Average Error: 10.6 → 10.6
Time: 17.0s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x - y \cdot z}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x - y \cdot z}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r34517741 = x;
        double r34517742 = y;
        double r34517743 = z;
        double r34517744 = r34517742 * r34517743;
        double r34517745 = r34517741 - r34517744;
        double r34517746 = t;
        double r34517747 = a;
        double r34517748 = r34517747 * r34517743;
        double r34517749 = r34517746 - r34517748;
        double r34517750 = r34517745 / r34517749;
        return r34517750;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r34517751 = x;
        double r34517752 = y;
        double r34517753 = z;
        double r34517754 = r34517752 * r34517753;
        double r34517755 = r34517751 - r34517754;
        double r34517756 = t;
        double r34517757 = a;
        double r34517758 = r34517757 * r34517753;
        double r34517759 = r34517756 - r34517758;
        double r34517760 = r34517755 / r34517759;
        return r34517760;
}

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

Original10.6
Target1.7
Herbie10.6
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.6

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

  3. Applied *-un-lft-identity10.6

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

  4. Applied associate-/r*10.6

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

  5. Simplified10.6

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

  6. Final simplification10.6

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

Reproduce

herbie shell --seed 2019192 
(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))))