Average Error: 16.7 → 15.4
Time: 5.7s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -7.88189740368713405 \cdot 10^{-146} \lor \neg \left(t \le 5.81100609547629455 \cdot 10^{62}\right):\\ \;\;\;\;1 \cdot \frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(\left(y \cdot \frac{b}{t} + 1\right) + a\right) \cdot 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -7.88189740368713405 \cdot 10^{-146} \lor \neg \left(t \le 5.81100609547629455 \cdot 10^{62}\right):\\
\;\;\;\;1 \cdot \frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(\left(y \cdot \frac{b}{t} + 1\right) + a\right) \cdot 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{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 r822065 = x;
        double r822066 = y;
        double r822067 = z;
        double r822068 = r822066 * r822067;
        double r822069 = t;
        double r822070 = r822068 / r822069;
        double r822071 = r822065 + r822070;
        double r822072 = a;
        double r822073 = 1.0;
        double r822074 = r822072 + r822073;
        double r822075 = b;
        double r822076 = r822066 * r822075;
        double r822077 = r822076 / r822069;
        double r822078 = r822074 + r822077;
        double r822079 = r822071 / r822078;
        return r822079;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r822080 = t;
        double r822081 = -7.881897403687134e-146;
        bool r822082 = r822080 <= r822081;
        double r822083 = 5.811006095476295e+62;
        bool r822084 = r822080 <= r822083;
        double r822085 = !r822084;
        bool r822086 = r822082 || r822085;
        double r822087 = 1.0;
        double r822088 = x;
        double r822089 = y;
        double r822090 = cbrt(r822080);
        double r822091 = r822090 * r822090;
        double r822092 = r822089 / r822091;
        double r822093 = z;
        double r822094 = r822093 / r822090;
        double r822095 = r822092 * r822094;
        double r822096 = r822088 + r822095;
        double r822097 = b;
        double r822098 = r822097 / r822080;
        double r822099 = r822089 * r822098;
        double r822100 = 1.0;
        double r822101 = r822099 + r822100;
        double r822102 = a;
        double r822103 = r822101 + r822102;
        double r822104 = r822103 * r822087;
        double r822105 = r822096 / r822104;
        double r822106 = r822087 * r822105;
        double r822107 = r822080 / r822093;
        double r822108 = r822089 / r822107;
        double r822109 = r822088 + r822108;
        double r822110 = r822102 + r822100;
        double r822111 = r822089 * r822097;
        double r822112 = r822111 / r822080;
        double r822113 = r822110 + r822112;
        double r822114 = r822109 / r822113;
        double r822115 = r822086 ? r822106 : r822114;
        return r822115;
}

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
Target13.4
Herbie15.4
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -7.881897403687134e-146 or 5.811006095476295e+62 < t

    1. Initial program 12.9

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

    3. Applied *-un-lft-identity12.9

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

    4. Applied times-frac10.8

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

    5. Simplified10.8

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

    7. Applied add-cube-cbrt10.9

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

    8. Applied times-frac7.3

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

    10. Applied add-cube-cbrt7.4

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

    12. Applied *-un-lft-identity7.4

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

    13. Applied *-un-lft-identity7.4

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

    14. Applied times-frac7.4

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

    15. Simplified7.4

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

    16. Simplified7.3

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

    if -7.881897403687134e-146 < t < 5.811006095476295e+62

    1. Initial program 21.8

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

    3. Applied associate-/l*26.2

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

  4. Final simplification15.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -7.88189740368713405 \cdot 10^{-146} \lor \neg \left(t \le 5.81100609547629455 \cdot 10^{62}\right):\\ \;\;\;\;1 \cdot \frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(\left(y \cdot \frac{b}{t} + 1\right) + a\right) \cdot 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))))