(+ (+ (+ a (* b x)) (* (* c x) x)) (* (* (* d x) x) x))

Average Error: 0.1 → 0.1

Time: 2.2s

Precision: binary64

Math

\[\left(\left(a + b \cdot x\right) + \left(c \cdot x\right) \cdot x\right) + \left(\left(d \cdot x\right) \cdot x\right) \cdot x\]

↓

\[\left(\left(a + b \cdot x\right) + \left(c \cdot x\right) \cdot x\right) + \left(\left(d \cdot x\right) \cdot x\right) \cdot x\]

C

double code(double a, double b, double x, double c, double d) {
	return ((double) (((double) (((double) (a + ((double) (b * x)))) + ((double) (((double) (c * x)) * x)))) + ((double) (((double) (((double) (d * x)) * x)) * x))));
}

↓

double code(double a, double b, double x, double c, double d) {
	return ((double) (((double) (((double) (a + ((double) (b * x)))) + ((double) (((double) (c * x)) * x)))) + ((double) (((double) (((double) (d * x)) * x)) * x))));
}

Error

Bits error versus a

Bits error versus b

Bits error versus x

Bits error versus c

Bits error versus d

Derivation

1. Initial program 0.1

   \[\left(\left(a + b \cdot x\right) + \left(c \cdot x\right) \cdot x\right) + \left(\left(d \cdot x\right) \cdot x\right) \cdot x\]

2. Final simplification 0.1

   \[\leadsto \left(\left(a + b \cdot x\right) + \left(c \cdot x\right) \cdot x\right) + \left(\left(d \cdot x\right) \cdot x\right) \cdot x\]

Reproduce

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