Average Error: 11.3 → 11.3
Time: 5.1s
Precision: binary64
\[\left(\left(B + D\right) \cdot \left(B - D\right) + \left(a \cdot B\right) \cdot \left(\left(2 \cdot A\right) \cdot b - a \cdot B\right)\right) + A \cdot \left(A \cdot \left(d - b \cdot b\right) - \left(2 \cdot B\right) \cdot c\right)\]
↓
\[\left(\left(B + D\right) \cdot \left(B - D\right) + \left(a \cdot B\right) \cdot \left(\left(2 \cdot A\right) \cdot b - a \cdot B\right)\right) + A \cdot \left(A \cdot \left(d - b \cdot b\right) - \left(2 \cdot B\right) \cdot c\right)\]
\left(\left(B + D\right) \cdot \left(B - D\right) + \left(a \cdot B\right) \cdot \left(\left(2 \cdot A\right) \cdot b - a \cdot B\right)\right) + A \cdot \left(A \cdot \left(d - b \cdot b\right) - \left(2 \cdot B\right) \cdot c\right)
↓
\left(\left(B + D\right) \cdot \left(B - D\right) + \left(a \cdot B\right) \cdot \left(\left(2 \cdot A\right) \cdot b - a \cdot B\right)\right) + A \cdot \left(A \cdot \left(d - b \cdot b\right) - \left(2 \cdot B\right) \cdot c\right)
double code(double B, double D, double a, double A, double b, double d, double c) {
	return ((double) (((double) (((double) (((double) (B + D)) * ((double) (B - D)))) + ((double) (((double) (a * B)) * ((double) (((double) (((double) (2.0 * A)) * b)) - ((double) (a * B)))))))) + ((double) (A * ((double) (((double) (A * ((double) (d - ((double) (b * b)))))) - ((double) (((double) (2.0 * B)) * c))))))));
}
↓
double code(double B, double D, double a, double A, double b, double d, double c) {
	return ((double) (((double) (((double) (((double) (B + D)) * ((double) (B - D)))) + ((double) (((double) (a * B)) * ((double) (((double) (((double) (2.0 * A)) * b)) - ((double) (a * B)))))))) + ((double) (A * ((double) (((double) (A * ((double) (d - ((double) (b * b)))))) - ((double) (((double) (2.0 * B)) * c))))))));
}

Error

Bits error versus B

Bits error versus D

Bits error versus a

Bits error versus A

Bits error versus b

Bits error versus d

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 11.3

    \[\left(\left(B + D\right) \cdot \left(B - D\right) + \left(a \cdot B\right) \cdot \left(\left(2 \cdot A\right) \cdot b - a \cdot B\right)\right) + A \cdot \left(A \cdot \left(d - b \cdot b\right) - \left(2 \cdot B\right) \cdot c\right)\]

  2. Final simplification11.3

    \[\leadsto \left(\left(B + D\right) \cdot \left(B - D\right) + \left(a \cdot B\right) \cdot \left(\left(2 \cdot A\right) \cdot b - a \cdot B\right)\right) + A \cdot \left(A \cdot \left(d - b \cdot b\right) - \left(2 \cdot B\right) \cdot c\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (B D a A b d c)
  :name "(+ (+ (* (+ B D) (- B D)) (* (* a B) (- (* (* 2 A) b) (* a B)))) (* A (- (* A (- d (* b b))) (* (* 2 B) c))))"
  :precision binary64
  (+ (+ (* (+ B D) (- B D)) (* (* a B) (- (* (* 2.0 A) b) (* a B)))) (* A (- (* A (- d (* b b))) (* (* 2.0 B) c)))))