Expression, p6

Percentage Accurate: 94.3% → 100.0%

Time: 11.4s

Alternatives: 8

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, 0.5× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(b + c\right) + 0.3333333333333333 \cdot \left(\left(d + a\right) + \left(d + a\right) \cdot 2\right)\right) \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (* 2.0 (+ (+ b c) (* 0.3333333333333333 (+ (+ d a) (* (+ d a) 2.0))))))

C

double code(double a, double b, double c, double d) {
	return 2.0 * ((b + c) + (0.3333333333333333 * ((d + a) + ((d + a) * 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 = 2.0d0 * ((b + c) + (0.3333333333333333d0 * ((d + a) + ((d + a) * 2.0d0))))
end function

Java

public static double code(double a, double b, double c, double d) {
	return 2.0 * ((b + c) + (0.3333333333333333 * ((d + a) + ((d + a) * 2.0))));
}

Python

def code(a, b, c, d):
	return 2.0 * ((b + c) + (0.3333333333333333 * ((d + a) + ((d + a) * 2.0))))

Julia

function code(a, b, c, d)
	return Float64(2.0 * Float64(Float64(b + c) + Float64(0.3333333333333333 * Float64(Float64(d + a) + Float64(Float64(d + a) * 2.0)))))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = 2.0 * ((b + c) + (0.3333333333333333 * ((d + a) + ((d + a) * 2.0))));
end

Wolfram

code[a_, b_, c_, d_] := N[(2.0 * N[(N[(b + c), $MachinePrecision] + N[(0.3333333333333333 * N[(N[(d + a), $MachinePrecision] + N[(N[(d + a), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 96.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c, double d) {
	return 2.0 * ((d + (b * 2.0)) + (a + (c - 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 * ((d + (b * 2.0d0)) + (a + (c - b)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 3: 14.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c + d \leq 16.018:\\ \;\;\;\;b \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(b + c\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (+ c d) 16.018) (* b 2.0) (* (+ b c) 2.0)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c + d) <= 16.018) {
		tmp = b * 2.0;
	} else {
		tmp = (b + c) * 2.0;
	}
	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) <= 16.018d0) then
        tmp = b * 2.0d0
    else
        tmp = (b + c) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c + d) <= 16.018) {
		tmp = b * 2.0;
	} else {
		tmp = (b + c) * 2.0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c + d) <= 16.018:
		tmp = b * 2.0
	else:
		tmp = (b + c) * 2.0
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (Float64(c + d) <= 16.018)
		tmp = Float64(b * 2.0);
	else
		tmp = Float64(Float64(b + c) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c + d) <= 16.018)
		tmp = b * 2.0;
	else
		tmp = (b + c) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[N[(c + d), $MachinePrecision], 16.018], N[(b * 2.0), $MachinePrecision], N[(N[(b + c), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 4: 94.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 5: 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

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1. Add Preprocessing

Alternative 6: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (d + (c + a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 7: 6.3% accurate, 3.0× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c, double d) {
	return b * 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 = b * 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 11.6% accurate, 3.0× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c, double d) {
	return c * 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 = c * 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

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 2024008 
(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))