Average Error: 2.9 → 0.0
Time: 21.2s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z} \cdot 1.128379167095512558560699289955664426088}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z} \cdot 1.128379167095512558560699289955664426088}{y} - x}
double f(double x, double y, double z) {
        double r19925944 = x;
        double r19925945 = y;
        double r19925946 = 1.1283791670955126;
        double r19925947 = z;
        double r19925948 = exp(r19925947);
        double r19925949 = r19925946 * r19925948;
        double r19925950 = r19925944 * r19925945;
        double r19925951 = r19925949 - r19925950;
        double r19925952 = r19925945 / r19925951;
        double r19925953 = r19925944 + r19925952;
        return r19925953;
}
↓
double f(double x, double y, double z) {
        double r19925954 = x;
        double r19925955 = 1.0;
        double r19925956 = z;
        double r19925957 = exp(r19925956);
        double r19925958 = 1.1283791670955126;
        double r19925959 = r19925957 * r19925958;
        double r19925960 = y;
        double r19925961 = r19925959 / r19925960;
        double r19925962 = r19925961 - r19925954;
        double r19925963 = r19925955 / r19925962;
        double r19925964 = r19925954 + r19925963;
        return r19925964;
}

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

Original2.9
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.9

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

  5. Applied div-sub2.9

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

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

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

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