Average Error: 10.4 → 10.4
Time: 21.5s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x - y \cdot z}{t - z \cdot a}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x - y \cdot z}{t - z \cdot a}
double f(double x, double y, double z, double t, double a) {
        double r32476533 = x;
        double r32476534 = y;
        double r32476535 = z;
        double r32476536 = r32476534 * r32476535;
        double r32476537 = r32476533 - r32476536;
        double r32476538 = t;
        double r32476539 = a;
        double r32476540 = r32476539 * r32476535;
        double r32476541 = r32476538 - r32476540;
        double r32476542 = r32476537 / r32476541;
        return r32476542;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r32476543 = x;
        double r32476544 = y;
        double r32476545 = z;
        double r32476546 = r32476544 * r32476545;
        double r32476547 = r32476543 - r32476546;
        double r32476548 = t;
        double r32476549 = a;
        double r32476550 = r32476545 * r32476549;
        double r32476551 = r32476548 - r32476550;
        double r32476552 = r32476547 / r32476551;
        return r32476552;
}

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

Original10.4
Target1.7
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344.0:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.4

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

  3. Applied clear-num10.8

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

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

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

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

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

  7. Applied times-frac10.8

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

  8. Applied add-cube-cbrt10.8

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{1} \cdot \frac{t - a \cdot z}{x - y \cdot z}}\]

  9. Applied times-frac10.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{t - a \cdot z}{x - y \cdot z}}}\]

  10. Simplified10.8

    \[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{t - a \cdot z}{x - y \cdot z}}\]

  11. Simplified10.4

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

  12. Final simplification10.4

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

Reproduce

herbie shell --seed 2019168 +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 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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