Expression, p6

Percentage Accurate: 94.3% → 100.0%

Time: 3.4s

Alternatives: 6

Speedup: 1.0×

Specification

\[\left(\left(\left(-14 \leq a \land a \leq -13\right) \land \left(-3 \leq b \land b \leq -2\right)\right) \land \left(3 \leq c \land c \leq 3.5\right)\right) \land \left(12.5 \leq d \land d \leq 13.5\right)\]

Math

\[\begin{array}{l} \\ \left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (* (+ a (+ b (+ c d))) 2.0))

C

double code(double a, double b, double c, double d) {
	return (a + (b + (c + d))) * 2.0;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = (a + (b + (c + d))) * 2.0d0
end function

Java

public static double code(double a, double b, double c, double d) {
	return (a + (b + (c + d))) * 2.0;
}

Python

def code(a, b, c, d):
	return (a + (b + (c + d))) * 2.0

Julia

function code(a, b, c, d)
	return Float64(Float64(a + Float64(b + Float64(c + d))) * 2.0)
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = (a + (b + (c + d))) * 2.0;
end

Wolfram

code[a_, b_, c_, d_] := N[(N[(a + N[(b + N[(c + d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]

Initial Program: 94.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (* (+ a (+ b (+ c d))) 2.0))

C

double code(double a, double b, double c, double d) {
	return (a + (b + (c + d))) * 2.0;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = (a + (b + (c + d))) * 2.0d0
end function

Java

public static double code(double a, double b, double c, double d) {
	return (a + (b + (c + d))) * 2.0;
}

Python

def code(a, b, c, d):
	return (a + (b + (c + d))) * 2.0

Julia

function code(a, b, c, d)
	return Float64(Float64(a + Float64(b + Float64(c + d))) * 2.0)
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = (a + (b + (c + d))) * 2.0;
end

Wolfram

code[a_, b_, c_, d_] := N[(N[(a + N[(b + N[(c + d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(b + \left(c + \left(a + d\right)\right)\right) \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (* 2.0 (+ b (+ c (+ a d)))))

C

double code(double a, double b, double c, double d) {
	return 2.0 * (b + (c + (a + d)));
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = 2.0d0 * (b + (c + (a + d)))
end function

Java

public static double code(double a, double b, double c, double d) {
	return 2.0 * (b + (c + (a + d)));
}

Python

def code(a, b, c, d):
	return 2.0 * (b + (c + (a + d)))

Julia

function code(a, b, c, d)
	return Float64(2.0 * Float64(b + Float64(c + Float64(a + d))))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = 2.0 * (b + (c + (a + d)));
end

Wolfram

code[a_, b_, c_, d_] := N[(2.0 * N[(b + N[(c + N[(a + d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.3%

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
2. Step-by-step derivation

   1. *-commutative 94.3%

      \[\leadsto \color{blue}{2 \cdot \left(a + \left(b + \left(c + d\right)\right)\right)} \]

   2. +-commutative 94.3%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right) \]

   3. +-commutative 94.3%

      \[\leadsto 2 \cdot \left(a + \left(\color{blue}{\left(d + c\right)} + b\right)\right) \]

   4. associate-+r+ 95.6%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(d + \left(c + b\right)\right)}\right) \]

   5. +-commutative 95.6%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + b\right) + d\right)}\right) \]

   6. associate-+r+ 95.0%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(c + \left(b + d\right)\right)}\right) \]

3. Simplified 95.0%

   \[\leadsto \color{blue}{2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right)} \]

4. Taylor expanded in a around 0 94.3%

   \[\leadsto 2 \cdot \color{blue}{\left(a + \left(b + \left(c + d\right)\right)\right)} \]
5. Step-by-step derivation

   1. associate-+r+ 93.9%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(a + b\right) + \left(c + d\right)\right)} \]

   2. +-commutative 93.9%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(b + a\right)} + \left(c + d\right)\right) \]

   3. associate-+l+ 94.2%

      \[\leadsto 2 \cdot \color{blue}{\left(b + \left(a + \left(c + d\right)\right)\right)} \]

   4. associate-+r+ 95.1%

      \[\leadsto 2 \cdot \left(b + \color{blue}{\left(\left(a + c\right) + d\right)}\right) \]

   5. +-commutative 95.1%

      \[\leadsto 2 \cdot \left(b + \left(\color{blue}{\left(c + a\right)} + d\right)\right) \]

   6. associate-+l+ 100.0%

      \[\leadsto 2 \cdot \left(b + \color{blue}{\left(c + \left(a + d\right)\right)}\right) \]

