r742673 = r742650 * r742642;
        double r742674 = r742673 / r742654;
        double r742675 = r742660 + r742674;
        double r742676 = r742672 / r742675;
        double r742677 = r742648 ? r742668 : r742676;
        return r742677;
}

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

Original16.4
Target13.5
Herbie15.6
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -2.465408554466323e-188 or 7.053515903621809e+176 < b

    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 div-inv19.9

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

    5. Applied div-inv19.9

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

    7. Applied add-cube-cbrt20.1

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

    8. Applied times-frac18.6

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

    if -2.465408554466323e-188 < b < 7.053515903621809e+176

    1. Initial program 12.6

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

    3. Applied clear-num12.6

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

    5. Applied associate-/r*12.2

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

  4. Final simplification15.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.465408554466323141555913071584577674662 \cdot 10^{-188} \lor \neg \left(b \le 7.053515903621808556448055808879062426153 \cdot 10^{176}\right):\\ \;\;\;\;\left(x + \left(y \cdot z\right) \cdot \frac{1}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{y}}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 
(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))))