Average Error: 10.2 → 3.2
Time: 20.3s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{1}{\frac{t - a \cdot z}{x}} + \frac{-y}{\frac{t}{z} - a}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{1}{\frac{t - a \cdot z}{x}} + \frac{-y}{\frac{t}{z} - a}
double f(double x, double y, double z, double t, double a) {
        double r493638 = x;
        double r493639 = y;
        double r493640 = z;
        double r493641 = r493639 * r493640;
        double r493642 = r493638 - r493641;
        double r493643 = t;
        double r493644 = a;
        double r493645 = r493644 * r493640;
        double r493646 = r493643 - r493645;
        double r493647 = r493642 / r493646;
        return r493647;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r493648 = 1.0;
        double r493649 = t;
        double r493650 = a;
        double r493651 = z;
        double r493652 = r493650 * r493651;
        double r493653 = r493649 - r493652;
        double r493654 = x;
        double r493655 = r493653 / r493654;
        double r493656 = r493648 / r493655;
        double r493657 = y;
        double r493658 = -r493657;
        double r493659 = r493649 / r493651;
        double r493660 = r493659 - r493650;
        double r493661 = r493658 / r493660;
        double r493662 = r493656 + r493661;
        return r493662;
}

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
Herbie3.2
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

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. Simplified7.8

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

  6. Applied sub-neg7.8

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

  7. Simplified2.9

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

  9. Applied clear-num3.2

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

  10. Final simplification3.2

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

Reproduce

herbie shell --seed 2019325 
(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))))