Average Error: 10.8 → 10.8
Time: 4.2s
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 r714867 = x;
        double r714868 = y;
        double r714869 = z;
        double r714870 = r714868 * r714869;
        double r714871 = r714867 - r714870;
        double r714872 = t;
        double r714873 = a;
        double r714874 = r714873 * r714869;
        double r714875 = r714872 - r714874;
        double r714876 = r714871 / r714875;
        return r714876;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r714877 = x;
        double r714878 = y;
        double r714879 = z;
        double r714880 = r714878 * r714879;
        double r714881 = r714877 - r714880;
        double r714882 = t;
        double r714883 = a;
        double r714884 = r714883 * r714879;
        double r714885 = r714882 - r714884;
        double r714886 = r714881 / r714885;
        return r714886;
}

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

Original10.8
Target1.8
Herbie10.8
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

  2. Final simplification10.8

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

Reproduce

herbie shell --seed 2020021 +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))))