Average Error: 10.3 → 8.8
Time: 16.6s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x}{t - a \cdot z} - \frac{y}{\sqrt[3]{t - a \cdot z} \cdot \sqrt[3]{t - a \cdot z}} \cdot \frac{z}{\sqrt[3]{\left(\sqrt[3]{t - a \cdot z} \cdot \sqrt[3]{t - a \cdot z}\right) \cdot \sqrt[3]{t - a \cdot z}}}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x}{t - a \cdot z} - \frac{y}{\sqrt[3]{t - a \cdot z} \cdot \sqrt[3]{t - a \cdot z}} \cdot \frac{z}{\sqrt[3]{\left(\sqrt[3]{t - a \cdot z} \cdot \sqrt[3]{t - a \cdot z}\right) \cdot \sqrt[3]{t - a \cdot z}}}
double f(double x, double y, double z, double t, double a) {
        double r32024310 = x;
        double r32024311 = y;
        double r32024312 = z;
        double r32024313 = r32024311 * r32024312;
        double r32024314 = r32024310 - r32024313;
        double r32024315 = t;
        double r32024316 = a;
        double r32024317 = r32024316 * r32024312;
        double r32024318 = r32024315 - r32024317;
        double r32024319 = r32024314 / r32024318;
        return r32024319;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r32024320 = x;
        double r32024321 = t;
        double r32024322 = a;
        double r32024323 = z;
        double r32024324 = r32024322 * r32024323;
        double r32024325 = r32024321 - r32024324;
        double r32024326 = r32024320 / r32024325;
        double r32024327 = y;
        double r32024328 = cbrt(r32024325);
        double r32024329 = r32024328 * r32024328;
        double r32024330 = r32024327 / r32024329;
        double r32024331 = r32024329 * r32024328;
        double r32024332 = cbrt(r32024331);
        double r32024333 = r32024323 / r32024332;
        double r32024334 = r32024330 * r32024333;
        double r32024335 = r32024326 - r32024334;
        return r32024335;
}

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

Original10.3
Target1.8
Herbie8.8
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344.0:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.3

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

  3. Applied div-sub10.3

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

  5. Applied add-cube-cbrt10.6

    \[\leadsto \frac{x}{t - a \cdot z} - \frac{y \cdot z}{\color{blue}{\left(\sqrt[3]{t - a \cdot z} \cdot \sqrt[3]{t - a \cdot z}\right) \cdot \sqrt[3]{t - a \cdot z}}}\]

  6. Applied times-frac8.8

    \[\leadsto \frac{x}{t - a \cdot z} - \color{blue}{\frac{y}{\sqrt[3]{t - a \cdot z} \cdot \sqrt[3]{t - a \cdot z}} \cdot \frac{z}{\sqrt[3]{t - a \cdot z}}}\]
  7. Using strategy rm

  8. Applied add-cbrt-cube8.8

    \[\leadsto \frac{x}{t - a \cdot z} - \frac{y}{\sqrt[3]{t - a \cdot z} \cdot \sqrt[3]{t - a \cdot z}} \cdot \frac{z}{\color{blue}{\sqrt[3]{\left(\sqrt[3]{t - a \cdot z} \cdot \sqrt[3]{t - a \cdot z}\right) \cdot \sqrt[3]{t - a \cdot z}}}}\]

  9. Final simplification8.8

    \[\leadsto \frac{x}{t - a \cdot z} - \frac{y}{\sqrt[3]{t - a \cdot z} \cdot \sqrt[3]{t - a \cdot z}} \cdot \frac{z}{\sqrt[3]{\left(\sqrt[3]{t - a \cdot z} \cdot \sqrt[3]{t - a \cdot z}\right) \cdot \sqrt[3]{t - a \cdot z}}}\]

Reproduce

herbie shell --seed 2019162 
(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))))