Average Error: 16.9 → 13.4
Time: 19.5s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.1227333896239291 \cdot 10^{43}:\\ \;\;\;\;\frac{x + \left(\sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right) \cdot \left(\sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \frac{z}{\sqrt[3]{t}}\right)}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \le 7.38048324604022139 \cdot 10^{87}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -8.1227333896239291 \cdot 10^{43}:\\
\;\;\;\;\frac{x + \left(\sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right) \cdot \left(\sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \frac{z}{\sqrt[3]{t}}\right)}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\

\mathbf{elif}\;t \le 7.38048324604022139 \cdot 10^{87}:\\
\;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r568072 = x;
        double r568073 = y;
        double r568074 = z;
        double r568075 = r568073 * r568074;
        double r568076 = t;
        double r568077 = r568075 / r568076;
        double r568078 = r568072 + r568077;
        double r568079 = a;
        double r568080 = 1.0;
        double r568081 = r568079 + r568080;
        double r568082 = b;
        double r568083 = r568073 * r568082;
        double r568084 = r568083 / r568076;
        double r568085 = r568081 + r568084;
        double r568086 = r568078 / r568085;
        return r568086;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r568087 = t;
        double r568088 = -8.122733389623929e+43;
        bool r568089 = r568087 <= r568088;
        double r568090 = x;
        double r568091 = y;
        double r568092 = cbrt(r568087);
        double r568093 = r568092 * r568092;
        double r568094 = r568091 / r568093;
        double r568095 = cbrt(r568094);
        double r568096 = r568095 * r568095;
        double r568097 = z;
        double r568098 = r568097 / r568092;
        double r568099 = r568095 * r568098;
        double r568100 = r568096 * r568099;
        double r568101 = r568090 + r568100;
        double r568102 = a;
        double r568103 = 1.0;
        double r568104 = r568102 + r568103;
        double r568105 = b;
        double r568106 = r568087 / r568105;
        double r568107 = r568091 / r568106;
        double r568108 = r568104 + r568107;
        double r568109 = r568101 / r568108;
        double r568110 = 7.380483246040221e+87;
        bool r568111 = r568087 <= r568110;
        double r568112 = r568091 * r568097;
        double r568113 = r568112 / r568087;
        double r568114 = r568090 + r568113;
        double r568115 = r568091 * r568105;
        double r568116 = 1.0;
        double r568117 = r568116 / r568087;
        double r568118 = r568115 * r568117;
        double r568119 = r568104 + r568118;
        double r568120 = r568114 / r568119;
        double r568121 = r568094 * r568098;
        double r568122 = r568090 + r568121;
        double r568123 = r568122 / r568108;
        double r568124 = r568111 ? r568120 : r568123;
        double r568125 = r568089 ? r568109 : r568124;
        return r568125;
}

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

Original16.9
Target13.2
Herbie13.4
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -8.122733389623929e+43

    1. Initial program 11.8

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

    3. Applied add-cube-cbrt11.9

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

    4. Applied times-frac8.0

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

    6. Applied associate-/l*2.7

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

    8. Applied add-cube-cbrt2.8

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

    9. Applied associate-*l*2.8

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

    if -8.122733389623929e+43 < t < 7.380483246040221e+87

    1. Initial program 20.5

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

    3. Applied div-inv20.5

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

    if 7.380483246040221e+87 < t

    1. Initial program 11.0

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

    3. Applied add-cube-cbrt11.2

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

    4. Applied times-frac7.4

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

    6. Applied associate-/l*2.6

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

  4. Final simplification13.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.1227333896239291 \cdot 10^{43}:\\ \;\;\;\;\frac{x + \left(\sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right) \cdot \left(\sqrt[3]{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \frac{z}{\sqrt[3]{t}}\right)}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \le 7.38048324604022139 \cdot 10^{87}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(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))))