Average Error: 11.0 → 11.0
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 r717219 = x;
        double r717220 = y;
        double r717221 = z;
        double r717222 = r717220 * r717221;
        double r717223 = r717219 - r717222;
        double r717224 = t;
        double r717225 = a;
        double r717226 = r717225 * r717221;
        double r717227 = r717224 - r717226;
        double r717228 = r717223 / r717227;
        return r717228;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r717229 = x;
        double r717230 = y;
        double r717231 = z;
        double r717232 = r717230 * r717231;
        double r717233 = r717229 - r717232;
        double r717234 = t;
        double r717235 = a;
        double r717236 = r717235 * r717231;
        double r717237 = r717234 - r717236;
        double r717238 = r717233 / r717237;
        return r717238;
}

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
Target1.8
Herbie11.0
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

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 2020020 
(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))))