Average Error: 10.2 → 10.4
Time: 15.4s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{\frac{1}{t - z \cdot a}}{\frac{1}{x - z \cdot y}}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{\frac{1}{t - z \cdot a}}{\frac{1}{x - z \cdot y}}
double f(double x, double y, double z, double t, double a) {
        double r35038716 = x;
        double r35038717 = y;
        double r35038718 = z;
        double r35038719 = r35038717 * r35038718;
        double r35038720 = r35038716 - r35038719;
        double r35038721 = t;
        double r35038722 = a;
        double r35038723 = r35038722 * r35038718;
        double r35038724 = r35038721 - r35038723;
        double r35038725 = r35038720 / r35038724;
        return r35038725;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r35038726 = 1.0;
        double r35038727 = t;
        double r35038728 = z;
        double r35038729 = a;
        double r35038730 = r35038728 * r35038729;
        double r35038731 = r35038727 - r35038730;
        double r35038732 = r35038726 / r35038731;
        double r35038733 = x;
        double r35038734 = y;
        double r35038735 = r35038728 * r35038734;
        double r35038736 = r35038733 - r35038735;
        double r35038737 = r35038726 / r35038736;
        double r35038738 = r35038732 / r35038737;
        return r35038738;
}

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

Original10.2
Target1.6
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 10.2

    \[\frac{x - y \cdot z}{t - a \cdot z}\]
  2. Using strategy rm

  3. Applied sub-neg10.2

    \[\leadsto \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}}\]
  4. Using strategy rm

  5. Applied clear-num10.6

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

  6. Simplified10.6

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

  8. Applied div-inv10.6

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

  9. Applied associate-/r*10.4

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

  10. Final simplification10.4

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

Reproduce

herbie shell --seed 2019163 
(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))))