Average Error: 3.1 → 0.1
Time: 3.1s
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 r587627 = x;
        double r587628 = y;
        double r587629 = 1.1283791670955126;
        double r587630 = z;
        double r587631 = exp(r587630);
        double r587632 = r587629 * r587631;
        double r587633 = r587627 * r587628;
        double r587634 = r587632 - r587633;
        double r587635 = r587628 / r587634;
        double r587636 = r587627 + r587635;
        return r587636;
}
↓
double f(double x, double y, double z) {
        double r587637 = x;
        double r587638 = 1.0;
        double r587639 = 1.1283791670955126;
        double r587640 = z;
        double r587641 = exp(r587640);
        double r587642 = y;
        double r587643 = r587641 / r587642;
        double r587644 = r587639 * r587643;
        double r587645 = r587644 - r587637;
        double r587646 = r587638 / r587645;
        double r587647 = r587637 + r587646;
        return r587647;
}

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

Original3.1
Target0.0
Herbie0.1
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.1

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

  3. Applied clear-num3.1

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

  4. Taylor expanded around inf 0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 
(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)))))