Expression, p6

Percentage Accurate: 94.3% → 100.0%

Time: 11.2s

Alternatives: 9

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

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

FPCore

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

C

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

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 + (2.0d0 * (a + d)))) * 0.3333333333333333d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

   1. add-cbrt-cube 94.1%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(b + \left(c + d\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)}} \cdot 2 \]

   2. pow1/3 67.0%

      \[\leadsto \color{blue}{{\left(\left(\left(a + \left(b + \left(c + d\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)\right)}^{0.3333333333333333}} \cdot 2 \]

   3. pow3 67.0%

      \[\leadsto {\color{blue}{\left({\left(a + \left(b + \left(c + d\right)\right)\right)}^{3}\right)}}^{0.3333333333333333} \cdot 2 \]

   4. +-commutative 67.0%

      \[\leadsto {\left({\left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right)}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   5. associate-+r+ 67.8%

      \[\leadsto {\left({\left(a + \color{blue}{\left(c + \left(d + b\right)\right)}\right)}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   6. +-commutative 67.8%

      \[\leadsto {\left({\left(a + \left(c + \color{blue}{\left(b + d\right)}\right)\right)}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   7. associate-+r+ 67.9%

      \[\leadsto {\left({\color{blue}{\left(\left(a + c\right) + \left(b + d\right)\right)}}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   8. +-commutative 67.9%

      \[\leadsto {\left({\color{blue}{\left(\left(b + d\right) + \left(a + c\right)\right)}}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

4. Applied egg-rr 67.9%

   \[\leadsto \color{blue}{{\left({\left(\left(b + d\right) + \left(a + c\right)\right)}^{3}\right)}^{0.3333333333333333}} \cdot 2 \]

5. Taylor expanded in b around inf 94.8%

   \[\leadsto \color{blue}{\left(b + 0.3333333333333333 \cdot \left(a + \left(c + \left(d + \left(2 \cdot a + \left(2 \cdot c + 2 \cdot d\right)\right)\right)\right)\right)\right)} \cdot 2 \]

6. Taylor expanded in c around 0 100.0%

   \[\leadsto \left(b + \color{blue}{\left(c + 0.3333333333333333 \cdot \left(a + \left(d + \left(2 \cdot a + 2 \cdot d\right)\right)\right)\right)}\right) \cdot 2 \]
7. Step-by-step derivation

   1. *-commutative 100.0%

      \[\leadsto \left(b + \left(c + \color{blue}{\left(a + \left(d + \left(2 \cdot a + 2 \cdot d\right)\right)\right) \cdot 0.3333333333333333}\right)\right) \cdot 2 \]

   2. distribute-lft-out 100.0%

      \[\leadsto \left(b + \left(c + \left(a + \left(d + \color{blue}{2 \cdot \left(a + d\right)}\right)\right) \cdot 0.3333333333333333\right)\right) \cdot 2 \]

8. Simplified 100.0%

   \[\leadsto \left(b + \color{blue}{\left(c + \left(a + \left(d + 2 \cdot \left(a + d\right)\right)\right) \cdot 0.3333333333333333\right)}\right) \cdot 2 \]

9. Final simplification 100.0%

   \[\leadsto 2 \cdot \left(b + \left(c + \left(a + \left(d + 2 \cdot \left(a + d\right)\right)\right) \cdot 0.3333333333333333\right)\right) \]
10. Add Preprocessing

Alternative 2: 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

1. Initial program 94.3%

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
2. Add Preprocessing

3. Final simplification 94.3%

   \[\leadsto 2 \cdot \left(a + \left(b + \left(c + d\right)\right)\right) \]
4. Add Preprocessing

Alternative 3: 95.1% 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%

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

   2. associate-+r+ 95.1%

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

   3. +-commutative 95.1%

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

3. Simplified 95.1%

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

5. Final simplification 95.1%

   \[\leadsto 2 \cdot \left(a + \left(c + \left(b + d\right)\right)\right) \]
6. Add Preprocessing

Alternative 4: 95.6% 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

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%

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

   2. associate-+r+ 95.1%

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

   3. +-commutative 95.1%

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

3. Simplified 95.1%

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

5. Taylor expanded in a around 0 94.3%

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

   1. +-commutative 94.3%

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

   2. associate-+l+ 94.6%

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

   3. +-commutative 94.6%

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

   4. associate-+r+ 95.6%

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

7. Simplified 95.6%

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

8. Final simplification 95.6%

   \[\leadsto 2 \cdot \left(b + \left(d + \left(c + a\right)\right)\right) \]
9. Add Preprocessing

Alternative 5: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

   1. add-cbrt-cube 94.1%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(b + \left(c + d\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)}} \cdot 2 \]

   2. pow1/3 67.0%

      \[\leadsto \color{blue}{{\left(\left(\left(a + \left(b + \left(c + d\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)\right)}^{0.3333333333333333}} \cdot 2 \]

