Average Error: 3.1 → 0.0
Time: 3.1s
Precision: binary64
\[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.1283791670955126}{\frac{y}{e^{z}}} - x}\]
x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.1283791670955126}{\frac{y}{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) ((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

Original3.1
Target0.1
Herbie0.0
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.1

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

  3. Applied clear-num_binary643.1

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

  4. Simplified0.0

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{y} - x}}\]
  5. Using strategy rm

  6. Applied associate-/l*_binary640.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020210 
(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)))))