Average Error: 3.0 → 1.9
Time: 14.4s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t = -\infty:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t = -\infty:\\
\;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r441208 = x;
        double r441209 = y;
        double r441210 = z;
        double r441211 = t;
        double r441212 = r441210 * r441211;
        double r441213 = r441209 - r441212;
        double r441214 = r441208 / r441213;
        return r441214;
}
↓
double f(double x, double y, double z, double t) {
        double r441215 = z;
        double r441216 = t;
        double r441217 = r441215 * r441216;
        double r441218 = -inf.0;
        bool r441219 = r441217 <= r441218;
        double r441220 = 1.0;
        double r441221 = y;
        double r441222 = x;
        double r441223 = r441221 / r441222;
        double r441224 = r441215 / r441222;
        double r441225 = r441224 * r441216;
        double r441226 = r441223 - r441225;
        double r441227 = r441220 / r441226;
        double r441228 = r441221 - r441217;
        double r441229 = r441222 / r441228;
        double r441230 = r441219 ? r441227 : r441229;
        return r441230;
}

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

Original3.0
Target1.7
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z t) < -inf.0

    1. Initial program 20.9

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

    3. Applied clear-num20.9

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

    5. Applied div-sub24.4

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

    6. Simplified4.3

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

    if -inf.0 < (* z t)

    1. Initial program 1.7

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t = -\infty:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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))))