Expression 3, p15

Average Error: 0.0 → 0.0

Time: 1.8s

Precision: binary64

Cost: 448

\[0 \leq x \land x \leq 2\]

Math

\[x \cdot \left(x \cdot x\right) + x \cdot x \]

↓

\[x \cdot \left(x + x \cdot x\right) \]

FPCore

(FPCore (x) :precision binary64 (+ (* x (* x x)) (* x x)))

↓

(FPCore (x) :precision binary64 (* x (+ x (* x x))))

C

double code(double x) {
	return (x * (x * x)) + (x * x);
}

↓

double code(double x) {
	return x * (x + (x * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * (x * x)) + (x * x)
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (x + (x * x))
end function

Java

public static double code(double x) {
	return (x * (x * x)) + (x * x);
}

↓

public static double code(double x) {
	return x * (x + (x * x));
}

Python

def code(x):
	return (x * (x * x)) + (x * x)

↓

def code(x):
	return x * (x + (x * x))

Julia

function code(x)
	return Float64(Float64(x * Float64(x * x)) + Float64(x * x))
end

↓

function code(x)
	return Float64(x * Float64(x + Float64(x * x)))
end

MATLAB

function tmp = code(x)
	tmp = (x * (x * x)) + (x * x);
end

↓

function tmp = code(x)
	tmp = x * (x + (x * x));
end

Wolfram

code[x_] := N[(N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(x * N[(x + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\left(\left(1 + x\right) \cdot x\right) \cdot x \]

Derivation

1. Initial program 0.0

   \[x \cdot \left(x \cdot x\right) + x \cdot x \]

2. Simplified 0.0

   \[\leadsto \color{blue}{x \cdot \left(x + x \cdot x\right)} \]
   Proof

   [Start] 0.0	\[ x \cdot \left(x \cdot x\right) + x \cdot x \]
   rational_best-simplify-62 [=>] 0.0	\[ \color{blue}{x \cdot x - \left(-x \cdot \left(x \cdot x\right)\right)} \]
   rational_best-simplify-3 [=>] 0.0	\[ x \cdot x - \left(-\color{blue}{\left(x \cdot x\right) \cdot x}\right) \]
   rational_best-simplify-52 [=>] 0.0	\[ x \cdot x - \color{blue}{x \cdot \left(-x \cdot x\right)} \]
   rational_best-simplify-110 [=>] 0.0	\[ \color{blue}{x \cdot \left(x - \left(-x \cdot x\right)\right)} \]
   rational_best-simplify-61 [=>] 0.0	\[ x \cdot \color{blue}{\left(x + \left(-\left(-x \cdot x\right)\right)\right)} \]
   rational_best-simplify-51 [=>] 0.0	\[ x \cdot \left(x + \color{blue}{x \cdot x}\right) \]

3. Final simplification 0.0

   \[\leadsto x \cdot \left(x + x \cdot x\right) \]

Reproduce

herbie shell --seed 2023104 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (and (<= 0.0 x) (<= x 2.0))

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))