Average Error: 10.6 → 10.6
Time: 3.6s
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 r775787 = x;
        double r775788 = y;
        double r775789 = z;
        double r775790 = r775788 * r775789;
        double r775791 = r775787 - r775790;
        double r775792 = t;
        double r775793 = a;
        double r775794 = r775793 * r775789;
        double r775795 = r775792 - r775794;
        double r775796 = r775791 / r775795;
        return r775796;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r775797 = x;
        double r775798 = y;
        double r775799 = z;
        double r775800 = r775798 * r775799;
        double r775801 = r775797 - r775800;
        double r775802 = t;
        double r775803 = a;
        double r775804 = r775803 * r775799;
        double r775805 = r775802 - r775804;
        double r775806 = r775801 / r775805;
        return r775806;
}

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

Original10.6
Target1.8
Herbie10.6
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.6

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

  2. Final simplification10.6

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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