Average Error: 2.8 → 0.1
Time: 3.0s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1 \cdot \left(1.12837916709551256 \cdot \frac{e^{z}}{y} - x\right)}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1 \cdot \left(1.12837916709551256 \cdot \frac{e^{z}}{y} - x\right)}
double f(double x, double y, double z) {
        double r388280 = x;
        double r388281 = y;
        double r388282 = 1.1283791670955126;
        double r388283 = z;
        double r388284 = exp(r388283);
        double r388285 = r388282 * r388284;
        double r388286 = r388280 * r388281;
        double r388287 = r388285 - r388286;
        double r388288 = r388281 / r388287;
        double r388289 = r388280 + r388288;
        return r388289;
}
↓
double f(double x, double y, double z) {
        double r388290 = x;
        double r388291 = 1.0;
        double r388292 = 1.1283791670955126;
        double r388293 = z;
        double r388294 = exp(r388293);
        double r388295 = y;
        double r388296 = r388294 / r388295;
        double r388297 = r388292 * r388296;
        double r388298 = r388297 - r388290;
        double r388299 = r388291 * r388298;
        double r388300 = r388291 / r388299;
        double r388301 = r388290 + r388300;
        return r388301;
}

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

Original2.8
Target0.0
Herbie0.1
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

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

  3. Applied clear-num2.8

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity2.8

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

  6. Applied *-un-lft-identity2.8

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

  7. Applied times-frac2.8

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

  8. Simplified2.8

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020083 
(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)))))