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

Percentage Accurate: 99.8% → 99.8%

Time: 5.5s

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

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

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-63} \lor \neg \left(y \leq 28000000000000 \lor \neg \left(y \leq 8.6 \cdot 10^{+56}\right) \land y \leq 7.5 \cdot 10^{+108}\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e-63)
         (not
          (or (<= y 28000000000000.0)
              (and (not (<= y 8.6e+56)) (<= y 7.5e+108)))))
   (* 3.0 (* x y))
   (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e-63) || !((y <= 28000000000000.0) || (!(y <= 8.6e+56) && (y <= 7.5e+108)))) {
		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 ((y <= (-6.2d-63)) .or. (.not. (y <= 28000000000000.0d0) .or. (.not. (y <= 8.6d+56)) .and. (y <= 7.5d+108))) 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 ((y <= -6.2e-63) || !((y <= 28000000000000.0) || (!(y <= 8.6e+56) && (y <= 7.5e+108)))) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e-63) or not ((y <= 28000000000000.0) or (not (y <= 8.6e+56) and (y <= 7.5e+108))):
		tmp = 3.0 * (x * y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e-63) || !((y <= 28000000000000.0) || (!(y <= 8.6e+56) && (y <= 7.5e+108))))
		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 ((y <= -6.2e-63) || ~(((y <= 28000000000000.0) || (~((y <= 8.6e+56)) && (y <= 7.5e+108)))))
		tmp = 3.0 * (x * y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e-63], N[Not[Or[LessEqual[y, 28000000000000.0], And[N[Not[LessEqual[y, 8.6e+56]], $MachinePrecision], LessEqual[y, 7.5e+108]]]], $MachinePrecision]], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999968e-63 or 2.8e13 < y < 8.6000000000000007e56 or 7.50000000000000039e108 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.8%

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

   3. Taylor expanded in y around inf 73.1%

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

   if -6.19999999999999968e-63 < y < 2.8e13 or 8.6000000000000007e56 < y < 7.50000000000000039e108

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 75.1%

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

      1. mul-1-neg 75.1%

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

   4. Simplified 75.1%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-63} \lor \neg \left(y \leq 28000000000000 \lor \neg \left(y \leq 8.6 \cdot 10^{+56}\right) \land y \leq 7.5 \cdot 10^{+108}\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot 3\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+108}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x 3.0))))
   (if (<= y -5.8e-63)
     t_0
     (if (<= y 3.5e+14)
       (- z)
       (if (<= y 8.4e+57) t_0 (if (<= y 8e+108) (- z) (* 3.0 (* x y))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * 3.0);
	double tmp;
	if (y <= -5.8e-63) {
		tmp = t_0;
	} else if (y <= 3.5e+14) {
		tmp = -z;
	} else if (y <= 8.4e+57) {
		tmp = t_0;
	} else if (y <= 8e+108) {
		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) :: t_0
    real(8) :: tmp
    t_0 = y * (x * 3.0d0)
    if (y <= (-5.8d-63)) then
        tmp = t_0
    else if (y <= 3.5d+14) then
        tmp = -z
    else if (y <= 8.4d+57) then
        tmp = t_0
    else if (y <= 8d+108) 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 t_0 = y * (x * 3.0);
	double tmp;
	if (y <= -5.8e-63) {
		tmp = t_0;
	} else if (y <= 3.5e+14) {
		tmp = -z;
	} else if (y <= 8.4e+57) {
		tmp = t_0;
	} else if (y <= 8e+108) {
		tmp = -z;
	} else {
		tmp = 3.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * 3.0)
	tmp = 0
	if y <= -5.8e-63:
		tmp = t_0
	elif y <= 3.5e+14:
		tmp = -z
	elif y <= 8.4e+57:
		tmp = t_0
	elif y <= 8e+108:
		tmp = -z
	else:
		tmp = 3.0 * (x * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * 3.0))
	tmp = 0.0
	if (y <= -5.8e-63)
		tmp = t_0;
	elseif (y <= 3.5e+14)
		tmp = Float64(-z);
	elseif (y <= 8.4e+57)
		tmp = t_0;
	elseif (y <= 8e+108)
		tmp = Float64(-z);
	else
		tmp = Float64(3.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * 3.0);
	tmp = 0.0;
	if (y <= -5.8e-63)
		tmp = t_0;
	elseif (y <= 3.5e+14)
		tmp = -z;
	elseif (y <= 8.4e+57)
		tmp = t_0;
	elseif (y <= 8e+108)
		tmp = -z;
	else
		tmp = 3.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e-63], t$95$0, If[LessEqual[y, 3.5e+14], (-z), If[LessEqual[y, 8.4e+57], t$95$0, If[LessEqual[y, 8e+108], (-z), N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999995e-63 or 3.5e14 < y < 8.39999999999999964e57

