Average Error: 10.7 → 10.7
Time: 19.6s
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 r38260876 = x;
        double r38260877 = y;
        double r38260878 = z;
        double r38260879 = r38260877 * r38260878;
        double r38260880 = r38260876 - r38260879;
        double r38260881 = t;
        double r38260882 = a;
        double r38260883 = r38260882 * r38260878;
        double r38260884 = r38260881 - r38260883;
        double r38260885 = r38260880 / r38260884;
        return r38260885;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r38260886 = x;
        double r38260887 = z;
        double r38260888 = y;
        double r38260889 = r38260887 * r38260888;
        double r38260890 = r38260886 - r38260889;
        double r38260891 = t;
        double r38260892 = a;
        double r38260893 = r38260892 * r38260887;
        double r38260894 = r38260891 - r38260893;
        double r38260895 = r38260890 / r38260894;
        return r38260895;
}

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
Target1.9
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

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

Reproduce

herbie shell --seed 2019171 
(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))))