Average Error: 16.0 → 12.7
Time: 12.3s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.815216233822953719290430647737818642386 \cdot 10^{-70} \lor \neg \left(y \le 22447358570953045353285915739422720\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{t} \cdot \left(z \cdot y\right)}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.815216233822953719290430647737818642386 \cdot 10^{-70} \lor \neg \left(y \le 22447358570953045353285915739422720\right):\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{1}{t} \cdot \left(z \cdot y\right)}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r577988 = x;
        double r577989 = y;
        double r577990 = z;
        double r577991 = r577989 * r577990;
        double r577992 = t;
        double r577993 = r577991 / r577992;
        double r577994 = r577988 + r577993;
        double r577995 = a;
        double r577996 = 1.0;
        double r577997 = r577995 + r577996;
        double r577998 = b;
        double r577999 = r577989 * r577998;
        double r578000 = r577999 / r577992;
        double r578001 = r577997 + r578000;
        double r578002 = r577994 / r578001;
        return r578002;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r578003 = y;
        double r578004 = -1.8152162338229537e-70;
        bool r578005 = r578003 <= r578004;
        double r578006 = 2.2447358570953045e+34;
        bool r578007 = r578003 <= r578006;
        double r578008 = !r578007;
        bool r578009 = r578005 || r578008;
        double r578010 = x;
        double r578011 = t;
        double r578012 = z;
        double r578013 = r578011 / r578012;
        double r578014 = r578003 / r578013;
        double r578015 = r578010 + r578014;
        double r578016 = a;
        double r578017 = 1.0;
        double r578018 = r578016 + r578017;
        double r578019 = b;
        double r578020 = r578019 / r578011;
        double r578021 = r578003 * r578020;
        double r578022 = r578018 + r578021;
        double r578023 = r578015 / r578022;
        double r578024 = 1.0;
        double r578025 = r578024 / r578011;
        double r578026 = r578012 * r578003;
        double r578027 = r578025 * r578026;
        double r578028 = r578010 + r578027;
        double r578029 = r578003 * r578019;
        double r578030 = r578011 / r578029;
        double r578031 = r578024 / r578030;
        double r578032 = r578018 + r578031;
        double r578033 = r578028 / r578032;
        double r578034 = r578009 ? r578023 : r578033;
        return r578034;
}

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
Target13.0
Herbie12.7
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.8152162338229537e-70 or 2.2447358570953045e+34 < y

    1. Initial program 27.6

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

    3. Applied associate-/l*24.9

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

    5. Applied *-un-lft-identity24.9

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

    6. Applied times-frac21.1

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

    7. Simplified21.1

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

    if -1.8152162338229537e-70 < y < 2.2447358570953045e+34

    1. Initial program 3.7

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

    3. Applied associate-/l*8.2

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

    5. Applied div-inv8.2

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

    6. Applied *-un-lft-identity8.2

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

    7. Applied times-frac3.8

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

    8. Simplified3.8

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

    10. Applied clear-num3.8

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

  4. Final simplification12.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.815216233822953719290430647737818642386 \cdot 10^{-70} \lor \neg \left(y \le 22447358570953045353285915739422720\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{t} \cdot \left(z \cdot y\right)}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 
(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))))