Average Error: 16.6 → 13.2
Time: 15.6s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.456503524337497909720375927850262703403 \cdot 10^{46} \lor \neg \left(t \le 6.661904461324813894273113559045132359071 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{x + \frac{z}{t} \cdot y}{\left(1 + a\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(1 + a\right) + \frac{b \cdot y}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.456503524337497909720375927850262703403 \cdot 10^{46} \lor \neg \left(t \le 6.661904461324813894273113559045132359071 \cdot 10^{-43}\right):\\
\;\;\;\;\frac{x + \frac{z}{t} \cdot y}{\left(1 + a\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r640255 = x;
        double r640256 = y;
        double r640257 = z;
        double r640258 = r640256 * r640257;
        double r640259 = t;
        double r640260 = r640258 / r640259;
        double r640261 = r640255 + r640260;
        double r640262 = a;
        double r640263 = 1.0;
        double r640264 = r640262 + r640263;
        double r640265 = b;
        double r640266 = r640256 * r640265;
        double r640267 = r640266 / r640259;
        double r640268 = r640264 + r640267;
        double r640269 = r640261 / r640268;
        return r640269;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r640270 = t;
        double r640271 = -1.456503524337498e+46;
        bool r640272 = r640270 <= r640271;
        double r640273 = 6.661904461324814e-43;
        bool r640274 = r640270 <= r640273;
        double r640275 = !r640274;
        bool r640276 = r640272 || r640275;
        double r640277 = x;
        double r640278 = z;
        double r640279 = r640278 / r640270;
        double r640280 = y;
        double r640281 = r640279 * r640280;
        double r640282 = r640277 + r640281;
        double r640283 = 1.0;
        double r640284 = a;
        double r640285 = r640283 + r640284;
        double r640286 = 1.0;
        double r640287 = r640270 / r640280;
        double r640288 = b;
        double r640289 = r640287 / r640288;
        double r640290 = r640286 / r640289;
        double r640291 = r640285 + r640290;
        double r640292 = r640282 / r640291;
        double r640293 = r640280 * r640278;
        double r640294 = r640293 / r640270;
        double r640295 = r640277 + r640294;
        double r640296 = r640288 * r640280;
        double r640297 = r640296 / r640270;
        double r640298 = r640285 + r640297;
        double r640299 = r640295 / r640298;
        double r640300 = r640276 ? r640292 : r640299;
        return r640300;
}

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

Original16.6
Target12.8
Herbie13.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.456503524337498e+46 or 6.661904461324814e-43 < t

    1. Initial program 11.0

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

    3. Applied clear-num11.0

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

    4. Simplified8.4

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

    6. Applied *-un-lft-identity8.4

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

    7. Applied times-frac4.4

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

    8. Simplified4.4

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

    if -1.456503524337498e+46 < t < 6.661904461324814e-43

    1. Initial program 22.2

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

  4. Final simplification13.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.456503524337497909720375927850262703403 \cdot 10^{46} \lor \neg \left(t \le 6.661904461324813894273113559045132359071 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{x + \frac{z}{t} \cdot y}{\left(1 + a\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(1 + a\right) + \frac{b \cdot y}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))