Average Error: 10.7 → 11.1
Time: 51.5s
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 r37631321 = x;
        double r37631322 = y;
        double r37631323 = z;
        double r37631324 = r37631322 * r37631323;
        double r37631325 = r37631321 - r37631324;
        double r37631326 = t;
        double r37631327 = a;
        double r37631328 = r37631327 * r37631323;
        double r37631329 = r37631326 - r37631328;
        double r37631330 = r37631325 / r37631329;
        return r37631330;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r37631331 = 1.0;
        double r37631332 = t;
        double r37631333 = a;
        double r37631334 = z;
        double r37631335 = r37631333 * r37631334;
        double r37631336 = r37631332 - r37631335;
        double r37631337 = x;
        double r37631338 = y;
        double r37631339 = r37631334 * r37631338;
        double r37631340 = r37631337 - r37631339;
        double r37631341 = r37631336 / r37631340;
        double r37631342 = r37631331 / r37631341;
        return r37631342;
}

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

Original10.7
Target1.7
Herbie11.1
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.7

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

  3. Applied clear-num11.1

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

  4. Final simplification11.1

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

Reproduce

herbie shell --seed 2019168 
(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))))