Average Error: 2.9 → 2.1
Time: 7.3s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y - z \cdot t \le -2.066141103408040992318038433191118152835 \cdot 10^{236}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;y - z \cdot t \le -2.066141103408040992318038433191118152835 \cdot 10^{236}:\\
\;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{y - z \cdot t}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r593550 = x;
        double r593551 = y;
        double r593552 = z;
        double r593553 = t;
        double r593554 = r593552 * r593553;
        double r593555 = r593551 - r593554;
        double r593556 = r593550 / r593555;
        return r593556;
}
↓
double f(double x, double y, double z, double t) {
        double r593557 = y;
        double r593558 = z;
        double r593559 = t;
        double r593560 = r593558 * r593559;
        double r593561 = r593557 - r593560;
        double r593562 = -2.066141103408041e+236;
        bool r593563 = r593561 <= r593562;
        double r593564 = 1.0;
        double r593565 = x;
        double r593566 = r593557 / r593565;
        double r593567 = r593565 / r593558;
        double r593568 = r593559 / r593567;
        double r593569 = r593566 - r593568;
        double r593570 = r593564 / r593569;
        double r593571 = r593565 / r593561;
        double r593572 = r593563 ? r593570 : r593571;
        return r593572;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.9
Target1.8
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- y (* z t)) < -2.066141103408041e+236

    1. Initial program 9.9

      \[\frac{x}{y - z \cdot t}\]
    2. Using strategy rm

    3. Applied clear-num10.2

      \[\leadsto \color{blue}{\frac{1}{\frac{y - z \cdot t}{x}}}\]
    4. Using strategy rm

    5. Applied div-sub13.5

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} - \frac{z \cdot t}{x}}}\]

    6. Simplified4.8

      \[\leadsto \frac{1}{\frac{y}{x} - \color{blue}{\frac{t}{\frac{x}{z}}}}\]

    if -2.066141103408041e+236 < (- y (* z t))

    1. Initial program 1.7

      \[\frac{x}{y - z \cdot t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \cdot t \le -2.066141103408040992318038433191118152835 \cdot 10^{236}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e50) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 2.13783064348764444e131) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t)))))

  (/ x (- y (* z t))))