Average Error: 10.7 → 10.7
Time: 17.9s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x - z \cdot y}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x - z \cdot y}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r43536214 = x;
        double r43536215 = y;
        double r43536216 = z;
        double r43536217 = r43536215 * r43536216;
        double r43536218 = r43536214 - r43536217;
        double r43536219 = t;
        double r43536220 = a;
        double r43536221 = r43536220 * r43536216;
        double r43536222 = r43536219 - r43536221;
        double r43536223 = r43536218 / r43536222;
        return r43536223;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r43536224 = x;
        double r43536225 = z;
        double r43536226 = y;
        double r43536227 = r43536225 * r43536226;
        double r43536228 = r43536224 - r43536227;
        double r43536229 = t;
        double r43536230 = a;
        double r43536231 = r43536230 * r43536225;
        double r43536232 = r43536229 - r43536231;
        double r43536233 = r43536228 / r43536232;
        return r43536233;
}

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

Original10.7
Target1.9
Herbie10.7
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.7

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

  2. Final simplification10.7

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

Reproduce

herbie shell --seed 2019171 
(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))))