Average Error: 16.4 → 13.1
Time: 8.6s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.535795100336089874765535724165452300231 \cdot 10^{58} \lor \neg \left(t \le 862649904951615160320\right):\\ \;\;\;\;\frac{\sqrt[3]{x + \frac{y}{\frac{t}{z}}} \cdot \sqrt[3]{x + \frac{y}{\frac{t}{z}}}}{\frac{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}{\sqrt[3]{x + \frac{y}{\frac{t}{z}}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5.535795100336089874765535724165452300231 \cdot 10^{58} \lor \neg \left(t \le 862649904951615160320\right):\\
\;\;\;\;\frac{\sqrt[3]{x + \frac{y}{\frac{t}{z}}} \cdot \sqrt[3]{x + \frac{y}{\frac{t}{z}}}}{\frac{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}{\sqrt[3]{x + \frac{y}{\frac{t}{z}}}}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r787172 = x;
        double r787173 = y;
        double r787174 = z;
        double r787175 = r787173 * r787174;
        double r787176 = t;
        double r787177 = r787175 / r787176;
        double r787178 = r787172 + r787177;
        double r787179 = a;
        double r787180 = 1.0;
        double r787181 = r787179 + r787180;
        double r787182 = b;
        double r787183 = r787173 * r787182;
        double r787184 = r787183 / r787176;
        double r787185 = r787181 + r787184;
        double r787186 = r787178 / r787185;
        return r787186;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r787187 = t;
        double r787188 = -5.53579510033609e+58;
        bool r787189 = r787187 <= r787188;
        double r787190 = 8.626499049516152e+20;
        bool r787191 = r787187 <= r787190;
        double r787192 = !r787191;
        bool r787193 = r787189 || r787192;
        double r787194 = x;
        double r787195 = y;
        double r787196 = z;
        double r787197 = r787187 / r787196;
        double r787198 = r787195 / r787197;
        double r787199 = r787194 + r787198;
        double r787200 = cbrt(r787199);
        double r787201 = r787200 * r787200;
        double r787202 = a;
        double r787203 = 1.0;
        double r787204 = r787202 + r787203;
        double r787205 = cbrt(r787187);
        double r787206 = r787205 * r787205;
        double r787207 = r787195 / r787206;
        double r787208 = b;
        double r787209 = r787208 / r787205;
        double r787210 = r787207 * r787209;
        double r787211 = r787204 + r787210;
        double r787212 = r787211 / r787200;
        double r787213 = r787201 / r787212;
        double r787214 = r787195 * r787196;
        double r787215 = r787214 / r787187;
        double r787216 = r787194 + r787215;
        double r787217 = r787195 * r787208;
        double r787218 = 1.0;
        double r787219 = r787218 / r787187;
        double r787220 = r787217 * r787219;
        double r787221 = r787204 + r787220;
        double r787222 = r787216 / r787221;
        double r787223 = r787193 ? r787213 : r787222;
        return r787223;
}

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

Original16.4
Target12.7
Herbie13.1
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -5.53579510033609e+58 or 8.626499049516152e+20 < t

    1. Initial program 11.7

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

    3. Applied add-cube-cbrt11.8

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

    4. Applied times-frac8.6

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

    6. Applied associate-/l*3.5

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

    8. Applied add-cube-cbrt4.4

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

    9. Applied associate-/l*4.5

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

    if -5.53579510033609e+58 < t < 8.626499049516152e+20

    1. Initial program 20.2

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

    3. Applied div-inv20.2

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

  4. Final simplification13.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.535795100336089874765535724165452300231 \cdot 10^{58} \lor \neg \left(t \le 862649904951615160320\right):\\ \;\;\;\;\frac{\sqrt[3]{x + \frac{y}{\frac{t}{z}}} \cdot \sqrt[3]{x + \frac{y}{\frac{t}{z}}}}{\frac{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}{\sqrt[3]{x + \frac{y}{\frac{t}{z}}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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))))