Average Error: 0.1 → 0.1
Time: 2.2s
Precision: binary64
\[\left(\left(a0 + a1x\right) + \left(a2 \cdot x\right) \cdot x\right) + \left(\left(a3 \cdot x\right) \cdot x\right) \cdot x\]
↓
\[\left(\left(a0 + a1x\right) + \left(a2 \cdot x\right) \cdot x\right) + \left(\left(a3 \cdot x\right) \cdot x\right) \cdot x\]
\left(\left(a0 + a1x\right) + \left(a2 \cdot x\right) \cdot x\right) + \left(\left(a3 \cdot x\right) \cdot x\right) \cdot x
↓
\left(\left(a0 + a1x\right) + \left(a2 \cdot x\right) \cdot x\right) + \left(\left(a3 \cdot x\right) \cdot x\right) \cdot x
double code(double a0, double a1x, double a2, double x, double a3) {
	return ((double) (((double) (((double) (a0 + a1x)) + ((double) (((double) (a2 * x)) * x)))) + ((double) (((double) (((double) (a3 * x)) * x)) * x))));
}
↓
double code(double a0, double a1x, double a2, double x, double a3) {
	return ((double) (((double) (((double) (a0 + a1x)) + ((double) (((double) (a2 * x)) * x)))) + ((double) (((double) (((double) (a3 * x)) * x)) * x))));
}

Error

Bits error versus a0

Bits error versus a1x

Bits error versus a2

Bits error versus x

Bits error versus a3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(a0 + a1x\right) + \left(a2 \cdot x\right) \cdot x\right) + \left(\left(a3 \cdot x\right) \cdot x\right) \cdot x\]

  2. Final simplification0.1

    \[\leadsto \left(\left(a0 + a1x\right) + \left(a2 \cdot x\right) \cdot x\right) + \left(\left(a3 \cdot x\right) \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a0 a1x a2 x a3)
  :name "(+ (+ (+ a0 a1x) (* (* a2 x) x)) (* (* (* a3 x) x) x))"
  :precision binary64
  (+ (+ (+ a0 a1x) (* (* a2 x) x)) (* (* (* a3 x) x) x)))