Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Average Error: 10.5 → 10.6

Time: 18.4s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r33736048 = x;
        double r33736049 = y;
        double r33736050 = z;
        double r33736051 = r33736049 * r33736050;
        double r33736052 = r33736048 - r33736051;
        double r33736053 = t;
        double r33736054 = a;
        double r33736055 = r33736054 * r33736050;
        double r33736056 = r33736053 - r33736055;
        double r33736057 = r33736052 / r33736056;
        return r33736057;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r33736058 = x;
        double r33736059 = z;
        double r33736060 = y;
        double r33736061 = r33736059 * r33736060;
        double r33736062 = r33736058 - r33736061;
        double r33736063 = 1.0;
        double r33736064 = t;
        double r33736065 = a;
        double r33736066 = r33736065 * r33736059;
        double r33736067 = r33736064 - r33736066;
        double r33736068 = r33736063 / r33736067;
        double r33736069 = r33736062 * r33736068;
        return r33736069;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.5
Target	1.8
Herbie	10.6

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

Derivation

1. Initial program 10.5

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

3. Applied div-inv 10.6

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

4. Final simplification 10.6

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

Reproduce

herbie shell --seed 2019170 
(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))))