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

Average Error: 0.2 → 0.2

Time: 11.4s

Precision: binary64

Cost: 768

Math

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

↓

\[\frac{-x}{\frac{-1}{x}} + x \cdot \left(x + x\right) \]

FPCore

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

↓

(FPCore (x) :precision binary64 (+ (/ (- x) (/ -1.0 x)) (* x (+ x x))))

C

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

↓

double code(double x) {
	return (-x / (-1.0 / x)) + (x * (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 = (-x / ((-1.0d0) / x)) + (x * (x + x))
end function

Java

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

↓

public static double code(double x) {
	return (-x / (-1.0 / x)) + (x * (x + x));
}

Python

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

↓

def code(x):
	return (-x / (-1.0 / x)) + (x * (x + x))

Julia

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

↓

function code(x)
	return Float64(Float64(Float64(-x) / Float64(-1.0 / x)) + Float64(x * Float64(x + x)))
end

MATLAB

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

↓

function tmp = code(x)
	tmp = (-x / (-1.0 / x)) + (x * (x + x));
end

Wolfram

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

↓

code[x_] := N[(N[((-x) / N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.2

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

2. Simplified 0.2

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

   [Start] 0.2	\[ \left(x \cdot 3\right) \cdot x \]
   rational.json-simplify-2 [=>] 0.2	\[ \color{blue}{x \cdot \left(x \cdot 3\right)} \]
   rational.json-simplify-43 [<=] 0.2	\[ \color{blue}{3 \cdot \left(x \cdot x\right)} \]

3. Applied egg-rr 0.2

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

4. Applied egg-rr 41.6

   \[\leadsto \color{blue}{\frac{\frac{1}{x \cdot \left(x + x\right)} + \frac{\frac{x + x}{\left(x \cdot x\right) \cdot \frac{x \cdot x}{x}}}{2}}{\frac{1}{x \cdot \left(x + x\right)} \cdot \frac{\frac{x + x}{\left(x \cdot x\right) \cdot \frac{x \cdot x}{x}}}{2}}} \]

5. Simplified 0.6

   \[\leadsto \color{blue}{\frac{2}{\frac{2 \cdot \frac{1}{x}}{x}} + x \cdot \left(x + x\right)} \]
   Proof

   [Start] 41.6	\[ \frac{\frac{1}{x \cdot \left(x + x\right)} + \frac{\frac{x + x}{\left(x \cdot x\right) \cdot \frac{x \cdot x}{x}}}{2}}{\frac{1}{x \cdot \left(x + x\right)} \cdot \frac{\frac{x + x}{\left(x \cdot x\right) \cdot \frac{x \cdot x}{x}}}{2}} \]
   rational.json-simplify-28 [=>] 13.2	\[ \color{blue}{\frac{1}{\frac{1}{x \cdot \left(x + x\right)}} + \frac{1}{\frac{\frac{x + x}{\left(x \cdot x\right) \cdot \frac{x \cdot x}{x}}}{2}}} \]
   rational.json-simplify-1 [=>] 13.2	\[ \color{blue}{\frac{1}{\frac{\frac{x + x}{\left(x \cdot x\right) \cdot \frac{x \cdot x}{x}}}{2}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}}} \]
   rational.json-simplify-61 [=>] 13.2	\[ \color{blue}{\frac{2}{\frac{\frac{x + x}{\left(x \cdot x\right) \cdot \frac{x \cdot x}{x}}}{1}}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   rational.json-simplify-7 [=>] 13.2	\[ \frac{2}{\color{blue}{\frac{x + x}{\left(x \cdot x\right) \cdot \frac{x \cdot x}{x}}}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   rational.json-simplify-46 [=>] 0.7	\[ \frac{2}{\color{blue}{\frac{\frac{x + x}{x \cdot x}}{\frac{x \cdot x}{x}}}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   rational.json-simplify-49 [=>] 0.7	\[ \frac{2}{\frac{\frac{x + x}{x \cdot x}}{\color{blue}{x \cdot \frac{x}{x}}}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   rational.json-simplify-46 [=>] 0.7	\[ \frac{2}{\color{blue}{\frac{\frac{\frac{x + x}{x \cdot x}}{x}}{\frac{x}{x}}}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   rational.json-simplify-60 [=>] 0.7	\[ \frac{2}{\color{blue}{\frac{\frac{x + x}{x \cdot x}}{x}}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   rational.json-simplify-28 [=>] 0.7	\[ \frac{2}{\frac{\color{blue}{\frac{1}{x} + \frac{1}{x}}}{x}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   rational.json-simplify-7 [<=] 0.7	\[ \frac{2}{\frac{\frac{1}{x} + \color{blue}{\frac{\frac{1}{x}}{1}}}{x}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   rational.json-simplify-31 [=>] 0.7	\[ \frac{2}{\frac{\color{blue}{\left(1 + 1\right) \cdot \frac{\frac{1}{x}}{1}}}{x}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   metadata-eval [=>] 0.7	\[ \frac{2}{\frac{\color{blue}{2} \cdot \frac{\frac{1}{x}}{1}}{x}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   rational.json-simplify-7 [=>] 0.7	\[ \frac{2}{\frac{2 \cdot \color{blue}{\frac{1}{x}}}{x}} + \frac{1}{\frac{1}{x \cdot \left(x + x\right)}} \]
   rational.json-simplify-51 [<=] 0.7	\[ \frac{2}{\frac{2 \cdot \frac{1}{x}}{x}} + \frac{1}{\frac{1}{\color{blue}{x \cdot x + x \cdot x}}} \]

6. Applied egg-rr 0.2

   \[\leadsto \color{blue}{\left(-\frac{x}{\frac{-1}{x}}\right)} + x \cdot \left(x + x\right) \]

7. Simplified 0.2

   \[\leadsto \color{blue}{\frac{-x}{\frac{-1}{x}}} + x \cdot \left(x + x\right) \]
   Proof

   [Start] 0.2	\[ \left(-\frac{x}{\frac{-1}{x}}\right) + x \cdot \left(x + x\right) \]
   rational.json-simplify-10 [=>] 0.2	\[ \color{blue}{\frac{\frac{x}{\frac{-1}{x}}}{-1}} + x \cdot \left(x + x\right) \]
   rational.json-simplify-44 [=>] 0.2	\[ \color{blue}{\frac{\frac{x}{-1}}{\frac{-1}{x}}} + x \cdot \left(x + x\right) \]
   rational.json-simplify-10 [<=] 0.2	\[ \frac{\color{blue}{-x}}{\frac{-1}{x}} + x \cdot \left(x + x\right) \]

8. Final simplification 0.2

   \[\leadsto \frac{-x}{\frac{-1}{x}} + x \cdot \left(x + x\right) \]

Alternatives

Alternative 1
Error	0.2
Cost	576

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

Alternative 2
Error	0.2
Cost	320

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

Reproduce

herbie shell --seed 2023075 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))