Average Error: 2.7 → 0.1
Time: 10.2s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r398530 = x;
        double r398531 = y;
        double r398532 = 1.1283791670955126;
        double r398533 = z;
        double r398534 = exp(r398533);
        double r398535 = r398532 * r398534;
        double r398536 = r398530 * r398531;
        double r398537 = r398535 - r398536;
        double r398538 = r398531 / r398537;
        double r398539 = r398530 + r398538;
        return r398539;
}
↓
double f(double x, double y, double z) {
        double r398540 = x;
        double r398541 = 1.0;
        double r398542 = 1.1283791670955126;
        double r398543 = z;
        double r398544 = exp(r398543);
        double r398545 = y;
        double r398546 = r398544 / r398545;
        double r398547 = r398542 * r398546;
        double r398548 = r398547 - r398540;
        double r398549 = r398541 / r398548;
        double r398550 = r398540 + r398549;
        return r398550;
}

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

Original2.7
Target0.1
Herbie0.1
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.7

    \[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.7

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}{y}}}\]

  4. Simplified0.1

    \[\leadsto x + \frac{1}{\color{blue}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}}\]

  5. Final simplification0.1

    \[\leadsto x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.12837916709551256 y) (exp z)) x)))

  (+ x (/ y (- (* 1.12837916709551256 (exp z)) (* x y)))))