(+ (- (* (* a a) d) (* (* (* a a) R) R)) (* b (- b (* (* 2 a) c))))

Average Error: 9.6 → 9.6

Time: 2.9s

Precision: binary64

Math

\[\left(\left(a \cdot a\right) \cdot d - \left(\left(a \cdot a\right) \cdot R\right) \cdot R\right) + b \cdot \left(b - \left(2 \cdot a\right) \cdot c\right)\]

↓

\[\left(\left(a \cdot a\right) \cdot d - \left(\left(a \cdot a\right) \cdot R\right) \cdot R\right) + b \cdot \left(b - \left(2 \cdot a\right) \cdot c\right)\]

C

double code(double a, double d, double R, double b, double c) {
	return ((double) (((double) (((double) (((double) (a * a)) * d)) - ((double) (((double) (((double) (a * a)) * R)) * R)))) + ((double) (b * ((double) (b - ((double) (((double) (2.0 * a)) * c))))))));
}

↓

double code(double a, double d, double R, double b, double c) {
	return ((double) (((double) (((double) (((double) (a * a)) * d)) - ((double) (((double) (((double) (a * a)) * R)) * R)))) + ((double) (b * ((double) (b - ((double) (((double) (2.0 * a)) * c))))))));
}

Error

Bits error versus a

Bits error versus d

Bits error versus R

Bits error versus b

Bits error versus c

Derivation

1. Initial program 9.6

   \[\left(\left(a \cdot a\right) \cdot d - \left(\left(a \cdot a\right) \cdot R\right) \cdot R\right) + b \cdot \left(b - \left(2 \cdot a\right) \cdot c\right)\]

2. Final simplification 9.6

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

Reproduce

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