Average Error: 10.7 → 10.7
Time: 4.0s
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 r675605 = x;
        double r675606 = y;
        double r675607 = z;
        double r675608 = r675606 * r675607;
        double r675609 = r675605 - r675608;
        double r675610 = t;
        double r675611 = a;
        double r675612 = r675611 * r675607;
        double r675613 = r675610 - r675612;
        double r675614 = r675609 / r675613;
        return r675614;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r675615 = x;
        double r675616 = y;
        double r675617 = z;
        double r675618 = r675616 * r675617;
        double r675619 = r675615 - r675618;
        double r675620 = t;
        double r675621 = a;
        double r675622 = r675621 * r675617;
        double r675623 = r675620 - r675622;
        double r675624 = r675619 / r675623;
        return r675624;
}

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

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

Derivation

  1. Initial program 10.7

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

  2. Final simplification10.7

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(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 3.5139522372978296e-86) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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