Average Error: 16.0 → 12.2
Time: 9.1s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.93323669588324535 \cdot 10^{36} \lor \neg \left(t \le 62788810252579463200\right):\\ \;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot z}{t} + x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.93323669588324535 \cdot 10^{36} \lor \neg \left(t \le 62788810252579463200\right):\\
\;\;\;\;\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}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{y \cdot z}{t} + x}{\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 r863100 = x;
        double r863101 = y;
        double r863102 = z;
        double r863103 = r863101 * r863102;
        double r863104 = t;
        double r863105 = r863103 / r863104;
        double r863106 = r863100 + r863105;
        double r863107 = a;
        double r863108 = 1.0;
        double r863109 = r863107 + r863108;
        double r863110 = b;
        double r863111 = r863101 * r863110;
        double r863112 = r863111 / r863104;
        double r863113 = r863109 + r863112;
        double r863114 = r863106 / r863113;
        return r863114;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r863115 = t;
        double r863116 = -3.9332366958832453e+36;
        bool r863117 = r863115 <= r863116;
        double r863118 = 6.278881025257946e+19;
        bool r863119 = r863115 <= r863118;
        double r863120 = !r863119;
        bool r863121 = r863117 || r863120;
        double r863122 = x;
        double r863123 = y;
        double r863124 = cbrt(r863115);
        double r863125 = r863124 * r863124;
        double r863126 = r863123 / r863125;
        double r863127 = z;
        double r863128 = r863127 / r863124;
        double r863129 = r863126 * r863128;
        double r863130 = r863122 + r863129;
        double r863131 = a;
        double r863132 = 1.0;
        double r863133 = r863131 + r863132;
        double r863134 = b;
        double r863135 = r863115 / r863134;
        double r863136 = r863123 / r863135;
        double r863137 = r863133 + r863136;
        double r863138 = r863130 / r863137;
        double r863139 = r863123 * r863127;
        double r863140 = r863139 / r863115;
        double r863141 = r863140 + r863122;
        double r863142 = r863123 * r863134;
        double r863143 = r863142 / r863115;
        double r863144 = r863133 + r863143;
        double r863145 = r863141 / r863144;
        double r863146 = r863121 ? r863138 : r863145;
        return r863146;
}

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

Original16.0
Target12.9
Herbie12.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.9332366958832453e+36 or 6.278881025257946e+19 < t

    1. Initial program 11.5

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

    3. Applied add-cube-cbrt11.7

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

    4. Applied times-frac7.9

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

    6. Applied associate-/l*3.4

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

    if -3.9332366958832453e+36 < t < 6.278881025257946e+19

    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 pow119.9

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

  4. Final simplification12.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.93323669588324535 \cdot 10^{36} \lor \neg \left(t \le 62788810252579463200\right):\\ \;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot z}{t} + x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))))