Average Error: 3.0 → 0.0
Time: 3.8s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z}}{\frac{y}{1.12837916709551256}} - \frac{x}{1}}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z}}{\frac{y}{1.12837916709551256}} - \frac{x}{1}}
double code(double x, double y, double z) {
	return (x + (y / ((1.1283791670955126 * exp(z)) - (x * y))));
}
↓
double code(double x, double y, double z) {
	return (x + (1.0 / ((exp(z) / (y / 1.1283791670955126)) - (x / 1.0))));
}

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
Target0.1
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 add-exp-log3.0

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

  4. Applied prod-exp3.0

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

  5. Simplified3.0

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

  7. Applied clear-num3.0

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

  9. Applied div-sub3.0

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

  10. Simplified3.0

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

  11. Simplified0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2020058 
(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)))))