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

Percentage Accurate: 99.8% → 99.8%

Time: 6.1s

Alternatives: 6

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, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (3.0 * (x * 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 = (3.0d0 * (x * y)) - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-*l* 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around 0 99.9%

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

Alternative 2: 70.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+58} \lor \neg \left(x \leq 6.1 \cdot 10^{-6}\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.5e+58) (not (<= x 6.1e-6))) (* 3.0 (* x y)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e+58) || !(x <= 6.1e-6)) {
		tmp = 3.0 * (x * y);
	} 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 ((x <= (-6.5d+58)) .or. (.not. (x <= 6.1d-6))) then
        tmp = 3.0d0 * (x * y)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e+58) || !(x <= 6.1e-6)) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.5e+58) or not (x <= 6.1e-6):
		tmp = 3.0 * (x * y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.5e+58) || !(x <= 6.1e-6))
		tmp = Float64(3.0 * Float64(x * y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.5e+58) || ~((x <= 6.1e-6)))
		tmp = 3.0 * (x * y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e+58], N[Not[LessEqual[x, 6.1e-6]], $MachinePrecision]], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -6.49999999999999998e58 or 6.10000000000000004e-6 < x

   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 73.0%

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

   if -6.49999999999999998e58 < x < 6.10000000000000004e-6

   1. Initial program 99.9%

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

      1. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 73.1%

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

      1. neg-mul-1 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+58} \lor \neg \left(x \leq 6.1 \cdot 10^{-6}\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 650:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.8e+58) (* x (* 3.0 y)) (if (<= x 650.0) (- z) (* y (* 3.0 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e+58) {
		tmp = x * (3.0 * y);
	} else if (x <= 650.0) {
		tmp = -z;
	} else {
		tmp = y * (3.0 * x);
	}
	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 (x <= (-4.8d+58)) then
        tmp = x * (3.0d0 * y)
    else if (x <= 650.0d0) then
        tmp = -z
    else
        tmp = y * (3.0d0 * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e+58) {
		tmp = x * (3.0 * y);
	} else if (x <= 650.0) {
		tmp = -z;
	} else {
		tmp = y * (3.0 * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.8e+58:
		tmp = x * (3.0 * y)
	elif x <= 650.0:
		tmp = -z
	else:
		tmp = y * (3.0 * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.8e+58)
		tmp = Float64(x * Float64(3.0 * y));
	elseif (x <= 650.0)
		tmp = Float64(-z);
	else
		tmp = Float64(y * Float64(3.0 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.8e+58)
		tmp = x * (3.0 * y);
	elseif (x <= 650.0)
		tmp = -z;
	else
		tmp = y * (3.0 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.8e+58], N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 650.0], (-z), N[(y * N[(3.0 * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e58

   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 99.9%

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

   6. Taylor expanded in x around inf 74.8%

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

      1. associate-*r* 74.8%

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

      2. *-commutative 74.8%

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

      3. associate-*r* 74.8%

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

   8. Simplified 74.8%

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

   if -4.8e58 < x < 650

   1. Initial program 99.9%

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

      1. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 73.5%

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

      1. neg-mul-1 73.5%

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

   7. Simplified 73.5%

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

   if 650 < x

   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 z around inf 89.5%

      \[\leadsto \color{blue}{z \cdot \left(3 \cdot \frac{x \cdot y}{z} - 1\right)} \]
   6. Step-by-step derivation

      1. clear-num 89.5%

         \[\leadsto z \cdot \left(3 \cdot \color{blue}{\frac{1}{\frac{z}{x \cdot y}}} - 1\right) \]

      2. associate-/r/ 89.4%

         \[\leadsto z \cdot \left(3 \cdot \color{blue}{\left(\frac{1}{z} \cdot \left(x \cdot y\right)\right)} - 1\right) \]

   7. Applied egg-rr 89.4%

      \[\leadsto z \cdot \left(3 \cdot \color{blue}{\left(\frac{1}{z} \cdot \left(x \cdot y\right)\right)} - 1\right) \]

   8. Taylor expanded in z around 0 73.4%

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

      1. associate-*r* 73.5%

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

   10. Simplified 73.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 650:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-7}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.3e+58) (* x (* 3.0 y)) (if (<= x 2.4e-7) (- z) (* 3.0 (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.3e+58) {
		tmp = x * (3.0 * y);
	} else if (x <= 2.4e-7) {
		tmp = -z;
	} else {
		tmp = 3.0 * (x * y);
	}
	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 (x <= (-4.3d+58)) then
        tmp = x * (3.0d0 * y)
    else if (x <= 2.4d-7) then
        tmp = -z
    else
        tmp = 3.0d0 * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.3e+58) {
		tmp = x * (3.0 * y);
	} else if (x <= 2.4e-7) {
		tmp = -z;
	} else {
		tmp = 3.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.3e+58:
		tmp = x * (3.0 * y)
	elif x <= 2.4e-7:
		tmp = -z
	else:
		tmp = 3.0 * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.3e+58)
		tmp = Float64(x * Float64(3.0 * y));
	elseif (x <= 2.4e-7)
		tmp = Float64(-z);
	else
		tmp = Float64(3.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.3e+58)
		tmp = x * (3.0 * y);
	elseif (x <= 2.4e-7)
		tmp = -z;
	else
		tmp = 3.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.3e+58], N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-7], (-z), N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.29999999999999991e58

   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 99.9%

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

   6. Taylor expanded in x around inf 74.8%

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

      1. associate-*r* 74.8%

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

      2. *-commutative 74.8%

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

      3. associate-*r* 74.8%

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

   8. Simplified 74.8%

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

   if -4.29999999999999991e58 < x < 2.39999999999999979e-7

   1. Initial program 99.9%

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

      1. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 73.1%

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

      1. neg-mul-1 73.1%

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

   7. Simplified 73.1%

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

   if 2.39999999999999979e-7 < x

   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 71.0%

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

Alternative 5: 50.1% 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 99.9%

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

   1. associate-*l* 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around 0 52.1%

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

   1. neg-mul-1 52.1%

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

7. Simplified 52.1%

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

Alternative 6: 2.3% accurate, 7.0× 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 z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

   1. associate-*l* 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around 0 52.1%

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

   1. neg-mul-1 52.1%

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

7. Simplified 52.1%

   \[\leadsto \color{blue}{-z} \]
8. Step-by-step derivation

   1. neg-sub0 52.1%

      \[\leadsto \color{blue}{0 - z} \]

   2. sub-neg 52.1%

      \[\leadsto \color{blue}{0 + \left(-z\right)} \]

   3. add-sqr-sqrt 26.6%

      \[\leadsto 0 + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}} \]

   4. sqrt-unprod 18.5%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \]

   5. sqr-neg 18.5%

      \[\leadsto 0 + \sqrt{\color{blue}{z \cdot z}} \]

   6. sqrt-unprod 1.1%

      \[\leadsto 0 + \color{blue}{\sqrt{z} \cdot \sqrt{z}} \]

   7. add-sqr-sqrt 2.2%

      \[\leadsto 0 + \color{blue}{z} \]

9. Applied egg-rr 2.2%

   \[\leadsto \color{blue}{0 + z} \]
10. Step-by-step derivation

    1. +-lft-identity 2.2%

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

11. Simplified 2.2%

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

Developer Target 1: 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 2024138 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* x (* 3 y)) z))

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