6. Simplified 100.0%

   \[\leadsto 2 \cdot \color{blue}{\left(b + \left(c + \left(a + d\right)\right)\right)} \]

7. Final simplification 100.0%

   \[\leadsto 2 \cdot \left(b + \left(c + \left(a + d\right)\right)\right) \]

Alternative 2: 13.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c + d \leq 16.05805:\\ \;\;\;\;2 \cdot \left(a + d\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c + \left(a + d\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (+ c d) 16.05805) (* 2.0 (+ a d)) (* 2.0 (+ c (+ a d)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c + d) <= 16.05805) {
		tmp = 2.0 * (a + d);
	} else {
		tmp = 2.0 * (c + (a + d));
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((c + d) <= 16.05805d0) then
        tmp = 2.0d0 * (a + d)
    else
        tmp = 2.0d0 * (c + (a + d))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c + d) <= 16.05805) {
		tmp = 2.0 * (a + d);
	} else {
		tmp = 2.0 * (c + (a + d));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c + d) <= 16.05805:
		tmp = 2.0 * (a + d)
	else:
		tmp = 2.0 * (c + (a + d))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (Float64(c + d) <= 16.05805)
		tmp = Float64(2.0 * Float64(a + d));
	else
		tmp = Float64(2.0 * Float64(c + Float64(a + d)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c + d) <= 16.05805)
		tmp = 2.0 * (a + d);
	else
		tmp = 2.0 * (c + (a + d));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[N[(c + d), $MachinePrecision], 16.05805], N[(2.0 * N[(a + d), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c + N[(a + d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 c d) < 16.058050000000001

   1. Initial program 94.7%

      \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
   2. Step-by-step derivation

      1. *-commutative 94.7%

         \[\leadsto \color{blue}{2 \cdot \left(a + \left(b + \left(c + d\right)\right)\right)} \]

      2. +-commutative 94.7%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right) \]

      3. +-commutative 94.7%

         \[\leadsto 2 \cdot \left(a + \left(\color{blue}{\left(d + c\right)} + b\right)\right) \]

      4. associate-+r+ 95.4%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(d + \left(c + b\right)\right)}\right) \]

      5. +-commutative 95.4%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + b\right) + d\right)}\right) \]

      6. associate-+r+ 94.7%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(c + \left(b + d\right)\right)}\right) \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right)} \]

   4. Taylor expanded in b around 0 6.3%

      \[\leadsto 2 \cdot \color{blue}{\left(a + \left(c + d\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 6.3%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(c + d\right) + a\right)} \]

   6. Simplified 6.3%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c + d\right) + a\right)} \]

   7. Taylor expanded in c around 0 12.5%

      \[\leadsto 2 \cdot \color{blue}{\left(a + d\right)} \]

   if 16.058050000000001 < (+.f64 c d)

   1. Initial program 94.1%

      \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
   2. Step-by-step derivation

      1. *-commutative 94.1%

         \[\leadsto \color{blue}{2 \cdot \left(a + \left(b + \left(c + d\right)\right)\right)} \]

      2. +-commutative 94.1%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right) \]

      3. +-commutative 94.1%

         \[\leadsto 2 \cdot \left(a + \left(\color{blue}{\left(d + c\right)} + b\right)\right) \]

      4. associate-+r+ 95.7%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(d + \left(c + b\right)\right)}\right) \]

      5. +-commutative 95.7%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + b\right) + d\right)}\right) \]

      6. associate-+r+ 95.1%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(c + \left(b + d\right)\right)}\right) \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right)} \]

   4. Taylor expanded in b around 0 14.2%

      \[\leadsto 2 \cdot \color{blue}{\left(a + \left(c + d\right)\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 14.2%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(a + c\right) + d\right)} \]

      2. +-commutative 14.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c + a\right)} + d\right) \]

      3. associate-+l+ 14.2%

         \[\leadsto 2 \cdot \color{blue}{\left(c + \left(a + d\right)\right)} \]

   6. Simplified 14.2%

      \[\leadsto 2 \cdot \color{blue}{\left(c + \left(a + d\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 13.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c + d \leq 16.05805:\\ \;\;\;\;2 \cdot \left(a + d\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c + \left(a + d\right)\right)\\ \end{array} \]

Alternative 3: 95.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right) \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (* 2.0 (+ a (+ c (+ b d)))))

C

double code(double a, double b, double c, double d) {
	return 2.0 * (a + (c + (b + d)));
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = 2.0d0 * (a + (c + (b + d)))
end function

