Expression, p6

Percentage Accurate: 94.3% → 96.3%

Time: 10.6s

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: 96.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 2: 94.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 3: 95.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 4: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 5: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 6: 13.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 7: 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

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

Alternative 8: 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

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

Developer target: 94.1% 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 2023343 
(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))