Average Error: 16.8 → 14.3
Time: 7.3s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.309289604935398694661904518216916342979 \cdot 10^{121}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \left(\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt[3]{b} \cdot \sqrt[3]{b}}{\sqrt[3]{1}}\right) \cdot \frac{\sqrt[3]{b}}{\sqrt[3]{t}}}\\ \mathbf{elif}\;y \le 7.19042889409541425182067272563551310774 \cdot 10^{107}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.309289604935398694661904518216916342979 \cdot 10^{121}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \left(\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt[3]{b} \cdot \sqrt[3]{b}}{\sqrt[3]{1}}\right) \cdot \frac{\sqrt[3]{b}}{\sqrt[3]{t}}}\\

\mathbf{elif}\;y \le 7.19042889409541425182067272563551310774 \cdot 10^{107}:\\
\;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r940208 = x;
        double r940209 = y;
        double r940210 = z;
        double r940211 = r940209 * r940210;
        double r940212 = t;
        double r940213 = r940211 / r940212;
        double r940214 = r940208 + r940213;
        double r940215 = a;
        double r940216 = 1.0;
        double r940217 = r940215 + r940216;
        double r940218 = b;
        double r940219 = r940209 * r940218;
        double r940220 = r940219 / r940212;
        double r940221 = r940217 + r940220;
        double r940222 = r940214 / r940221;
        return r940222;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r940223 = y;
        double r940224 = -5.309289604935399e+121;
        bool r940225 = r940223 <= r940224;
        double r940226 = x;
        double r940227 = t;
        double r940228 = z;
        double r940229 = r940227 / r940228;
        double r940230 = r940223 / r940229;
        double r940231 = r940226 + r940230;
        double r940232 = a;
        double r940233 = 1.0;
        double r940234 = r940232 + r940233;
        double r940235 = cbrt(r940227);
        double r940236 = r940235 * r940235;
        double r940237 = r940223 / r940236;
        double r940238 = b;
        double r940239 = cbrt(r940238);
        double r940240 = r940239 * r940239;
        double r940241 = 1.0;
        double r940242 = cbrt(r940241);
        double r940243 = r940240 / r940242;
        double r940244 = r940237 * r940243;
        double r940245 = r940239 / r940235;
        double r940246 = r940244 * r940245;
        double r940247 = r940234 + r940246;
        double r940248 = r940231 / r940247;
        double r940249 = 7.190428894095414e+107;
        bool r940250 = r940223 <= r940249;
        double r940251 = r940223 / r940227;
        double r940252 = r940251 * r940228;
        double r940253 = r940226 + r940252;
        double r940254 = r940223 * r940238;
        double r940255 = r940254 / r940227;
        double r940256 = r940234 + r940255;
        double r940257 = r940253 / r940256;
        double r940258 = r940238 / r940235;
        double r940259 = r940237 * r940258;
        double r940260 = r940234 + r940259;
        double r940261 = r940231 / r940260;
        double r940262 = r940250 ? r940257 : r940261;
        double r940263 = r940225 ? r940248 : r940262;
        return r940263;
}

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
Target13.4
Herbie14.3
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -5.309289604935399e+121

    1. Initial program 38.0

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

    3. Applied associate-/l*33.9

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

    5. Applied add-cube-cbrt34.0

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

    6. Applied times-frac29.8

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

    8. Applied *-un-lft-identity29.8

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

    9. Applied cbrt-prod29.8

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

    10. Applied add-cube-cbrt29.8

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

    11. Applied times-frac29.8

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

    12. Applied associate-*r*29.8

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

    if -5.309289604935399e+121 < y < 7.190428894095414e+107

    1. Initial program 7.6

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

    3. Applied associate-/l*9.8

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

    5. Applied associate-/r/7.6

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

    if 7.190428894095414e+107 < y

    1. Initial program 37.1

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

    3. Applied associate-/l*33.2

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

    5. Applied add-cube-cbrt33.3

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

    6. Applied times-frac29.5

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

  4. Final simplification14.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.309289604935398694661904518216916342979 \cdot 10^{121}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \left(\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt[3]{b} \cdot \sqrt[3]{b}}{\sqrt[3]{1}}\right) \cdot \frac{\sqrt[3]{b}}{\sqrt[3]{t}}}\\ \mathbf{elif}\;y \le 7.19042889409541425182067272563551310774 \cdot 10^{107}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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))))