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

Percentage Accurate: 99.8% → 99.8%

Time: 4.0s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. fma-neg 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 70.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 0.106:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.8e+56) (- z) (if (<= z 0.106) (* 3.0 (* x y)) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.8e+56) {
		tmp = -z;
	} else if (z <= 0.106) {
		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 (z <= (-6.8d+56)) then
        tmp = -z
    else if (z <= 0.106d0) 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 (z <= -6.8e+56) {
		tmp = -z;
	} else if (z <= 0.106) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.8e+56:
		tmp = -z
	elif z <= 0.106:
		tmp = 3.0 * (x * y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.8e+56)
		tmp = Float64(-z);
	elseif (z <= 0.106)
		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 (z <= -6.8e+56)
		tmp = -z;
	elseif (z <= 0.106)
		tmp = 3.0 * (x * y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.8e+56], (-z), If[LessEqual[z, 0.106], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000002e56 or 0.105999999999999997 < z

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 79.1%

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

      1. mul-1-neg 79.1%

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

   6. Simplified 79.1%

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

   if -6.80000000000000002e56 < z < 0.105999999999999997

   1. Initial program 99.7%

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

      1. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. add-sqr-sqrt 48.3%

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

      3. associate-*r* 48.3%

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

      4. fma-neg 48.3%

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

      5. add-sqr-sqrt 24.8%

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

      6. sqrt-unprod 42.1%

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

      7. sqr-neg 42.1%

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

      8. sqrt-unprod 17.9%

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

      9. add-sqr-sqrt 37.6%

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

   5. Applied egg-rr 37.6%

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

   6. Taylor expanded in y around inf 77.6%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 0.106:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+57}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 0.93:\\ \;\;\;\;\left(x \cdot 3\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.6e+57) (- z) (if (<= z 0.93) (* (* x 3.0) y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e+57) {
		tmp = -z;
	} else if (z <= 0.93) {
		tmp = (x * 3.0) * 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 (z <= (-1.6d+57)) then
        tmp = -z
    else if (z <= 0.93d0) then
        tmp = (x * 3.0d0) * y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e+57) {
		tmp = -z;
	} else if (z <= 0.93) {
		tmp = (x * 3.0) * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.6e+57:
		tmp = -z
	elif z <= 0.93:
		tmp = (x * 3.0) * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.6e+57)
		tmp = Float64(-z);
	elseif (z <= 0.93)
		tmp = Float64(Float64(x * 3.0) * y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.6e+57)
		tmp = -z;
	elseif (z <= 0.93)
		tmp = (x * 3.0) * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.6e+57], (-z), If[LessEqual[z, 0.93], N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000015e57 or 0.930000000000000049 < z

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 79.1%

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

      1. mul-1-neg 79.1%

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

   6. Simplified 79.1%

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

   if -1.60000000000000015e57 < z < 0.930000000000000049

   1. Initial program 99.7%

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

      1. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. add-sqr-sqrt 48.3%

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

      3. associate-*r* 48.3%

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

      4. fma-neg 48.3%

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

      5. add-sqr-sqrt 24.8%

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

      6. sqrt-unprod 42.1%

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

      7. sqr-neg 42.1%

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

      8. sqrt-unprod 17.9%

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

      9. add-sqr-sqrt 37.6%

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

   5. Applied egg-rr 37.6%

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

   6. Taylor expanded in y around inf 77.6%

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

      1. associate-*r* 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-*r* 77.5%

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

   8. Simplified 77.5%

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

      1. add-sqr-sqrt 43.6%

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

      2. pow2 43.6%

         \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \left(3 \cdot y\right)}\right)}^{2}} \]

   10. Applied egg-rr 43.6%

       \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \left(3 \cdot y\right)}\right)}^{2}} \]
   11. Step-by-step derivation

       1. unpow2 43.6%

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

       2. add-sqr-sqrt 77.5%

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

       3. associate-*r* 77.6%

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

       4. *-commutative 77.6%

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

   12. Applied egg-rr 77.6%

       \[\leadsto \color{blue}{\left(3 \cdot x\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+57}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 0.93:\\ \;\;\;\;\left(x \cdot 3\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 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 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
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. Taylor expanded in x around 0 99.8%

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

5. Final simplification 99.8%

   \[\leadsto 3 \cdot \left(x \cdot y\right) - z \]

Alternative 5: 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]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]

2. Final simplification 99.8%

   \[\leadsto \left(x \cdot 3\right) \cdot y - z \]

Alternative 6: 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 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
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. Taylor expanded in x around 0 48.8%

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

   1. mul-1-neg 48.8%

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

6. Simplified 48.8%

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

7. Final simplification 48.8%

   \[\leadsto -z \]

Alternative 7: 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 99.8%

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

   1. *-commutative 99.8%

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

   2. add-sqr-sqrt 52.9%

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

   3. associate-*r* 52.9%

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

   4. fma-neg 52.9%

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

   5. add-sqr-sqrt 23.7%

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

   6. sqrt-unprod 30.1%

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

   7. sqr-neg 30.1%

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

   8. sqrt-unprod 13.0%

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

   9. add-sqr-sqrt 26.4%

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

5. Applied egg-rr 26.4%

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

6. Taylor expanded in y around 0 2.3%

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

7. Final simplification 2.3%

   \[\leadsto z \]

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 2023292 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3.0 y)) z)

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