Average Error: 16.7 → 15.4
Time: 5.2s
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 r662539 = x;
        double r662540 = y;
        double r662541 = z;
        double r662542 = r662540 * r662541;
        double r662543 = t;
        double r662544 = r662542 / r662543;
        double r662545 = r662539 + r662544;
        double r662546 = a;
        double r662547 = 1.0;
        double r662548 = r662546 + r662547;
        double r662549 = b;
        double r662550 = r662540 * r662549;
        double r662551 = r662550 / r662543;
        double r662552 = r662548 + r662551;
        double r662553 = r662545 / r662552;
        return r662553;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r662554 = t;
        double r662555 = -7.881897403687134e-146;
        bool r662556 = r662554 <= r662555;
        double r662557 = 5.811006095476295e+62;
        bool r662558 = r662554 <= r662557;
        double r662559 = !r662558;
        bool r662560 = r662556 || r662559;
        double r662561 = 1.0;
        double r662562 = x;
        double r662563 = y;
        double r662564 = cbrt(r662554);
        double r662565 = r662564 * r662564;
        double r662566 = r662563 / r662565;
        double r662567 = z;
        double r662568 = r662567 / r662564;
        double r662569 = r662566 * r662568;
        double r662570 = r662562 + r662569;
        double r662571 = b;
        double r662572 = r662571 / r662554;
        double r662573 = r662563 * r662572;
        double r662574 = 1.0;
        double r662575 = r662573 + r662574;
        double r662576 = a;
        double r662577 = r662575 + r662576;
        double r662578 = r662577 * r662561;
        double r662579 = r662570 / r662578;
        double r662580 = r662561 * r662579;
        double r662581 = r662554 / r662567;
        double r662582 = r662563 / r662581;
        double r662583 = r662562 + r662582;
        double r662584 = r662576 + r662574;
        double r662585 = r662563 * r662571;
        double r662586 = r662585 / r662554;
        double r662587 = r662584 + r662586;
        double r662588 = r662583 / r662587;
        double r662589 = r662560 ? r662580 : r662588;
        return r662589;
}

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))))