Average Error: 36.7 → 35.4
Time: 2.1s
Precision: binary64
\[x - a \cdot \left(\frac{x \cdot a}{a \cdot a + b \cdot b} + \frac{y \cdot b}{a \cdot a + b \cdot b}\right)\]
↓
\[x - \frac{a}{a \cdot a + b \cdot b} \cdot \left(x \cdot a + y \cdot b\right)\]
x - a \cdot \left(\frac{x \cdot a}{a \cdot a + b \cdot b} + \frac{y \cdot b}{a \cdot a + b \cdot b}\right)
↓
x - \frac{a}{a \cdot a + b \cdot b} \cdot \left(x \cdot a + y \cdot b\right)
double code(double x, double a, double b, double y) {
	return ((double) (x - ((double) (a * ((double) (((double) (((double) (x * a)) / ((double) (((double) (a * a)) + ((double) (b * b)))))) + ((double) (((double) (y * b)) / ((double) (((double) (a * a)) + ((double) (b * b))))))))))));
}
↓
double code(double x, double a, double b, double y) {
	return ((double) (x - ((double) (((double) (a / ((double) (((double) (a * a)) + ((double) (b * b)))))) * ((double) (((double) (x * a)) + ((double) (y * b))))))));
}

Error

Bits error versus x

Bits error versus a

Bits error versus b

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 36.7

    \[x - a \cdot \left(\frac{x \cdot a}{a \cdot a + b \cdot b} + \frac{y \cdot b}{a \cdot a + b \cdot b}\right)\]

  2. Simplified35.4

    \[\leadsto \color{blue}{x - \frac{a}{a \cdot a + b \cdot b} \cdot \left(x \cdot a + y \cdot b\right)}\]

  3. Final simplification35.4

    \[\leadsto x - \frac{a}{a \cdot a + b \cdot b} \cdot \left(x \cdot a + y \cdot b\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x a b y)
  :name "(- x (* a (+ (/ (* x a) (+ (* a a) (* b b))) (/ (* y b) (+ (* a a) (* b b))))))"
  :precision binary64
  (- x (* a (+ (/ (* x a) (+ (* a a) (* b b))) (/ (* y b) (+ (* a a) (* b b)))))))