Average Error: 0.1 → 0.1
Time: 1.5s
Precision: binary64
\[\left(\left(a \cdot x\right) \cdot x + b \cdot x\right) + c\]
↓
\[c + x \cdot \left(a \cdot x + b\right)\]
\left(\left(a \cdot x\right) \cdot x + b \cdot x\right) + c
↓
c + x \cdot \left(a \cdot x + b\right)
double code(double a, double x, double b, double c) {
	return ((double) (((double) (((double) (((double) (a * x)) * x)) + ((double) (b * x)))) + c));
}
↓
double code(double a, double x, double b, double c) {
	return ((double) (c + ((double) (x * ((double) (((double) (a * x)) + b))))));
}

Error

Bits error versus a

Bits error versus x

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

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