Average Error: 10.7 → 3.0
Time: 13.1s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}
double f(double x, double y, double z, double t, double a) {
        double r544645 = x;
        double r544646 = y;
        double r544647 = z;
        double r544648 = r544646 * r544647;
        double r544649 = r544645 - r544648;
        double r544650 = t;
        double r544651 = a;
        double r544652 = r544651 * r544647;
        double r544653 = r544650 - r544652;
        double r544654 = r544649 / r544653;
        return r544654;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r544655 = x;
        double r544656 = t;
        double r544657 = a;
        double r544658 = z;
        double r544659 = r544657 * r544658;
        double r544660 = r544656 - r544659;
        double r544661 = r544655 / r544660;
        double r544662 = y;
        double r544663 = r544656 / r544658;
        double r544664 = r544663 - r544657;
        double r544665 = r544662 / r544664;
        double r544666 = r544661 - r544665;
        return r544666;
}

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

Original10.7
Target1.7
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 10.7

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

  3. Applied div-sub10.7

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

  4. Simplified8.3

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

  6. Applied div-sub8.3

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

  7. Simplified3.0

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

  8. Final simplification3.0

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

Reproduce

herbie shell --seed 2019196 
(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)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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