Average Error: 10.5 → 10.5
Time: 10.2s
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 r2962 = x;
        double r2963 = y;
        double r2964 = z;
        double r2965 = r2963 * r2964;
        double r2966 = r2962 - r2965;
        double r2967 = t;
        double r2968 = a;
        double r2969 = r2968 * r2964;
        double r2970 = r2967 - r2969;
        double r2971 = r2966 / r2970;
        return r2971;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2972 = x;
        double r2973 = y;
        double r2974 = z;
        double r2975 = r2973 * r2974;
        double r2976 = r2972 - r2975;
        double r2977 = t;
        double r2978 = a;
        double r2979 = r2978 * r2974;
        double r2980 = r2977 - r2979;
        double r2981 = r2976 / r2980;
        return r2981;
}

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

Original10.5
Target1.9
Herbie10.5
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.5

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

  2. Final simplification10.5

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

Reproduce

herbie shell --seed 2020025 +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))))