Average Error: 11.0 → 11.0
Time: 20.4s
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 r44890269 = x;
        double r44890270 = y;
        double r44890271 = z;
        double r44890272 = r44890270 * r44890271;
        double r44890273 = r44890269 - r44890272;
        double r44890274 = t;
        double r44890275 = a;
        double r44890276 = r44890275 * r44890271;
        double r44890277 = r44890274 - r44890276;
        double r44890278 = r44890273 / r44890277;
        return r44890278;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r44890279 = x;
        double r44890280 = y;
        double r44890281 = z;
        double r44890282 = r44890280 * r44890281;
        double r44890283 = r44890279 - r44890282;
        double r44890284 = t;
        double r44890285 = a;
        double r44890286 = r44890285 * r44890281;
        double r44890287 = r44890284 - r44890286;
        double r44890288 = r44890283 / r44890287;
        return r44890288;
}

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

Original11.0
Target1.7
Herbie11.0
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 11.0

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

  2. Final simplification11.0

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

Reproduce

herbie shell --seed 2019174 +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))))