Average Error: 3.0 → 0.0
Time: 2.6s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r456990 = x;
        double r456991 = y;
        double r456992 = 1.1283791670955126;
        double r456993 = z;
        double r456994 = exp(r456993);
        double r456995 = r456992 * r456994;
        double r456996 = r456990 * r456991;
        double r456997 = r456995 - r456996;
        double r456998 = r456991 / r456997;
        double r456999 = r456990 + r456998;
        return r456999;
}
↓
double f(double x, double y, double z) {
        double r457000 = x;
        double r457001 = 1.0;
        double r457002 = 1.1283791670955126;
        double r457003 = z;
        double r457004 = exp(r457003);
        double r457005 = y;
        double r457006 = r457004 / r457005;
        double r457007 = r457002 * r457006;
        double r457008 = r457007 - r457000;
        double r457009 = r457001 / r457008;
        double r457010 = r457000 + r457009;
        return r457010;
}

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
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.0

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

  3. Applied clear-num3.0

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

  4. Taylor expanded around inf 0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(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)))))