Average Error: 2.8 → 0.0
Time: 13.3s
Precision: 64
\[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}\]
x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}
double f(double x, double y, double z) {
        double r17063641 = x;
        double r17063642 = y;
        double r17063643 = 1.1283791670955126;
        double r17063644 = z;
        double r17063645 = exp(r17063644);
        double r17063646 = r17063643 * r17063645;
        double r17063647 = r17063641 * r17063642;
        double r17063648 = r17063646 - r17063647;
        double r17063649 = r17063642 / r17063648;
        double r17063650 = r17063641 + r17063649;
        return r17063650;
}
↓
double f(double x, double y, double z) {
        double r17063651 = x;
        double r17063652 = 1.0;
        double r17063653 = z;
        double r17063654 = exp(r17063653);
        double r17063655 = 1.1283791670955126;
        double r17063656 = r17063654 * r17063655;
        double r17063657 = y;
        double r17063658 = r17063656 / r17063657;
        double r17063659 = r17063658 - r17063651;
        double r17063660 = r17063652 / r17063659;
        double r17063661 = r17063651 + r17063660;
        return r17063661;
}

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
Herbie0.0
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

    \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied insert-posit1623.6

    \[\leadsto x + \color{blue}{\left(\left(\frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\right)\right)}\]
  4. Using strategy rm

  5. Applied clear-num23.6

    \[\leadsto x + \left(\color{blue}{\left(\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}\right)}\right)\]

  6. Simplified22.6

    \[\leadsto x + \left(\left(\frac{1}{\color{blue}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}}\right)\right)\]
  7. Using strategy rm

  8. Applied remove-posit160.0

    \[\leadsto x + \color{blue}{\frac{1}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}}\]

  9. Final simplification0.0

    \[\leadsto x + \frac{1}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))