Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F

Average Error: 0.2 → 0.2

Time: 3.3s

Precision: binary64

Cost: 320

Math

\[\left(x \cdot 3\right) \cdot x \]

↓

\[3 \cdot \left(x \cdot x\right) \]

FPCore

(FPCore (x) :precision binary64 (* (* x 3.0) x))

↓

(FPCore (x) :precision binary64 (* 3.0 (* x x)))

C

double code(double x) {
	return (x * 3.0) * x;
}

↓

double code(double x) {
	return 3.0 * (x * x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * 3.0d0) * x
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * (x * x)
end function

Java

public static double code(double x) {
	return (x * 3.0) * x;
}

↓

public static double code(double x) {
	return 3.0 * (x * x);
}

Python

def code(x):
	return (x * 3.0) * x

↓

def code(x):
	return 3.0 * (x * x)

Julia

function code(x)
	return Float64(Float64(x * 3.0) * x)
end

↓

function code(x)
	return Float64(3.0 * Float64(x * x))
end

MATLAB

function tmp = code(x)
	tmp = (x * 3.0) * x;
end

↓

function tmp = code(x)
	tmp = 3.0 * (x * x);
end

Wolfram

code[x_] := N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision]

↓

code[x_] := N[(3.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.2

   \[\left(x \cdot 3\right) \cdot x \]

2. Taylor expanded in x around 0 0.2

   \[\leadsto \color{blue}{3 \cdot {x}^{2}} \]

3. Simplified 0.2

   \[\leadsto \color{blue}{3 \cdot \left(x \cdot x\right)} \]
   Proof

   [Start] 0.2	\[ 3 \cdot {x}^{2} \]
   unpow2 [=>] 0.2	\[ 3 \cdot \color{blue}{\left(x \cdot x\right)} \]

4. Final simplification 0.2

   \[\leadsto 3 \cdot \left(x \cdot x\right) \]

Reproduce

herbie shell --seed 2023054 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))