Average Error: 16.6 → 16.6
Time: 11.2s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
double f(double x, double y, double z, double t, double a, double b) {
        double r483207 = x;
        double r483208 = y;
        double r483209 = z;
        double r483210 = r483208 * r483209;
        double r483211 = t;
        double r483212 = r483210 / r483211;
        double r483213 = r483207 + r483212;
        double r483214 = a;
        double r483215 = 1.0;
        double r483216 = r483214 + r483215;
        double r483217 = b;
        double r483218 = r483208 * r483217;
        double r483219 = r483218 / r483211;
        double r483220 = r483216 + r483219;
        double r483221 = r483213 / r483220;
        return r483221;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r483222 = x;
        double r483223 = y;
        double r483224 = z;
        double r483225 = r483223 * r483224;
        double r483226 = t;
        double r483227 = r483225 / r483226;
        double r483228 = r483222 + r483227;
        double r483229 = a;
        double r483230 = 1.0;
        double r483231 = r483229 + r483230;
        double r483232 = b;
        double r483233 = r483223 * r483232;
        double r483234 = r483233 / r483226;
        double r483235 = r483231 + r483234;
        double r483236 = r483228 / r483235;
        return r483236;
}

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

Original16.6
Target12.9
Herbie16.6
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.2817596076120453e-54 or 1.055181792592207e-16 < t

    1. Initial program 11.6

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

    3. Applied add-cube-cbrt11.7

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

    4. Applied associate-/r*11.7

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

    6. Applied *-un-lft-identity11.7

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

    7. Applied *-un-lft-identity11.7

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

    8. Applied times-frac11.7

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

    9. Simplified11.7

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

    10. Simplified8.9

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

    12. Applied *-un-lft-identity8.9

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

    13. Applied times-frac4.7

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

    14. Simplified4.7

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

    if -2.2817596076120453e-54 < t < 1.055181792592207e-16

    1. Initial program 23.0

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

    3. Applied div-inv23.1

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

  4. Final simplification16.6

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

Reproduce

herbie shell --seed 2019291 
(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 3.0369671037372459e-130) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1) (/ (* y b) t))))