Average Error: 10.8 → 11.0
Time: 17.2s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\left(x - z \cdot y\right) \cdot \frac{1}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\left(x - z \cdot y\right) \cdot \frac{1}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r31781848 = x;
        double r31781849 = y;
        double r31781850 = z;
        double r31781851 = r31781849 * r31781850;
        double r31781852 = r31781848 - r31781851;
        double r31781853 = t;
        double r31781854 = a;
        double r31781855 = r31781854 * r31781850;
        double r31781856 = r31781853 - r31781855;
        double r31781857 = r31781852 / r31781856;
        return r31781857;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r31781858 = x;
        double r31781859 = z;
        double r31781860 = y;
        double r31781861 = r31781859 * r31781860;
        double r31781862 = r31781858 - r31781861;
        double r31781863 = 1.0;
        double r31781864 = t;
        double r31781865 = a;
        double r31781866 = r31781865 * r31781859;
        double r31781867 = r31781864 - r31781866;
        double r31781868 = r31781863 / r31781867;
        double r31781869 = r31781862 * r31781868;
        return r31781869;
}

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
Target1.7
Herbie11.0
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.8

    \[\frac{x - y \cdot z}{t - a \cdot z}\]
  2. Using strategy rm

  3. Applied div-inv11.0

    \[\leadsto \color{blue}{\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}}\]

  4. Final simplification11.0

    \[\leadsto \left(x - z \cdot y\right) \cdot \frac{1}{t - a \cdot z}\]

Reproduce

herbie shell --seed 2019172 
(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))))