Average Error: 10.5 → 10.5
Time: 3.5s
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 r708772 = x;
        double r708773 = y;
        double r708774 = z;
        double r708775 = r708773 * r708774;
        double r708776 = r708772 - r708775;
        double r708777 = t;
        double r708778 = a;
        double r708779 = r708778 * r708774;
        double r708780 = r708777 - r708779;
        double r708781 = r708776 / r708780;
        return r708781;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r708782 = x;
        double r708783 = y;
        double r708784 = z;
        double r708785 = r708783 * r708784;
        double r708786 = r708782 - r708785;
        double r708787 = t;
        double r708788 = a;
        double r708789 = r708788 * r708784;
        double r708790 = r708787 - r708789;
        double r708791 = r708786 / r708790;
        return r708791;
}

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. Using strategy rm

  3. Applied clear-num10.8

    \[\leadsto \color{blue}{\frac{1}{\frac{t - a \cdot z}{x - y \cdot z}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity10.8

    \[\leadsto \frac{1}{\frac{t - a \cdot z}{\color{blue}{1 \cdot \left(x - y \cdot z\right)}}}\]

  6. Applied *-un-lft-identity10.8

    \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \left(t - a \cdot z\right)}}{1 \cdot \left(x - y \cdot z\right)}}\]

  7. Applied times-frac10.8

    \[\leadsto \frac{1}{\color{blue}{\frac{1}{1} \cdot \frac{t - a \cdot z}{x - y \cdot z}}}\]

  8. Applied add-cube-cbrt10.8

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{1} \cdot \frac{t - a \cdot z}{x - y \cdot z}}\]

  9. Applied times-frac10.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{t - a \cdot z}{x - y \cdot z}}}\]

  10. Simplified10.8

    \[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{t - a \cdot z}{x - y \cdot z}}\]

  11. Simplified10.5

    \[\leadsto 1 \cdot \color{blue}{\frac{x - y \cdot z}{t - a \cdot z}}\]

  12. Final simplification10.5

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

Reproduce

herbie shell --seed 2020018 
(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))))