Average Error: 16.8 → 13.7
Time: 5.0s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -7.09677384719647 \cdot 10^{-15} \lor \neg \left(y \le 5.699432921841444 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\left(a + 1\right) + \frac{y \cdot b}{t}}{x + \frac{y}{t} \cdot z}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -7.09677384719647 \cdot 10^{-15} \lor \neg \left(y \le 5.699432921841444 \cdot 10^{-104}\right):\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r1242372 = x;
        double r1242373 = y;
        double r1242374 = z;
        double r1242375 = r1242373 * r1242374;
        double r1242376 = t;
        double r1242377 = r1242375 / r1242376;
        double r1242378 = r1242372 + r1242377;
        double r1242379 = a;
        double r1242380 = 1.0;
        double r1242381 = r1242379 + r1242380;
        double r1242382 = b;
        double r1242383 = r1242373 * r1242382;
        double r1242384 = r1242383 / r1242376;
        double r1242385 = r1242381 + r1242384;
        double r1242386 = r1242378 / r1242385;
        return r1242386;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1242387 = y;
        double r1242388 = -7.09677384719647e-15;
        bool r1242389 = r1242387 <= r1242388;
        double r1242390 = 5.699432921841444e-104;
        bool r1242391 = r1242387 <= r1242390;
        double r1242392 = !r1242391;
        bool r1242393 = r1242389 || r1242392;
        double r1242394 = x;
        double r1242395 = t;
        double r1242396 = z;
        double r1242397 = r1242395 / r1242396;
        double r1242398 = r1242387 / r1242397;
        double r1242399 = r1242394 + r1242398;
        double r1242400 = a;
        double r1242401 = 1.0;
        double r1242402 = r1242400 + r1242401;
        double r1242403 = b;
        double r1242404 = r1242403 / r1242395;
        double r1242405 = r1242387 * r1242404;
        double r1242406 = r1242402 + r1242405;
        double r1242407 = r1242399 / r1242406;
        double r1242408 = 1.0;
        double r1242409 = r1242387 * r1242403;
        double r1242410 = r1242409 / r1242395;
        double r1242411 = r1242402 + r1242410;
        double r1242412 = r1242387 / r1242395;
        double r1242413 = r1242412 * r1242396;
        double r1242414 = r1242394 + r1242413;
        double r1242415 = r1242411 / r1242414;
        double r1242416 = r1242408 / r1242415;
        double r1242417 = r1242393 ? r1242407 : r1242416;
        return r1242417;
}

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
Target13.3
Herbie13.7
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -7.09677384719647e-15 or 5.699432921841444e-104 < y

    1. Initial program 26.8

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

    3. Applied associate-/l*24.3

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

    5. Applied *-un-lft-identity24.3

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

    6. Applied times-frac20.8

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

    7. Simplified20.8

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

    if -7.09677384719647e-15 < y < 5.699432921841444e-104

    1. Initial program 3.3

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

    3. Applied associate-/l*8.4

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

    5. Applied associate-/r/3.7

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

    7. Applied clear-num4.0

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

  4. Final simplification13.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7.09677384719647 \cdot 10^{-15} \lor \neg \left(y \le 5.699432921841444 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\left(a + 1\right) + \frac{y \cdot b}{t}}{x + \frac{y}{t} \cdot z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(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))))