Average Error: 10.3 → 10.4
Time: 19.8s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\left(x - z \cdot y\right) \cdot \frac{1}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\left(x - z \cdot y\right) \cdot \frac{1}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r32633682 = x;
        double r32633683 = y;
        double r32633684 = z;
        double r32633685 = r32633683 * r32633684;
        double r32633686 = r32633682 - r32633685;
        double r32633687 = t;
        double r32633688 = a;
        double r32633689 = r32633688 * r32633684;
        double r32633690 = r32633687 - r32633689;
        double r32633691 = r32633686 / r32633690;
        return r32633691;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r32633692 = x;
        double r32633693 = z;
        double r32633694 = y;
        double r32633695 = r32633693 * r32633694;
        double r32633696 = r32633692 - r32633695;
        double r32633697 = 1.0;
        double r32633698 = t;
        double r32633699 = a;
        double r32633700 = r32633699 * r32633693;
        double r32633701 = r32633698 - r32633700;
        double r32633702 = r32633697 / r32633701;
        double r32633703 = r32633696 * r32633702;
        return r32633703;
}

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

Original10.3
Target1.6
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.3

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

  3. Applied div-inv10.4

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

  4. Final simplification10.4

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

Reproduce

herbie shell --seed 2019179 +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)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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