Average Error: 2.9 → 0.0
Time: 3.1s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1 \cdot \left(\frac{1.12837916709551256 \cdot e^{z}}{y} - x\right)}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1 \cdot \left(\frac{1.12837916709551256 \cdot e^{z}}{y} - x\right)}
double f(double x, double y, double z) {
        double r475393 = x;
        double r475394 = y;
        double r475395 = 1.1283791670955126;
        double r475396 = z;
        double r475397 = exp(r475396);
        double r475398 = r475395 * r475397;
        double r475399 = r475393 * r475394;
        double r475400 = r475398 - r475399;
        double r475401 = r475394 / r475400;
        double r475402 = r475393 + r475401;
        return r475402;
}
↓
double f(double x, double y, double z) {
        double r475403 = x;
        double r475404 = 1.0;
        double r475405 = 1.1283791670955126;
        double r475406 = z;
        double r475407 = exp(r475406);
        double r475408 = r475405 * r475407;
        double r475409 = y;
        double r475410 = r475408 / r475409;
        double r475411 = r475410 - r475403;
        double r475412 = r475404 * r475411;
        double r475413 = r475404 / r475412;
        double r475414 = r475403 + r475413;
        return r475414;
}

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

Original2.9
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.9

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

  3. Applied clear-num2.9

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

  5. Applied *-un-lft-identity2.9

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

  6. Applied *-un-lft-identity2.9

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

  7. Applied times-frac2.9

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

  8. Simplified2.9

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

  9. Simplified0.1

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

  11. Applied associate-*r/0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2020020 +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)))))