Average Error: 2.8 → 0.1
Time: 9.3s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{\sqrt{1}}{1.12837916709551256 \cdot \frac{\sqrt{e^{z}}}{\frac{y}{\sqrt{e^{z}}}} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{\sqrt{1}}{1.12837916709551256 \cdot \frac{\sqrt{e^{z}}}{\frac{y}{\sqrt{e^{z}}}} - x}
double f(double x, double y, double z) {
        double r394753 = x;
        double r394754 = y;
        double r394755 = 1.1283791670955126;
        double r394756 = z;
        double r394757 = exp(r394756);
        double r394758 = r394755 * r394757;
        double r394759 = r394753 * r394754;
        double r394760 = r394758 - r394759;
        double r394761 = r394754 / r394760;
        double r394762 = r394753 + r394761;
        return r394762;
}
↓
double f(double x, double y, double z) {
        double r394763 = x;
        double r394764 = 1.0;
        double r394765 = sqrt(r394764);
        double r394766 = 1.1283791670955126;
        double r394767 = z;
        double r394768 = exp(r394767);
        double r394769 = sqrt(r394768);
        double r394770 = y;
        double r394771 = r394770 / r394769;
        double r394772 = r394769 / r394771;
        double r394773 = r394766 * r394772;
        double r394774 = r394773 - r394763;
        double r394775 = r394765 / r394774;
        double r394776 = r394763 + r394775;
        return r394776;
}

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

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 add-sqr-sqrt2.8

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

  6. Applied associate-/l*2.8

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

  7. Simplified0.1

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

  9. Applied add-sqr-sqrt0.1

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

  10. Applied associate-/l*0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +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)))))