Average Error: 3.0 → 0.0
Time: 3.0s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r375284 = x;
        double r375285 = y;
        double r375286 = 1.1283791670955126;
        double r375287 = z;
        double r375288 = exp(r375287);
        double r375289 = r375286 * r375288;
        double r375290 = r375284 * r375285;
        double r375291 = r375289 - r375290;
        double r375292 = r375285 / r375291;
        double r375293 = r375284 + r375292;
        return r375293;
}
↓
double f(double x, double y, double z) {
        double r375294 = x;
        double r375295 = 1.0;
        double r375296 = 1.1283791670955126;
        double r375297 = z;
        double r375298 = exp(r375297);
        double r375299 = y;
        double r375300 = r375298 / r375299;
        double r375301 = r375296 * r375300;
        double r375302 = r375301 - r375294;
        double r375303 = r375295 / r375302;
        double r375304 = r375294 + r375303;
        return r375304;
}

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

Original3.0
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.0

    \[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num3.0

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}}\]

  4. Taylor expanded around inf 0.0

    \[\leadsto x + \frac{1}{\color{blue}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}}\]

  5. Final simplification0.0

    \[\leadsto x + \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}\]

Reproduce

herbie shell --seed 2020036 +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)))))