(- (* (- c (* a b)) (- c (* a b))) (* (- 1 (* a a)) (- (- d (* b b)) (* R R))))

Average Error: 7.4 → 7.4

Time: 4.3s

Precision: binary64

Math

\[\left(c - a \cdot b\right) \cdot \left(c - a \cdot b\right) - \left(1 - a \cdot a\right) \cdot \left(\left(d - b \cdot b\right) - R \cdot R\right)\]

↓

\[\left(c - a \cdot b\right) \cdot \left(c - a \cdot b\right) - \left(1 - a \cdot a\right) \cdot \left(\left(d - b \cdot b\right) - R \cdot R\right)\]

C

double code(double c, double a, double b, double d, double R) {
	return ((double) (((double) (((double) (c - ((double) (a * b)))) * ((double) (c - ((double) (a * b)))))) - ((double) (((double) (1.0 - ((double) (a * a)))) * ((double) (((double) (d - ((double) (b * b)))) - ((double) (R * R))))))));
}

↓

double code(double c, double a, double b, double d, double R) {
	return ((double) (((double) (((double) (c - ((double) (a * b)))) * ((double) (c - ((double) (a * b)))))) - ((double) (((double) (1.0 - ((double) (a * a)))) * ((double) (((double) (d - ((double) (b * b)))) - ((double) (R * R))))))));
}

Error

Bits error versus c

Bits error versus a

Bits error versus b

Bits error versus d

Bits error versus R

Derivation

1. Initial program 7.4

   \[\left(c - a \cdot b\right) \cdot \left(c - a \cdot b\right) - \left(1 - a \cdot a\right) \cdot \left(\left(d - b \cdot b\right) - R \cdot R\right)\]

2. Final simplification 7.4

   \[\leadsto \left(c - a \cdot b\right) \cdot \left(c - a \cdot b\right) - \left(1 - a \cdot a\right) \cdot \left(\left(d - b \cdot b\right) - R \cdot R\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (c a b d R)
  :name "(- (* (- c (* a b)) (- c (* a b))) (* (- 1 (* a a)) (- (- d (* b b)) (* R R))))"
  :precision binary64
  (- (* (- c (* a b)) (- c (* a b))) (* (- 1.0 (* a a)) (- (- d (* b b)) (* R R)))))