Average Error: 1.6 → 3.3
Time: 14.0s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|
double f(double x, double y, double z) {
        double r31539 = x;
        double r31540 = 4.0;
        double r31541 = r31539 + r31540;
        double r31542 = y;
        double r31543 = r31541 / r31542;
        double r31544 = r31539 / r31542;
        double r31545 = z;
        double r31546 = r31544 * r31545;
        double r31547 = r31543 - r31546;
        double r31548 = fabs(r31547);
        return r31548;
}
↓
double f(double x, double y, double z) {
        double r31549 = x;
        double r31550 = 4.0;
        double r31551 = r31549 + r31550;
        double r31552 = z;
        double r31553 = r31549 * r31552;
        double r31554 = r31551 - r31553;
        double r31555 = y;
        double r31556 = r31554 / r31555;
        double r31557 = fabs(r31556);
        return r31557;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (- (/ (+ x 4.0) y) (* (/ x y) z)) < -6.139715348477763e+64 or 7.965541593339039e-69 < (- (/ (+ x 4.0) y) (* (/ x y) z))

    1. Initial program 0.1

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]

    if -6.139715348477763e+64 < (- (/ (+ x 4.0) y) (* (/ x y) z)) < 7.965541593339039e-69

    1. Initial program 3.9

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    2. Using strategy rm

    3. Applied associate-*l/0.3

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]

    4. Applied sub-div0.3

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.3

    \[\leadsto \left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\]

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))