Average Error: 2.8 → 0.0
Time: 9.6s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{e^{z} \cdot \frac{1.128379167095512558560699289955664426088}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{e^{z} \cdot \frac{1.128379167095512558560699289955664426088}{y} - x}
double f(double x, double y, double z) {
        double r489496 = x;
        double r489497 = y;
        double r489498 = 1.1283791670955126;
        double r489499 = z;
        double r489500 = exp(r489499);
        double r489501 = r489498 * r489500;
        double r489502 = r489496 * r489497;
        double r489503 = r489501 - r489502;
        double r489504 = r489497 / r489503;
        double r489505 = r489496 + r489504;
        return r489505;
}
↓
double f(double x, double y, double z) {
        double r489506 = x;
        double r489507 = 1.0;
        double r489508 = z;
        double r489509 = exp(r489508);
        double r489510 = 1.1283791670955126;
        double r489511 = y;
        double r489512 = r489510 / r489511;
        double r489513 = r489509 * r489512;
        double r489514 = r489513 - r489506;
        double r489515 = r489507 / r489514;
        double r489516 = r489506 + r489515;
        return r489516;
}

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-num2.9

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 +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)))))