Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Percentage Accurate: 99.8% → 99.8%

Time: 5.2s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot y - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * 3.0d0) * y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Python

def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot y - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * 3.0d0) * y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Python

def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x \cdot y, 3, -z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (* x y) 3.0 (- z)))

C

double code(double x, double y, double z) {
	return fma((x * y), 3.0, -z);
}

Julia

function code(x, y, z)
	return fma(Float64(x * y), 3.0, Float64(-z))
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] * 3.0 + (-z)), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
2. Step-by-step derivation

   1. associate-*l* 99.9%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 99.9%

   \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} - z \]
6. Step-by-step derivation

   1. *-commutative 99.9%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 3} - z \]

   2. fma-neg 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot y, 3, -z\right)} \]

7. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot y, 3, -z\right)} \]
8. Add Preprocessing

Alternative 2: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-172} \lor \neg \left(y \leq 4.2 \cdot 10^{+45}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.15e-172) (not (<= y 4.2e+45))) (* (* x y) 3.0) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.15e-172) || !(y <= 4.2e+45)) {
		tmp = (x * y) * 3.0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.15d-172)) .or. (.not. (y <= 4.2d+45))) then
        tmp = (x * y) * 3.0d0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.15e-172) || !(y <= 4.2e+45)) {
		tmp = (x * y) * 3.0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.15e-172) or not (y <= 4.2e+45):
		tmp = (x * y) * 3.0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.15e-172) || !(y <= 4.2e+45))
		tmp = Float64(Float64(x * y) * 3.0);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.15e-172) || ~((y <= 4.2e+45)))
		tmp = (x * y) * 3.0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.15e-172], N[Not[LessEqual[y, 4.2e+45]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 3.0), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if y < -2.1499999999999999e-172 or 4.1999999999999999e45 < y

   1. Initial program 99.8%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Step-by-step derivation

      1. associate-*l* 99.8%

         \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} - z \]

   6. Taylor expanded in x around inf 69.2%

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

   if -2.1499999999999999e-172 < y < 4.1999999999999999e45

   1. Initial program 99.9%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 77.2%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   6. Step-by-step derivation

      1. mul-1-neg 77.2%

         \[\leadsto \color{blue}{-z} \]

   7. Simplified 77.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-172} \lor \neg \left(y \leq 4.2 \cdot 10^{+45}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.4e-176)
   (* y (* x 3.0))
   (if (<= y 2.8e+43) (- z) (* (* x y) 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.4e-176) {
		tmp = y * (x * 3.0);
	} else if (y <= 2.8e+43) {
		tmp = -z;
	} else {
		tmp = (x * y) * 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.4d-176)) then
        tmp = y * (x * 3.0d0)
    else if (y <= 2.8d+43) then
        tmp = -z
    else
        tmp = (x * y) * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.4e-176) {
		tmp = y * (x * 3.0);
	} else if (y <= 2.8e+43) {
		tmp = -z;
	} else {
		tmp = (x * y) * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.4e-176:
		tmp = y * (x * 3.0)
	elif y <= 2.8e+43:
		tmp = -z
	else:
		tmp = (x * y) * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.4e-176)
		tmp = Float64(y * Float64(x * 3.0));
	elseif (y <= 2.8e+43)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x * y) * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.4e-176)
		tmp = y * (x * 3.0);
	elseif (y <= 2.8e+43)
		tmp = -z;
	else
		tmp = (x * y) * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.4e-176], N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+43], (-z), N[(N[(x * y), $MachinePrecision] * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3999999999999997e-176

   1. Initial program 99.8%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Step-by-step derivation

      1. associate-*l* 99.8%

         \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} - z \]

   6. Taylor expanded in x around inf 64.7%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 64.7%

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

      2. associate-*l* 64.7%

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

      3. *-commutative 64.7%

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

   8. Simplified 64.7%

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

   9. Taylor expanded in x around 0 64.7%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 64.6%

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

   11. Simplified 64.6%

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

   if -5.3999999999999997e-176 < y < 2.80000000000000019e43

   1. Initial program 99.9%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   6. Step-by-step derivation

      1. mul-1-neg 77.0%

         \[\leadsto \color{blue}{-z} \]

   7. Simplified 77.0%

      \[\leadsto \color{blue}{-z} \]

   if 2.80000000000000019e43 < y

   1. Initial program 99.8%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Step-by-step derivation

      1. associate-*l* 99.8%

         \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} - z \]

