Average Error: 10.0 → 2.9
Time: 9.7s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}
double f(double x, double y, double z, double t, double a) {
        double r14863684 = x;
        double r14863685 = y;
        double r14863686 = z;
        double r14863687 = r14863685 * r14863686;
        double r14863688 = r14863684 - r14863687;
        double r14863689 = t;
        double r14863690 = a;
        double r14863691 = r14863690 * r14863686;
        double r14863692 = r14863689 - r14863691;
        double r14863693 = r14863688 / r14863692;
        return r14863693;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r14863694 = x;
        double r14863695 = t;
        double r14863696 = a;
        double r14863697 = z;
        double r14863698 = r14863696 * r14863697;
        double r14863699 = r14863695 - r14863698;
        double r14863700 = r14863694 / r14863699;
        double r14863701 = y;
        double r14863702 = r14863695 / r14863697;
        double r14863703 = r14863702 - r14863696;
        double r14863704 = r14863701 / r14863703;
        double r14863705 = r14863700 - r14863704;
        return r14863705;
}

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

Original10.0
Target1.7
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344.0:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.0

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

  3. Applied div-sub10.0

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

  5. Applied associate-/l*7.7

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

  6. Taylor expanded around 0 2.9

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

  7. Final simplification2.9

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

Reproduce

herbie shell --seed 2019156 
(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))))