Average Error: 10.2 → 10.3
Time: 4.1s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{\frac{1}{t - a \cdot z}}{\frac{1}{x - y \cdot z}}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{\frac{1}{t - a \cdot z}}{\frac{1}{x - y \cdot z}}
double f(double x, double y, double z, double t, double a) {
        double r999926 = x;
        double r999927 = y;
        double r999928 = z;
        double r999929 = r999927 * r999928;
        double r999930 = r999926 - r999929;
        double r999931 = t;
        double r999932 = a;
        double r999933 = r999932 * r999928;
        double r999934 = r999931 - r999933;
        double r999935 = r999930 / r999934;
        return r999935;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r999936 = 1.0;
        double r999937 = t;
        double r999938 = a;
        double r999939 = z;
        double r999940 = r999938 * r999939;
        double r999941 = r999937 - r999940;
        double r999942 = r999936 / r999941;
        double r999943 = x;
        double r999944 = y;
        double r999945 = r999944 * r999939;
        double r999946 = r999943 - r999945;
        double r999947 = r999936 / r999946;
        double r999948 = r999942 / r999947;
        return r999948;
}

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

Original10.2
Target1.6
Herbie10.3
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.2

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

  3. Applied clear-num10.4

    \[\leadsto \color{blue}{\frac{1}{\frac{t - a \cdot z}{x - y \cdot z}}}\]
  4. Using strategy rm

  5. Applied div-inv10.5

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

  6. Applied associate-/r*10.3

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

  7. Final simplification10.3

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

Reproduce

herbie shell --seed 2019362 +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))))