Average Error: 11.1 → 11.1
Time: 18.1s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x - y \cdot z}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x - y \cdot z}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r38619673 = x;
        double r38619674 = y;
        double r38619675 = z;
        double r38619676 = r38619674 * r38619675;
        double r38619677 = r38619673 - r38619676;
        double r38619678 = t;
        double r38619679 = a;
        double r38619680 = r38619679 * r38619675;
        double r38619681 = r38619678 - r38619680;
        double r38619682 = r38619677 / r38619681;
        return r38619682;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r38619683 = x;
        double r38619684 = y;
        double r38619685 = z;
        double r38619686 = r38619684 * r38619685;
        double r38619687 = r38619683 - r38619686;
        double r38619688 = t;
        double r38619689 = a;
        double r38619690 = r38619689 * r38619685;
        double r38619691 = r38619688 - r38619690;
        double r38619692 = r38619687 / r38619691;
        return r38619692;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.1
Target1.7
Herbie11.1
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 11.1

    \[\frac{x - y \cdot z}{t - a \cdot z}\]

  2. Taylor expanded around inf 11.1

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

  3. Final simplification11.1

    \[\leadsto \frac{x - y \cdot z}{t - a \cdot z}\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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