   6. Taylor expanded in x around inf 75.9%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+45}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.4e-176)
   (* x (* y 3.0))
   (if (<= y 4.8e+45) (- z) (* (* x y) 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.4e-176) {
		tmp = x * (y * 3.0);
	} else if (y <= 4.8e+45) {
		tmp = -z;
	} else {
		tmp = (x * y) * 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.4d-176)) then
        tmp = x * (y * 3.0d0)
    else if (y <= 4.8d+45) then
        tmp = -z
    else
        tmp = (x * y) * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.4e-176) {
		tmp = x * (y * 3.0);
	} else if (y <= 4.8e+45) {
		tmp = -z;
	} else {
		tmp = (x * y) * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.4e-176:
		tmp = x * (y * 3.0)
	elif y <= 4.8e+45:
		tmp = -z
	else:
		tmp = (x * y) * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.4e-176)
		tmp = Float64(x * Float64(y * 3.0));
	elseif (y <= 4.8e+45)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x * y) * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.4e-176)
		tmp = x * (y * 3.0);
	elseif (y <= 4.8e+45)
		tmp = -z;
	else
		tmp = (x * y) * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.4e-176], N[(x * N[(y * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+45], (-z), N[(N[(x * y), $MachinePrecision] * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3999999999999997e-176

   1. Initial program 99.8%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Step-by-step derivation

      1. associate-*l* 99.8%

         \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} - z \]

   6. Taylor expanded in x around inf 64.7%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 64.7%

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

      2. associate-*l* 64.7%

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

      3. *-commutative 64.7%

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

   8. Simplified 64.7%

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

   if -5.3999999999999997e-176 < y < 4.79999999999999979e45

   1. Initial program 99.9%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   6. Step-by-step derivation

      1. mul-1-neg 77.0%

         \[\leadsto \color{blue}{-z} \]

   7. Simplified 77.0%

      \[\leadsto \color{blue}{-z} \]

   if 4.79999999999999979e45 < y

   1. Initial program 99.8%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Step-by-step derivation

      1. associate-*l* 99.8%

         \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} - z \]

   6. Taylor expanded in x around inf 75.9%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+45}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(x \cdot 3\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* y (* x 3.0)) z))

C

double code(double x, double y, double z) {
	return (y * (x * 3.0)) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y * (x * 3.0d0)) - z
end function

Java

public static double code(double x, double y, double z) {
	return (y * (x * 3.0)) - z;
}

Python

def code(x, y, z):
	return (y * (x * 3.0)) - z

Julia

function code(x, y, z)
	return Float64(Float64(y * Float64(x * 3.0)) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y * (x * 3.0)) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
2. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto y \cdot \left(x \cdot 3\right) - z \]
4. Add Preprocessing

Alternative 6: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot y\right) \cdot 3 - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x y) 3.0) z))

C

double code(double x, double y, double z) {
	return ((x * y) * 3.0) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * y) * 3.0d0) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * y) * 3.0) - z;
}

Python

def code(x, y, z):
	return ((x * y) * 3.0) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * y) * 3.0) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * y) * 3.0) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] * 3.0), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
2. Step-by-step derivation

   1. associate-*l* 99.9%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 99.9%

   \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} - z \]

6. Final simplification 99.9%

   \[\leadsto \left(x \cdot y\right) \cdot 3 - z \]
7. Add Preprocessing

Alternative 7: 50.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ -z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- z))

C

double code(double x, double y, double z) {
	return -z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -z
end function

Java

public static double code(double x, double y, double z) {
	return -z;
}

Python

def code(x, y, z):
	return -z

Julia

function code(x, y, z)
	return Float64(-z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -z;
end

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
2. Step-by-step derivation

   1. associate-*l* 99.9%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 50.7%

   \[\leadsto \color{blue}{-1 \cdot z} \]
6. Step-by-step derivation

   1. mul-1-neg 50.7%

      \[\leadsto \color{blue}{-z} \]

7. Simplified 50.7%

   \[\leadsto \color{blue}{-z} \]
8. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(3 \cdot y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* x (* 3.0 y)) z))

C

double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (3.0d0 * y)) - z
end function

Java

public static double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Python

def code(x, y, z):
	return (x * (3.0 * y)) - z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(3.0 * y)) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (3.0 * y)) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))