Average Error: 2.9 → 0.8
Time: 9.1s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t = -\infty \lor \neg \left(z \cdot t \le 8.104691396034629497642141956511498930967 \cdot 10^{229}\right):\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t = -\infty \lor \neg \left(z \cdot t \le 8.104691396034629497642141956511498930967 \cdot 10^{229}\right):\\
\;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r472656 = x;
        double r472657 = y;
        double r472658 = z;
        double r472659 = t;
        double r472660 = r472658 * r472659;
        double r472661 = r472657 - r472660;
        double r472662 = r472656 / r472661;
        return r472662;
}
↓
double f(double x, double y, double z, double t) {
        double r472663 = z;
        double r472664 = t;
        double r472665 = r472663 * r472664;
        double r472666 = -inf.0;
        bool r472667 = r472665 <= r472666;
        double r472668 = 8.10469139603463e+229;
        bool r472669 = r472665 <= r472668;
        double r472670 = !r472669;
        bool r472671 = r472667 || r472670;
        double r472672 = 1.0;
        double r472673 = y;
        double r472674 = x;
        double r472675 = r472673 / r472674;
        double r472676 = r472664 / r472674;
        double r472677 = r472676 * r472663;
        double r472678 = r472675 - r472677;
        double r472679 = r472672 / r472678;
        double r472680 = r472673 - r472665;
        double r472681 = r472674 / r472680;
        double r472682 = r472671 ? r472679 : r472681;
        return r472682;
}

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
Target1.7
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z t) < -inf.0 or 8.10469139603463e+229 < (* z t)

    1. Initial program 16.9

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

    3. Applied clear-num17.2

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

    4. Simplified17.2

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

    6. Applied div-sub20.8

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

    7. Simplified4.5

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

    if -inf.0 < (* z t) < 8.10469139603463e+229

    1. Initial program 0.1

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t = -\infty \lor \neg \left(z \cdot t \le 8.104691396034629497642141956511498930967 \cdot 10^{229}\right):\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(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))))