Java

public static double code(double a, double b, double c, double d) {
	return 2.0 * (a + (c + (b + d)));
}

Python

def code(a, b, c, d):
	return 2.0 * (a + (c + (b + d)))

Julia

function code(a, b, c, d)
	return Float64(2.0 * Float64(a + Float64(c + Float64(b + d))))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = 2.0 * (a + (c + (b + d)));
end

Wolfram

code[a_, b_, c_, d_] := N[(2.0 * N[(a + N[(c + N[(b + d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.3%

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
2. Step-by-step derivation

   1. *-commutative 94.3%

      \[\leadsto \color{blue}{2 \cdot \left(a + \left(b + \left(c + d\right)\right)\right)} \]

   2. +-commutative 94.3%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right) \]

   3. +-commutative 94.3%

      \[\leadsto 2 \cdot \left(a + \left(\color{blue}{\left(d + c\right)} + b\right)\right) \]

   4. associate-+r+ 95.6%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(d + \left(c + b\right)\right)}\right) \]

   5. +-commutative 95.6%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + b\right) + d\right)}\right) \]

   6. associate-+r+ 95.0%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(c + \left(b + d\right)\right)}\right) \]

3. Simplified 95.0%

   \[\leadsto \color{blue}{2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right)} \]

4. Final simplification 95.0%

   \[\leadsto 2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right) \]

Alternative 4: 12.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq 12.82:\\ \;\;\;\;2 \cdot \left(a + d\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d 12.82) (* 2.0 (+ a d)) (* 2.0 c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= 12.82) {
		tmp = 2.0 * (a + d);
	} else {
		tmp = 2.0 * c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (d <= 12.82d0) then
        tmp = 2.0d0 * (a + d)
    else
        tmp = 2.0d0 * c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= 12.82) {
		tmp = 2.0 * (a + d);
	} else {
		tmp = 2.0 * c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= 12.82:
		tmp = 2.0 * (a + d)
	else:
		tmp = 2.0 * c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= 12.82)
		tmp = Float64(2.0 * Float64(a + d));
	else
		tmp = Float64(2.0 * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= 12.82)
		tmp = 2.0 * (a + d);
	else
		tmp = 2.0 * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, 12.82], N[(2.0 * N[(a + d), $MachinePrecision]), $MachinePrecision], N[(2.0 * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < 12.82

   1. Initial program 94.8%

      \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
   2. Step-by-step derivation

      1. *-commutative 94.8%

         \[\leadsto \color{blue}{2 \cdot \left(a + \left(b + \left(c + d\right)\right)\right)} \]

      2. +-commutative 94.8%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right) \]

      3. +-commutative 94.8%

         \[\leadsto 2 \cdot \left(a + \left(\color{blue}{\left(d + c\right)} + b\right)\right) \]

      4. associate-+r+ 95.6%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(d + \left(c + b\right)\right)}\right) \]

      5. +-commutative 95.6%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + b\right) + d\right)}\right) \]

      6. associate-+r+ 95.1%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(c + \left(b + d\right)\right)}\right) \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right)} \]

   4. Taylor expanded in b around 0 6.6%

      \[\leadsto 2 \cdot \color{blue}{\left(a + \left(c + d\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 6.6%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(c + d\right) + a\right)} \]

   6. Simplified 6.6%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c + d\right) + a\right)} \]

   7. Taylor expanded in c around 0 12.1%

      \[\leadsto 2 \cdot \color{blue}{\left(a + d\right)} \]

   if 12.82 < d

   1. Initial program 94.0%

      \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
   2. Step-by-step derivation

      1. *-commutative 94.0%

         \[\leadsto \color{blue}{2 \cdot \left(a + \left(b + \left(c + d\right)\right)\right)} \]

      2. +-commutative 94.0%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right) \]

      3. +-commutative 94.0%

         \[\leadsto 2 \cdot \left(a + \left(\color{blue}{\left(d + c\right)} + b\right)\right) \]

      4. associate-+r+ 95.6%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(d + \left(c + b\right)\right)}\right) \]

      5. +-commutative 95.6%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + b\right) + d\right)}\right) \]

      6. associate-+r+ 95.0%

         \[\leadsto 2 \cdot \left(a + \color{blue}{\left(c + \left(b + d\right)\right)}\right) \]

   3. Simplified 95.0%

      \[\leadsto \color{blue}{2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right)} \]

   4. Taylor expanded in c around inf 14.2%

      \[\leadsto 2 \cdot \color{blue}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 13.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq 12.82:\\ \;\;\;\;2 \cdot \left(a + d\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot c\\ \end{array} \]

