Average Error: 10.8 → 10.8
Time: 9.7s
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 r580595 = x;
        double r580596 = y;
        double r580597 = z;
        double r580598 = r580596 * r580597;
        double r580599 = r580595 - r580598;
        double r580600 = t;
        double r580601 = a;
        double r580602 = r580601 * r580597;
        double r580603 = r580600 - r580602;
        double r580604 = r580599 / r580603;
        return r580604;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r580605 = x;
        double r580606 = y;
        double r580607 = z;
        double r580608 = r580606 * r580607;
        double r580609 = r580605 - r580608;
        double r580610 = t;
        double r580611 = a;
        double r580612 = r580611 * r580607;
        double r580613 = r580610 - r580612;
        double r580614 = r580609 / r580613;
        return r580614;
}

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

Original10.8
Target1.9
Herbie10.8
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

  2. Final simplification10.8

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

Reproduce

herbie shell --seed 2019294 
(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 3.51395223729782958e-86) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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