Average Error: 10.4 → 10.4
Time: 20.2s
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 r25662081 = x;
        double r25662082 = y;
        double r25662083 = z;
        double r25662084 = r25662082 * r25662083;
        double r25662085 = r25662081 - r25662084;
        double r25662086 = t;
        double r25662087 = a;
        double r25662088 = r25662087 * r25662083;
        double r25662089 = r25662086 - r25662088;
        double r25662090 = r25662085 / r25662089;
        return r25662090;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25662091 = x;
        double r25662092 = y;
        double r25662093 = z;
        double r25662094 = r25662092 * r25662093;
        double r25662095 = r25662091 - r25662094;
        double r25662096 = t;
        double r25662097 = a;
        double r25662098 = r25662097 * r25662093;
        double r25662099 = r25662096 - r25662098;
        double r25662100 = r25662095 / r25662099;
        return r25662100;
}

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

Original10.4
Target1.8
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344.0:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.4

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

  2. Taylor expanded around inf 10.4

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

  3. Final simplification10.4

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

Reproduce

herbie shell --seed 2019158 
(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 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))