Average Error: 10.8 → 10.8
Time: 34.1s
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 r25787733 = x;
        double r25787734 = y;
        double r25787735 = z;
        double r25787736 = r25787734 * r25787735;
        double r25787737 = r25787733 - r25787736;
        double r25787738 = t;
        double r25787739 = a;
        double r25787740 = r25787739 * r25787735;
        double r25787741 = r25787738 - r25787740;
        double r25787742 = r25787737 / r25787741;
        return r25787742;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25787743 = x;
        double r25787744 = y;
        double r25787745 = z;
        double r25787746 = r25787744 * r25787745;
        double r25787747 = r25787743 - r25787746;
        double r25787748 = t;
        double r25787749 = a;
        double r25787750 = r25787749 * r25787745;
        double r25787751 = r25787748 - r25787750;
        double r25787752 = r25787747 / r25787751;
        return r25787752;
}

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

Original10.8
Target1.7
Herbie10.8
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

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

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

  4. Applied associate-/r*10.8

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

  5. Simplified10.8

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

  6. Final simplification10.8

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(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))))