Average Error: 10.8 → 10.8
Time: 1.0m
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 r38717137 = x;
        double r38717138 = y;
        double r38717139 = z;
        double r38717140 = r38717138 * r38717139;
        double r38717141 = r38717137 - r38717140;
        double r38717142 = t;
        double r38717143 = a;
        double r38717144 = r38717143 * r38717139;
        double r38717145 = r38717142 - r38717144;
        double r38717146 = r38717141 / r38717145;
        return r38717146;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r38717147 = x;
        double r38717148 = y;
        double r38717149 = z;
        double r38717150 = r38717148 * r38717149;
        double r38717151 = r38717147 - r38717150;
        double r38717152 = t;
        double r38717153 = a;
        double r38717154 = r38717153 * r38717149;
        double r38717155 = r38717152 - r38717154;
        double r38717156 = r38717151 / r38717155;
        return r38717156;
}

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

Original10.8
Target1.7
Herbie10.8
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

  2. Taylor expanded around inf 10.8

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

  3. Final simplification10.8

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

Reproduce

herbie shell --seed 2019200 
(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))))