Average Error: 2.8 → 0.0
Time: 12.1s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z}}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r235502 = x;
        double r235503 = y;
        double r235504 = 1.1283791670955126;
        double r235505 = z;
        double r235506 = exp(r235505);
        double r235507 = r235504 * r235506;
        double r235508 = r235502 * r235503;
        double r235509 = r235507 - r235508;
        double r235510 = r235503 / r235509;
        double r235511 = r235502 + r235510;
        return r235511;
}
↓
double f(double x, double y, double z) {
        double r235512 = x;
        double r235513 = 1.0;
        double r235514 = 1.1283791670955126;
        double r235515 = z;
        double r235516 = exp(r235515);
        double r235517 = r235514 * r235516;
        double r235518 = y;
        double r235519 = r235517 / r235518;
        double r235520 = r235519 - r235512;
        double r235521 = r235513 / r235520;
        double r235522 = r235512 + r235521;
        return r235522;
}

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

Derivation

  1. Initial program 2.8

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

  3. Applied clear-num2.8

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

  4. Simplified0.1

    \[\leadsto x + \frac{1}{\color{blue}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}}\]
  5. Using strategy rm

  6. Applied associate-*r/0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(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)))))