Average Error: 10.4 → 10.5
Time: 21.5s
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 r29423876 = x;
        double r29423877 = y;
        double r29423878 = z;
        double r29423879 = r29423877 * r29423878;
        double r29423880 = r29423876 - r29423879;
        double r29423881 = t;
        double r29423882 = a;
        double r29423883 = r29423882 * r29423878;
        double r29423884 = r29423881 - r29423883;
        double r29423885 = r29423880 / r29423884;
        return r29423885;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29423886 = 1.0;
        double r29423887 = t;
        double r29423888 = a;
        double r29423889 = z;
        double r29423890 = r29423888 * r29423889;
        double r29423891 = r29423887 - r29423890;
        double r29423892 = r29423886 / r29423891;
        double r29423893 = x;
        double r29423894 = y;
        double r29423895 = r29423894 * r29423889;
        double r29423896 = r29423893 - r29423895;
        double r29423897 = r29423886 / r29423896;
        double r29423898 = r29423892 / r29423897;
        return r29423898;
}

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

Original10.4
Target1.8
Herbie10.5
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344.0:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.4

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

  3. Applied clear-num10.7

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

  5. Applied div-inv10.8

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

  6. Applied associate-/r*10.5

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

  7. Final simplification10.5

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(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 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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