Alternative 5: 6.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot b \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (* 2.0 b))

C

double code(double a, double b, double c, double d) {
	return 2.0 * b;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = 2.0d0 * b
end function

Java

public static double code(double a, double b, double c, double d) {
	return 2.0 * b;
}

Python

def code(a, b, c, d):
	return 2.0 * b

Julia

function code(a, b, c, d)
	return Float64(2.0 * b)
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = 2.0 * b;
end

Wolfram

code[a_, b_, c_, d_] := N[(2.0 * b), $MachinePrecision]

Derivation

1. Initial program 94.3%

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
2. Step-by-step derivation

   1. *-commutative 94.3%

      \[\leadsto \color{blue}{2 \cdot \left(a + \left(b + \left(c + d\right)\right)\right)} \]

   2. +-commutative 94.3%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right) \]

   3. +-commutative 94.3%

      \[\leadsto 2 \cdot \left(a + \left(\color{blue}{\left(d + c\right)} + b\right)\right) \]

   4. associate-+r+ 95.6%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(d + \left(c + b\right)\right)}\right) \]

   5. +-commutative 95.6%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + b\right) + d\right)}\right) \]

   6. associate-+r+ 95.0%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(c + \left(b + d\right)\right)}\right) \]

3. Simplified 95.0%

   \[\leadsto \color{blue}{2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right)} \]

4. Taylor expanded in b around inf 6.1%

   \[\leadsto 2 \cdot \color{blue}{b} \]

5. Final simplification 6.1%

   \[\leadsto 2 \cdot b \]

Alternative 6: 11.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot c \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (* 2.0 c))

C

double code(double a, double b, double c, double d) {
	return 2.0 * c;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = 2.0d0 * c
end function

Java

public static double code(double a, double b, double c, double d) {
	return 2.0 * c;
}

Python

def code(a, b, c, d):
	return 2.0 * c

Julia

function code(a, b, c, d)
	return Float64(2.0 * c)
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = 2.0 * c;
end

Wolfram

code[a_, b_, c_, d_] := N[(2.0 * c), $MachinePrecision]

Derivation

1. Initial program 94.3%

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
2. Step-by-step derivation

   1. *-commutative 94.3%

      \[\leadsto \color{blue}{2 \cdot \left(a + \left(b + \left(c + d\right)\right)\right)} \]

   2. +-commutative 94.3%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right) \]

   3. +-commutative 94.3%

      \[\leadsto 2 \cdot \left(a + \left(\color{blue}{\left(d + c\right)} + b\right)\right) \]

   4. associate-+r+ 95.6%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(d + \left(c + b\right)\right)}\right) \]

   5. +-commutative 95.6%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + b\right) + d\right)}\right) \]

   6. associate-+r+ 95.0%

      \[\leadsto 2 \cdot \left(a + \color{blue}{\left(c + \left(b + d\right)\right)}\right) \]

3. Simplified 95.0%

   \[\leadsto \color{blue}{2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right)} \]

4. Taylor expanded in c around inf 11.7%

   \[\leadsto 2 \cdot \color{blue}{c} \]

5. Final simplification 11.7%

   \[\leadsto 2 \cdot c \]

Developer target: 94.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2 \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (+ (* (+ a b) 2.0) (* (+ c d) 2.0)))

C

double code(double a, double b, double c, double d) {
	return ((a + b) * 2.0) + ((c + d) * 2.0);
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = ((a + b) * 2.0d0) + ((c + d) * 2.0d0)
end function

Java

public static double code(double a, double b, double c, double d) {
	return ((a + b) * 2.0) + ((c + d) * 2.0);
}

Python

def code(a, b, c, d):
	return ((a + b) * 2.0) + ((c + d) * 2.0)

Julia

function code(a, b, c, d)
	return Float64(Float64(Float64(a + b) * 2.0) + Float64(Float64(c + d) * 2.0))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = ((a + b) * 2.0) + ((c + d) * 2.0);
end

Wolfram

code[a_, b_, c_, d_] := N[(N[(N[(a + b), $MachinePrecision] * 2.0), $MachinePrecision] + N[(N[(c + d), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023314 
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :pre (and (and (and (and (<= -14.0 a) (<= a -13.0)) (and (<= -3.0 b) (<= b -2.0))) (and (<= 3.0 c) (<= c 3.5))) (and (<= 12.5 d) (<= d 13.5)))

  :herbie-target
  (+ (* (+ a b) 2.0) (* (+ c d) 2.0))

  (* (+ a (+ b (+ c d))) 2.0))