Average Error: 10.7 → 10.7
Time: 53.4s
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 r35198485 = x;
        double r35198486 = y;
        double r35198487 = z;
        double r35198488 = r35198486 * r35198487;
        double r35198489 = r35198485 - r35198488;
        double r35198490 = t;
        double r35198491 = a;
        double r35198492 = r35198491 * r35198487;
        double r35198493 = r35198490 - r35198492;
        double r35198494 = r35198489 / r35198493;
        return r35198494;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r35198495 = x;
        double r35198496 = y;
        double r35198497 = z;
        double r35198498 = r35198496 * r35198497;
        double r35198499 = r35198495 - r35198498;
        double r35198500 = t;
        double r35198501 = a;
        double r35198502 = r35198497 * r35198501;
        double r35198503 = r35198500 - r35198502;
        double r35198504 = r35198499 / r35198503;
        return r35198504;
}

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

Derivation

  1. Initial program 10.7

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

  3. Applied clear-num11.1

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

  5. Applied *-un-lft-identity11.1

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

  6. Applied *-un-lft-identity11.1

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

  7. Applied times-frac11.1

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

  8. Applied add-cube-cbrt11.1

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

  9. Applied times-frac11.1

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

  10. Simplified11.1

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

  11. Simplified10.7

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

  12. Final simplification10.7

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

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)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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