Average Error: 10.8 → 11.2
Time: 15.1s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{1}{\frac{t - a \cdot z}{x - z \cdot y}}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{1}{\frac{t - a \cdot z}{x - z \cdot y}}
double f(double x, double y, double z, double t, double a) {
        double r557263 = x;
        double r557264 = y;
        double r557265 = z;
        double r557266 = r557264 * r557265;
        double r557267 = r557263 - r557266;
        double r557268 = t;
        double r557269 = a;
        double r557270 = r557269 * r557265;
        double r557271 = r557268 - r557270;
        double r557272 = r557267 / r557271;
        return r557272;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r557273 = 1.0;
        double r557274 = t;
        double r557275 = a;
        double r557276 = z;
        double r557277 = r557275 * r557276;
        double r557278 = r557274 - r557277;
        double r557279 = x;
        double r557280 = y;
        double r557281 = r557276 * r557280;
        double r557282 = r557279 - r557281;
        double r557283 = r557278 / r557282;
        double r557284 = r557273 / r557283;
        return r557284;
}

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
Herbie11.2
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

  3. Applied clear-num11.2

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

  4. Simplified11.2

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

  5. Final simplification11.2

    \[\leadsto \frac{1}{\frac{t - a \cdot z}{x - z \cdot y}}\]

Reproduce

herbie shell --seed 2019209 +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 3.51395223729782958e-86) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))