Average Error: 2.7 → 0.1
Time: 2.6s
Precision: binary64
\[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]
x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}
(FPCore (x y z)
 :precision binary64
 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))
↓
(FPCore (x y z)
 :precision binary64
 (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x))))
double code(double x, double y, double z) {
	return ((double) (x + (y / ((double) (((double) (1.1283791670955126 * ((double) exp(z)))) - ((double) (x * y)))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (x + (1.0 / ((double) (((double) ((1.1283791670955126 / y) * ((double) exp(z)))) - x)))));
}

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
Target0.1
Herbie0.1
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program Error: 2.7 bits

    \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-numError: 2.7 bits

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}}\]

  4. SimplifiedError: 0.1 bits

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}}\]

  5. Final simplificationError: 0.1 bits

    \[\leadsto x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))