Average Error: 16.5 → 17.1
Time: 7.0s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\frac{x + y \cdot \frac{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 r418738 = x;
        double r418739 = y;
        double r418740 = z;
        double r418741 = r418739 * r418740;
        double r418742 = t;
        double r418743 = r418741 / r418742;
        double r418744 = r418738 + r418743;
        double r418745 = a;
        double r418746 = 1.0;
        double r418747 = r418745 + r418746;
        double r418748 = b;
        double r418749 = r418739 * r418748;
        double r418750 = r418749 / r418742;
        double r418751 = r418747 + r418750;
        double r418752 = r418744 / r418751;
        return r418752;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r418753 = x;
        double r418754 = y;
        double r418755 = z;
        double r418756 = t;
        double r418757 = r418755 / r418756;
        double r418758 = r418754 * r418757;
        double r418759 = r418753 + r418758;
        double r418760 = a;
        double r418761 = 1.0;
        double r418762 = r418760 + r418761;
        double r418763 = b;
        double r418764 = r418754 * r418763;
        double r418765 = r418764 / r418756;
        double r418766 = r418762 + r418765;
        double r418767 = r418759 / r418766;
        return r418767;
}

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

Original16.5
Target13.3
Herbie17.1
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.303222534554686e+122

    1. Initial program 37.4

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

    3. Applied *-un-lft-identity37.4

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

    4. Applied times-frac32.6

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

    5. Simplified32.6

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

    if -1.303222534554686e+122 < y

    1. Initial program 13.0

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

    3. Applied div-inv13.0

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

  4. Final simplification17.1

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

Reproduce

herbie shell --seed 2019304 
(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))))