Average Error: 3.0 → 0.1
Time: 13.6s
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 r268558 = x;
        double r268559 = y;
        double r268560 = 1.1283791670955126;
        double r268561 = z;
        double r268562 = exp(r268561);
        double r268563 = r268560 * r268562;
        double r268564 = r268558 * r268559;
        double r268565 = r268563 - r268564;
        double r268566 = r268559 / r268565;
        double r268567 = r268558 + r268566;
        return r268567;
}
↓
double f(double x, double y, double z) {
        double r268568 = x;
        double r268569 = 1.0;
        double r268570 = 1.1283791670955126;
        double r268571 = z;
        double r268572 = exp(r268571);
        double r268573 = y;
        double r268574 = r268572 / r268573;
        double r268575 = r268570 * r268574;
        double r268576 = r268575 - r268568;
        double r268577 = r268569 / r268576;
        double r268578 = r268568 + r268577;
        return r268578;
}

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

Original3.0
Target0.1
Herbie0.1
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.0

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

  3. Applied clear-num3.0

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

  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 2019322 
(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)))))