Average Error: 10.2 → 3.0
Time: 11.1s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{1}{\frac{t - z \cdot a}{x}} - \frac{y}{\frac{t}{z} - a}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{1}{\frac{t - z \cdot a}{x}} - \frac{y}{\frac{t}{z} - a}
double f(double x, double y, double z, double t, double a) {
        double r428990 = x;
        double r428991 = y;
        double r428992 = z;
        double r428993 = r428991 * r428992;
        double r428994 = r428990 - r428993;
        double r428995 = t;
        double r428996 = a;
        double r428997 = r428996 * r428992;
        double r428998 = r428995 - r428997;
        double r428999 = r428994 / r428998;
        return r428999;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r429000 = 1.0;
        double r429001 = t;
        double r429002 = z;
        double r429003 = a;
        double r429004 = r429002 * r429003;
        double r429005 = r429001 - r429004;
        double r429006 = x;
        double r429007 = r429005 / r429006;
        double r429008 = r429000 / r429007;
        double r429009 = y;
        double r429010 = r429001 / r429002;
        double r429011 = r429010 - r429003;
        double r429012 = r429009 / r429011;
        double r429013 = r429008 - r429012;
        return r429013;
}

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
Target1.8
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.2

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

  3. Applied div-sub10.2

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

  5. Applied associate-/l*7.6

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

  7. Applied div-sub7.6

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

  8. Simplified2.8

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

  10. Applied clear-num3.0

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

  11. Simplified3.0

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

  12. Final simplification3.0

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

Reproduce

herbie shell --seed 2019208 
(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 3.51395223729782958e-86) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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