Average Error: 2.8 → 0.1
Time: 10.0s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r409434 = x;
        double r409435 = y;
        double r409436 = 1.1283791670955126;
        double r409437 = z;
        double r409438 = exp(r409437);
        double r409439 = r409436 * r409438;
        double r409440 = r409434 * r409435;
        double r409441 = r409439 - r409440;
        double r409442 = r409435 / r409441;
        double r409443 = r409434 + r409442;
        return r409443;
}
↓
double f(double x, double y, double z) {
        double r409444 = x;
        double r409445 = 1.0;
        double r409446 = 1.1283791670955126;
        double r409447 = z;
        double r409448 = exp(r409447);
        double r409449 = y;
        double r409450 = r409448 / r409449;
        double r409451 = r409446 * r409450;
        double r409452 = r409451 - r409444;
        double r409453 = r409445 / r409452;
        double r409454 = r409444 + r409453;
        return r409454;
}

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

Target

Original2.8
Target0.0
Herbie0.1
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

    \[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.8

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}{y}}}\]

  4. Simplified0.1

    \[\leadsto x + \frac{1}{\color{blue}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}}\]

  5. Final simplification0.1

    \[\leadsto x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))