Average Error: 16.7 → 13.3
Time: 14.4s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.926403496931373984388403495533588251457 \cdot 10^{-63} \lor \neg \left(t \le 2.888050261675248381667778999049849702192 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(\sqrt[3]{\left(a + 1\right) + \frac{y \cdot b}{t}} \cdot \sqrt[3]{\left(a + 1\right) + \frac{y \cdot b}{t}}\right) \cdot \sqrt[3]{\left(a + 1\right) + \frac{y \cdot b}{t}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -8.926403496931373984388403495533588251457 \cdot 10^{-63} \lor \neg \left(t \le 2.888050261675248381667778999049849702192 \cdot 10^{-62}\right):\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r1096256 = x;
        double r1096257 = y;
        double r1096258 = z;
        double r1096259 = r1096257 * r1096258;
        double r1096260 = t;
        double r1096261 = r1096259 / r1096260;
        double r1096262 = r1096256 + r1096261;
        double r1096263 = a;
        double r1096264 = 1.0;
        double r1096265 = r1096263 + r1096264;
        double r1096266 = b;
        double r1096267 = r1096257 * r1096266;
        double r1096268 = r1096267 / r1096260;
        double r1096269 = r1096265 + r1096268;
        double r1096270 = r1096262 / r1096269;
        return r1096270;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1096271 = t;
        double r1096272 = -8.926403496931374e-63;
        bool r1096273 = r1096271 <= r1096272;
        double r1096274 = 2.8880502616752484e-62;
        bool r1096275 = r1096271 <= r1096274;
        double r1096276 = !r1096275;
        bool r1096277 = r1096273 || r1096276;
        double r1096278 = x;
        double r1096279 = y;
        double r1096280 = z;
        double r1096281 = r1096271 / r1096280;
        double r1096282 = r1096279 / r1096281;
        double r1096283 = r1096278 + r1096282;
        double r1096284 = a;
        double r1096285 = 1.0;
        double r1096286 = r1096284 + r1096285;
        double r1096287 = b;
        double r1096288 = r1096271 / r1096287;
        double r1096289 = r1096279 / r1096288;
        double r1096290 = r1096286 + r1096289;
        double r1096291 = r1096283 / r1096290;
        double r1096292 = r1096279 * r1096280;
        double r1096293 = r1096292 / r1096271;
        double r1096294 = r1096278 + r1096293;
        double r1096295 = r1096279 * r1096287;
        double r1096296 = r1096295 / r1096271;
        double r1096297 = r1096286 + r1096296;
        double r1096298 = cbrt(r1096297);
        double r1096299 = r1096298 * r1096298;
        double r1096300 = r1096299 * r1096298;
        double r1096301 = r1096294 / r1096300;
        double r1096302 = r1096277 ? r1096291 : r1096301;
        return r1096302;
}

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

Original16.7
Target13.4
Herbie13.3
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -8.926403496931374e-63 or 2.8880502616752484e-62 < t

    1. Initial program 12.0

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

    3. Applied associate-/l*9.2

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

    5. Applied associate-/l*6.1

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

    if -8.926403496931374e-63 < t < 2.8880502616752484e-62

    1. Initial program 24.4

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

    3. Applied add-cube-cbrt24.8

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

  4. Final simplification13.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.926403496931373984388403495533588251457 \cdot 10^{-63} \lor \neg \left(t \le 2.888050261675248381667778999049849702192 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(\sqrt[3]{\left(a + 1\right) + \frac{y \cdot b}{t}} \cdot \sqrt[3]{\left(a + 1\right) + \frac{y \cdot b}{t}}\right) \cdot \sqrt[3]{\left(a + 1\right) + \frac{y \cdot b}{t}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 
(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))))