Average Error: 10.4 → 10.4
Time: 4.1s
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 r843162 = x;
        double r843163 = y;
        double r843164 = z;
        double r843165 = r843163 * r843164;
        double r843166 = r843162 - r843165;
        double r843167 = t;
        double r843168 = a;
        double r843169 = r843168 * r843164;
        double r843170 = r843167 - r843169;
        double r843171 = r843166 / r843170;
        return r843171;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r843172 = x;
        double r843173 = y;
        double r843174 = z;
        double r843175 = r843173 * r843174;
        double r843176 = r843172 - r843175;
        double r843177 = t;
        double r843178 = a;
        double r843179 = r843178 * r843174;
        double r843180 = r843177 - r843179;
        double r843181 = r843176 / r843180;
        return r843181;
}

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

Original10.4
Target1.6
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.4

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

  2. Final simplification10.4

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

Reproduce

herbie shell --seed 2020100 
(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))))