   3. pow3 67.0%

      \[\leadsto {\color{blue}{\left({\left(a + \left(b + \left(c + d\right)\right)\right)}^{3}\right)}}^{0.3333333333333333} \cdot 2 \]

   4. +-commutative 67.0%

      \[\leadsto {\left({\left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right)}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   5. associate-+r+ 67.8%

      \[\leadsto {\left({\left(a + \color{blue}{\left(c + \left(d + b\right)\right)}\right)}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   6. +-commutative 67.8%

      \[\leadsto {\left({\left(a + \left(c + \color{blue}{\left(b + d\right)}\right)\right)}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   7. associate-+r+ 67.9%

      \[\leadsto {\left({\color{blue}{\left(\left(a + c\right) + \left(b + d\right)\right)}}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   8. +-commutative 67.9%

      \[\leadsto {\left({\color{blue}{\left(\left(b + d\right) + \left(a + c\right)\right)}}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

4. Applied egg-rr 67.9%

   \[\leadsto \color{blue}{{\left({\left(\left(b + d\right) + \left(a + c\right)\right)}^{3}\right)}^{0.3333333333333333}} \cdot 2 \]

5. Taylor expanded in c around inf 96.2%

   \[\leadsto \color{blue}{\left(c + 0.3333333333333333 \cdot \left(a + \left(b + \left(d + \left(2 \cdot a + \left(2 \cdot b + 2 \cdot d\right)\right)\right)\right)\right)\right)} \cdot 2 \]

6. Taylor expanded in b around 0 99.9%

   \[\leadsto \left(c + \color{blue}{\left(b + 0.3333333333333333 \cdot \left(a + \left(d + \left(2 \cdot a + 2 \cdot d\right)\right)\right)\right)}\right) \cdot 2 \]
7. Step-by-step derivation

   1. distribute-lft-in 99.9%

      \[\leadsto \left(c + \left(b + 0.3333333333333333 \cdot \left(a + \left(d + \color{blue}{2 \cdot \left(a + d\right)}\right)\right)\right)\right) \cdot 2 \]

   2. associate-+r+ 99.9%

      \[\leadsto \left(c + \left(b + 0.3333333333333333 \cdot \color{blue}{\left(\left(a + d\right) + 2 \cdot \left(a + d\right)\right)}\right)\right) \cdot 2 \]

   3. distribute-rgt1-in 99.9%

      \[\leadsto \left(c + \left(b + 0.3333333333333333 \cdot \color{blue}{\left(\left(2 + 1\right) \cdot \left(a + d\right)\right)}\right)\right) \cdot 2 \]

   4. metadata-eval 99.9%

      \[\leadsto \left(c + \left(b + 0.3333333333333333 \cdot \left(\color{blue}{3} \cdot \left(a + d\right)\right)\right)\right) \cdot 2 \]

   5. +-commutative 99.9%

      \[\leadsto \left(c + \left(b + 0.3333333333333333 \cdot \left(3 \cdot \color{blue}{\left(d + a\right)}\right)\right)\right) \cdot 2 \]

8. Simplified 99.9%

   \[\leadsto \left(c + \color{blue}{\left(b + 0.3333333333333333 \cdot \left(3 \cdot \left(d + a\right)\right)\right)}\right) \cdot 2 \]

9. Taylor expanded in c around 0 94.3%

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

    1. +-commutative 94.3%

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

    2. +-commutative 94.3%

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

    3. associate-+r+ 94.2%

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

    4. +-commutative 94.2%

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

    5. associate-+l+ 94.8%

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

    6. associate-+l+ 95.8%

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

    7. +-commutative 95.8%

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

    8. +-commutative 95.8%

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

11. Simplified 95.8%

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

12. Final simplification 95.8%

    \[\leadsto 2 \cdot \left(d + \left(a + \left(b + c\right)\right)\right) \]
13. Add Preprocessing

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[a_, b_, c_, d_] := N[(2.0 * N[(c + N[(b + 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. Add Preprocessing
3. Step-by-step derivation

   1. add-cbrt-cube 94.1%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(b + \left(c + d\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)}} \cdot 2 \]

   2. pow1/3 67.0%

      \[\leadsto \color{blue}{{\left(\left(\left(a + \left(b + \left(c + d\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)\right)}^{0.3333333333333333}} \cdot 2 \]

   3. pow3 67.0%

      \[\leadsto {\color{blue}{\left({\left(a + \left(b + \left(c + d\right)\right)\right)}^{3}\right)}}^{0.3333333333333333} \cdot 2 \]

   4. +-commutative 67.0%

      \[\leadsto {\left({\left(a + \color{blue}{\left(\left(c + d\right) + b\right)}\right)}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   5. associate-+r+ 67.8%

      \[\leadsto {\left({\left(a + \color{blue}{\left(c + \left(d + b\right)\right)}\right)}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   6. +-commutative 67.8%

      \[\leadsto {\left({\left(a + \left(c + \color{blue}{\left(b + d\right)}\right)\right)}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   7. associate-+r+ 67.9%

      \[\leadsto {\left({\color{blue}{\left(\left(a + c\right) + \left(b + d\right)\right)}}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

