Average Error: 3.1 → 0.2
Time: 16.0s
Precision: 64
\[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
↓
\[\frac{1}{\frac{\sqrt[3]{\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(e^{z} \cdot 1.1283791670955126\right)\right)}}{y} - x} + x\]
x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}
↓
\frac{1}{\frac{\sqrt[3]{\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(e^{z} \cdot 1.1283791670955126\right)\right)}}{y} - x} + x
double f(double x, double y, double z) {
        double r17443170 = x;
        double r17443171 = y;
        double r17443172 = 1.1283791670955126;
        double r17443173 = z;
        double r17443174 = exp(r17443173);
        double r17443175 = r17443172 * r17443174;
        double r17443176 = r17443170 * r17443171;
        double r17443177 = r17443175 - r17443176;
        double r17443178 = r17443171 / r17443177;
        double r17443179 = r17443170 + r17443178;
        return r17443179;
}
↓
double f(double x, double y, double z) {
        double r17443180 = 1.0;
        double r17443181 = z;
        double r17443182 = exp(r17443181);
        double r17443183 = 1.1283791670955126;
        double r17443184 = r17443182 * r17443183;
        double r17443185 = r17443184 * r17443184;
        double r17443186 = r17443184 * r17443185;
        double r17443187 = cbrt(r17443186);
        double r17443188 = y;
        double r17443189 = r17443187 / r17443188;
        double r17443190 = x;
        double r17443191 = r17443189 - r17443190;
        double r17443192 = r17443180 / r17443191;
        double r17443193 = r17443192 + r17443190;
        return r17443193;
}

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

Original3.1
Target0.0
Herbie0.2
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.1

    \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num3.1

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied div-sub3.1

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{y} - \frac{x \cdot y}{y}}}\]

  6. Simplified0.0

    \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{y} - \color{blue}{x}}\]
  7. Using strategy rm

  8. Applied add-cbrt-cube0.2

    \[\leadsto x + \frac{1}{\frac{\color{blue}{\sqrt[3]{\left(\left(1.1283791670955126 \cdot e^{z}\right) \cdot \left(1.1283791670955126 \cdot e^{z}\right)\right) \cdot \left(1.1283791670955126 \cdot e^{z}\right)}}}{y} - x}\]

  9. Final simplification0.2

    \[\leadsto \frac{1}{\frac{\sqrt[3]{\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(\left(e^{z} \cdot 1.1283791670955126\right) \cdot \left(e^{z} \cdot 1.1283791670955126\right)\right)}}{y} - x} + x\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

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