Average Error: 10.6 → 10.6
Time: 3.9s
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 r639246 = x;
        double r639247 = y;
        double r639248 = z;
        double r639249 = r639247 * r639248;
        double r639250 = r639246 - r639249;
        double r639251 = t;
        double r639252 = a;
        double r639253 = r639252 * r639248;
        double r639254 = r639251 - r639253;
        double r639255 = r639250 / r639254;
        return r639255;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r639256 = x;
        double r639257 = y;
        double r639258 = z;
        double r639259 = r639257 * r639258;
        double r639260 = r639256 - r639259;
        double r639261 = t;
        double r639262 = a;
        double r639263 = r639262 * r639258;
        double r639264 = r639261 - r639263;
        double r639265 = r639260 / r639264;
        return r639265;
}

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 +o rules:numerics
(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))))