Average Error: 2.7 → 0.0
Time: 41.5s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[\frac{1}{\frac{e^{z} \cdot 1.128379167095512558560699289955664426088}{y} - x} + x\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
\frac{1}{\frac{e^{z} \cdot 1.128379167095512558560699289955664426088}{y} - x} + x
double f(double x, double y, double z) {
        double r22528200 = x;
        double r22528201 = y;
        double r22528202 = 1.1283791670955126;
        double r22528203 = z;
        double r22528204 = exp(r22528203);
        double r22528205 = r22528202 * r22528204;
        double r22528206 = r22528200 * r22528201;
        double r22528207 = r22528205 - r22528206;
        double r22528208 = r22528201 / r22528207;
        double r22528209 = r22528200 + r22528208;
        return r22528209;
}
↓
double f(double x, double y, double z) {
        double r22528210 = 1.0;
        double r22528211 = z;
        double r22528212 = exp(r22528211);
        double r22528213 = 1.1283791670955126;
        double r22528214 = r22528212 * r22528213;
        double r22528215 = y;
        double r22528216 = r22528214 / r22528215;
        double r22528217 = x;
        double r22528218 = r22528216 - r22528217;
        double r22528219 = r22528210 / r22528218;
        double r22528220 = r22528219 + r22528217;
        return r22528220;
}

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

Original2.7
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.7

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

  3. Applied clear-num2.7

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

  5. Applied div-sub2.7

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 
(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)))))