   8. +-commutative 67.9%

      \[\leadsto {\left({\color{blue}{\left(\left(b + d\right) + \left(a + c\right)\right)}}^{3}\right)}^{0.3333333333333333} \cdot 2 \]

4. Applied egg-rr 67.9%

   \[\leadsto \color{blue}{{\left({\left(\left(b + d\right) + \left(a + c\right)\right)}^{3}\right)}^{0.3333333333333333}} \cdot 2 \]

5. Taylor expanded in c around inf 96.2%

   \[\leadsto \color{blue}{\left(c + 0.3333333333333333 \cdot \left(a + \left(b + \left(d + \left(2 \cdot a + \left(2 \cdot b + 2 \cdot d\right)\right)\right)\right)\right)\right)} \cdot 2 \]

6. Taylor expanded in b around 0 99.9%

   \[\leadsto \left(c + \color{blue}{\left(b + 0.3333333333333333 \cdot \left(a + \left(d + \left(2 \cdot a + 2 \cdot d\right)\right)\right)\right)}\right) \cdot 2 \]
7. Step-by-step derivation

   1. distribute-lft-in 99.9%

      \[\leadsto \left(c + \left(b + 0.3333333333333333 \cdot \left(a + \left(d + \color{blue}{2 \cdot \left(a + d\right)}\right)\right)\right)\right) \cdot 2 \]

   2. associate-+r+ 99.9%

      \[\leadsto \left(c + \left(b + 0.3333333333333333 \cdot \color{blue}{\left(\left(a + d\right) + 2 \cdot \left(a + d\right)\right)}\right)\right) \cdot 2 \]

   3. distribute-rgt1-in 99.9%

      \[\leadsto \left(c + \left(b + 0.3333333333333333 \cdot \color{blue}{\left(\left(2 + 1\right) \cdot \left(a + d\right)\right)}\right)\right) \cdot 2 \]

   4. metadata-eval 99.9%

      \[\leadsto \left(c + \left(b + 0.3333333333333333 \cdot \left(\color{blue}{3} \cdot \left(a + d\right)\right)\right)\right) \cdot 2 \]

   5. +-commutative 99.9%

      \[\leadsto \left(c + \left(b + 0.3333333333333333 \cdot \left(3 \cdot \color{blue}{\left(d + a\right)}\right)\right)\right) \cdot 2 \]

8. Simplified 99.9%

   \[\leadsto \left(c + \color{blue}{\left(b + 0.3333333333333333 \cdot \left(3 \cdot \left(d + a\right)\right)\right)}\right) \cdot 2 \]
9. Step-by-step derivation

   1. *-un-lft-identity 99.9%

      \[\leadsto \left(c + \color{blue}{1 \cdot \left(b + 0.3333333333333333 \cdot \left(3 \cdot \left(d + a\right)\right)\right)}\right) \cdot 2 \]

   2. associate-*r* 99.9%

      \[\leadsto \left(c + 1 \cdot \left(b + \color{blue}{\left(0.3333333333333333 \cdot 3\right) \cdot \left(d + a\right)}\right)\right) \cdot 2 \]

   3. metadata-eval 99.9%

      \[\leadsto \left(c + 1 \cdot \left(b + \color{blue}{1} \cdot \left(d + a\right)\right)\right) \cdot 2 \]

   4. *-un-lft-identity 99.9%

      \[\leadsto \left(c + 1 \cdot \left(b + \color{blue}{\left(d + a\right)}\right)\right) \cdot 2 \]

10. Applied egg-rr 99.9%

    \[\leadsto \left(c + \color{blue}{1 \cdot \left(b + \left(d + a\right)\right)}\right) \cdot 2 \]

11. Final simplification 99.9%

    \[\leadsto 2 \cdot \left(c + \left(b + \left(a + d\right)\right)\right) \]
12. Add Preprocessing

Alternative 7: 13.7% 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

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%

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

   2. associate-+r+ 95.1%

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

   3. +-commutative 95.1%

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

3. Simplified 95.1%

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

5. Taylor expanded in a around 0 94.3%

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

   1. +-commutative 94.3%

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

   2. associate-+l+ 94.6%

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

   3. +-commutative 94.6%

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

   4. associate-+r+ 95.6%

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

7. Simplified 95.6%

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

8. Taylor expanded in c around inf 14.5%

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

9. Final simplification 14.5%

   \[\leadsto 2 \cdot \left(b + c\right) \]
10. Add Preprocessing

Alternative 8: 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

1. Initial program 94.3%

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
2. Add Preprocessing

3. Taylor expanded in b around inf 5.8%

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

4. Final simplification 5.8%

   \[\leadsto b \cdot 2 \]
5. Add Preprocessing

Alternative 9: 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

1. Initial program 94.3%

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
2. Add Preprocessing

3. Taylor expanded in c around inf 12.1%

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

4. Final simplification 12.1%

   \[\leadsto c \cdot 2 \]
5. 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 2024010 
(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))