Average Error: 11.0 → 11.0
Time: 18.3s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x - z \cdot y}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x - z \cdot y}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r28271233 = x;
        double r28271234 = y;
        double r28271235 = z;
        double r28271236 = r28271234 * r28271235;
        double r28271237 = r28271233 - r28271236;
        double r28271238 = t;
        double r28271239 = a;
        double r28271240 = r28271239 * r28271235;
        double r28271241 = r28271238 - r28271240;
        double r28271242 = r28271237 / r28271241;
        return r28271242;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r28271243 = x;
        double r28271244 = z;
        double r28271245 = y;
        double r28271246 = r28271244 * r28271245;
        double r28271247 = r28271243 - r28271246;
        double r28271248 = t;
        double r28271249 = a;
        double r28271250 = r28271249 * r28271244;
        double r28271251 = r28271248 - r28271250;
        double r28271252 = r28271247 / r28271251;
        return r28271252;
}

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

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

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))))