Average Error: 2.8 → 0.1
Time: 2.7s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - \frac{x}{1}}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - \frac{x}{1}}
double f(double x, double y, double z) {
        double r399983 = x;
        double r399984 = y;
        double r399985 = 1.1283791670955126;
        double r399986 = z;
        double r399987 = exp(r399986);
        double r399988 = r399985 * r399987;
        double r399989 = r399983 * r399984;
        double r399990 = r399988 - r399989;
        double r399991 = r399984 / r399990;
        double r399992 = r399983 + r399991;
        return r399992;
}
↓
double f(double x, double y, double z) {
        double r399993 = x;
        double r399994 = 1.0;
        double r399995 = 1.1283791670955126;
        double r399996 = z;
        double r399997 = exp(r399996);
        double r399998 = y;
        double r399999 = r399997 / r399998;
        double r400000 = r399995 * r399999;
        double r400001 = r399993 / r399994;
        double r400002 = r400000 - r400001;
        double r400003 = r399994 / r400002;
        double r400004 = r399993 + r400003;
        return r400004;
}

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
Target0.1
Herbie0.1
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

    \[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.8

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied div-sub2.8

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.12837916709551256 \cdot e^{z}}{y} - \frac{x \cdot y}{y}}}\]

  6. Simplified2.8

    \[\leadsto x + \frac{1}{\color{blue}{1.12837916709551256 \cdot \frac{e^{z}}{y}} - \frac{x \cdot y}{y}}\]

  7. Simplified0.1

    \[\leadsto x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - \color{blue}{\frac{x}{1}}}\]

  8. Final simplification0.1

    \[\leadsto x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - \frac{x}{1}}\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(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)))))