Average Error: 16.8 → 13.1
Time: 9.2s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.42436157433539514 \cdot 10^{38}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\frac{t}{b}}{\sqrt[3]{y}}}}\\ \mathbf{elif}\;t \le 1.1580474353914635 \cdot 10^{-29}:\\ \;\;\;\;\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.42436157433539514 \cdot 10^{38}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\frac{t}{b}}{\sqrt[3]{y}}}}\\

\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 r847464 = x;
        double r847465 = y;
        double r847466 = z;
        double r847467 = r847465 * r847466;
        double r847468 = t;
        double r847469 = r847467 / r847468;
        double r847470 = r847464 + r847469;
        double r847471 = a;
        double r847472 = 1.0;
        double r847473 = r847471 + r847472;
        double r847474 = b;
        double r847475 = r847465 * r847474;
        double r847476 = r847475 / r847468;
        double r847477 = r847473 + r847476;
        double r847478 = r847470 / r847477;
        return r847478;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r847479 = t;
        double r847480 = -2.424361574335395e+38;
        bool r847481 = r847479 <= r847480;
        double r847482 = x;
        double r847483 = y;
        double r847484 = z;
        double r847485 = r847479 / r847484;
        double r847486 = r847483 / r847485;
        double r847487 = r847482 + r847486;
        double r847488 = a;
        double r847489 = 1.0;
        double r847490 = r847488 + r847489;
        double r847491 = cbrt(r847483);
        double r847492 = r847491 * r847491;
        double r847493 = b;
        double r847494 = r847479 / r847493;
        double r847495 = r847494 / r847491;
        double r847496 = r847492 / r847495;
        double r847497 = r847490 + r847496;
        double r847498 = r847487 / r847497;
        double r847499 = 1.1580474353914635e-29;
        bool r847500 = r847479 <= r847499;
        double r847501 = r847483 * r847484;
        double r847502 = r847501 / r847479;
        double r847503 = r847482 + r847502;
        double r847504 = 1.0;
        double r847505 = r847483 * r847493;
        double r847506 = r847505 / r847479;
        double r847507 = r847490 + r847506;
        double r847508 = r847504 / r847507;
        double r847509 = r847503 * r847508;
        double r847510 = r847483 / r847479;
        double r847511 = r847510 * r847484;
        double r847512 = r847482 + r847511;
        double r847513 = r847483 / r847494;
        double r847514 = r847490 + r847513;
        double r847515 = r847512 / r847514;
        double r847516 = r847500 ? r847509 : r847515;
        double r847517 = r847481 ? r847498 : r847516;
        return r847517;
}

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 < -2.424361574335395e+38

    1. Initial program 11.4

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

    3. Applied associate-/l*7.6

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

    5. Applied associate-/l*3.3

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

    7. Applied add-cube-cbrt3.4

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

    8. Applied associate-/l*3.4

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

    if -2.424361574335395e+38 < t < 1.1580474353914635e-29

    1. Initial program 21.9

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

    3. Applied div-inv21.9

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

    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

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.42436157433539514 \cdot 10^{38}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\frac{t}{b}}{\sqrt[3]{y}}}}\\ \mathbf{elif}\;t \le 1.1580474353914635 \cdot 10^{-29}:\\ \;\;\;\;\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]

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))))