Average Error: 16.8 → 13.1
Time: 6.3s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.13928765924485946 \cdot 10^{65}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}}\\ \mathbf{elif}\;t \le 1.1580474353914635 \cdot 10^{-29}:\\ \;\;\;\;\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -8.13928765924485946 \cdot 10^{65}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}}\\

\mathbf{elif}\;t \le 1.1580474353914635 \cdot 10^{-29}:\\
\;\;\;\;\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\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 r703066 = x;
        double r703067 = y;
        double r703068 = z;
        double r703069 = r703067 * r703068;
        double r703070 = t;
        double r703071 = r703069 / r703070;
        double r703072 = r703066 + r703071;
        double r703073 = a;
        double r703074 = 1.0;
        double r703075 = r703073 + r703074;
        double r703076 = b;
        double r703077 = r703067 * r703076;
        double r703078 = r703077 / r703070;
        double r703079 = r703075 + r703078;
        double r703080 = r703072 / r703079;
        return r703080;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r703081 = t;
        double r703082 = -8.139287659244859e+65;
        bool r703083 = r703081 <= r703082;
        double r703084 = x;
        double r703085 = y;
        double r703086 = z;
        double r703087 = r703081 / r703086;
        double r703088 = r703085 / r703087;
        double r703089 = r703084 + r703088;
        double r703090 = a;
        double r703091 = 1.0;
        double r703092 = r703090 + r703091;
        double r703093 = cbrt(r703085);
        double r703094 = r703093 * r703093;
        double r703095 = b;
        double r703096 = r703081 / r703095;
        double r703097 = r703093 / r703096;
        double r703098 = r703094 * r703097;
        double r703099 = r703092 + r703098;
        double r703100 = r703089 / r703099;
        double r703101 = 1.1580474353914635e-29;
        bool r703102 = r703081 <= r703101;
        double r703103 = r703085 * r703086;
        double r703104 = r703103 / r703081;
        double r703105 = r703084 + r703104;
        double r703106 = 1.0;
        double r703107 = r703085 * r703095;
        double r703108 = r703107 / r703081;
        double r703109 = r703092 + r703108;
        double r703110 = r703106 / r703109;
        double r703111 = r703105 * r703110;
        double r703112 = r703085 / r703081;
        double r703113 = r703112 * r703086;
        double r703114 = r703084 + r703113;
        double r703115 = r703085 / r703096;
        double r703116 = r703092 + r703115;
        double r703117 = r703114 / r703116;
        double r703118 = r703102 ? r703111 : r703117;
        double r703119 = r703083 ? r703100 : r703118;
        return r703119;
}

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

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

Derivation

  1. Split input into 3 regimes

  2. if t < -8.139287659244859e+65

    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 associate-/l*7.7

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

    5. Applied associate-/l*3.0

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

    7. Applied *-un-lft-identity3.0

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

    8. Applied *-un-lft-identity3.0

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

    9. Applied times-frac3.0

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

    10. Applied add-cube-cbrt3.1

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

    11. Applied times-frac3.1

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

    12. Simplified3.1

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

    if -8.139287659244859e+65 < t < 1.1580474353914635e-29

    1. Initial program 21.3

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

    3. Applied div-inv21.3

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

    if 1.1580474353914635e-29 < t

    1. Initial program 12.3

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

    3. Applied associate-/l*9.4

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

    5. Applied associate-/l*5.3

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

    7. Applied associate-/r/5.5

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

  4. Final simplification13.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.13928765924485946 \cdot 10^{65}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}}\\ \mathbf{elif}\;t \le 1.1580474353914635 \cdot 10^{-29}:\\ \;\;\;\;\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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))))