Average Error: 3.4 → 0.1
Time: 12.5s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1}{y} \cdot \left(e^{z} \cdot 1.128379167095512558560699289955664426088\right) - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1}{y} \cdot \left(e^{z} \cdot 1.128379167095512558560699289955664426088\right) - x}
double f(double x, double y, double z) {
        double r396441 = x;
        double r396442 = y;
        double r396443 = 1.1283791670955126;
        double r396444 = z;
        double r396445 = exp(r396444);
        double r396446 = r396443 * r396445;
        double r396447 = r396441 * r396442;
        double r396448 = r396446 - r396447;
        double r396449 = r396442 / r396448;
        double r396450 = r396441 + r396449;
        return r396450;
}
↓
double f(double x, double y, double z) {
        double r396451 = x;
        double r396452 = 1.0;
        double r396453 = y;
        double r396454 = r396452 / r396453;
        double r396455 = z;
        double r396456 = exp(r396455);
        double r396457 = 1.1283791670955126;
        double r396458 = r396456 * r396457;
        double r396459 = r396454 * r396458;
        double r396460 = r396459 - r396451;
        double r396461 = r396452 / r396460;
        double r396462 = r396451 + r396461;
        return r396462;
}

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

Original3.4
Target0.1
Herbie0.1
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.4

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

  3. Applied clear-num3.5

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

  4. Simplified0.1

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

  6. Applied div-inv0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(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)))))