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. add-sqr-sqrt 55.0%

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

      6. distribute-rgt-neg-in 55.0%

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

      7. flip-+ 21.5%

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

   4. Applied egg-rr 17.3%

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

      1. unpow2 17.3%

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

      2. swap-sqr 17.3%

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

      3. metadata-eval 17.3%

         \[\leadsto \frac{z \cdot z - \color{blue}{9} \cdot \left(\left(y \cdot x\right) \cdot \left(y \cdot x\right)\right)}{z - 3 \cdot \left(y \cdot x\right)} \]

      4. unpow2 17.3%

         \[\leadsto \frac{z \cdot z - 9 \cdot \color{blue}{{\left(y \cdot x\right)}^{2}}}{z - 3 \cdot \left(y \cdot x\right)} \]

      5. *-commutative 17.3%

         \[\leadsto \frac{z \cdot z - \color{blue}{{\left(y \cdot x\right)}^{2} \cdot 9}}{z - 3 \cdot \left(y \cdot x\right)} \]

      6. sub-neg 17.3%

         \[\leadsto \frac{z \cdot z - {\left(y \cdot x\right)}^{2} \cdot 9}{\color{blue}{z + \left(-3 \cdot \left(y \cdot x\right)\right)}} \]

      7. *-commutative 17.3%

         \[\leadsto \frac{z \cdot z - {\left(y \cdot x\right)}^{2} \cdot 9}{z + \left(-\color{blue}{\left(y \cdot x\right) \cdot 3}\right)} \]

      8. distribute-rgt-neg-in 17.3%

         \[\leadsto \frac{z \cdot z - {\left(y \cdot x\right)}^{2} \cdot 9}{z + \color{blue}{\left(y \cdot x\right) \cdot \left(-3\right)}} \]

      9. metadata-eval 17.3%

         \[\leadsto \frac{z \cdot z - {\left(y \cdot x\right)}^{2} \cdot 9}{z + \left(y \cdot x\right) \cdot \color{blue}{-3}} \]

   6. Simplified 17.3%

      \[\leadsto \color{blue}{\frac{z \cdot z - {\left(y \cdot x\right)}^{2} \cdot 9}{z + \left(y \cdot x\right) \cdot -3}} \]

   7. Taylor expanded in z around 0 60.9%

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

      1. associate-*r* 60.9%

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

      2. *-commutative 60.9%

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

   9. Simplified 60.9%

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

   10. Taylor expanded in y around 0 60.9%

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

       1. associate-*r* 60.9%

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

       2. *-commutative 60.9%

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

       3. associate-*l* 60.9%

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

   12. Simplified 60.9%

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

   if -5.7999999999999995e-63 < y < 3.5e14 or 8.39999999999999964e57 < y < 8.0000000000000003e108

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 75.1%

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

      1. mul-1-neg 75.1%

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

   4. Simplified 75.1%

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

   if 8.0000000000000003e108 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.7%

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

   3. Taylor expanded in y around inf 91.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+108}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \]

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 99.9%

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

2. Taylor expanded in x around 0 99.8%

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

3. Final simplification 99.8%

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

Alternative 5: 50.5% 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. Taylor expanded in x around 0 52.1%

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

   1. mul-1-neg 52.1%

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

4. Simplified 52.1%

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

5. Final simplification 52.1%

   \[\leadsto -z \]

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. *-commutative 99.9%

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

   2. associate-*r* 99.8%

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

   3. fma-neg 99.9%

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

   4. add-sqr-sqrt 48.9%

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

   5. sqrt-unprod 60.5%

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

   6. sqr-neg 60.5%

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

   7. sqrt-unprod 26.2%

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

   8. add-sqr-sqrt 48.3%

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

3. Applied egg-rr 48.3%

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

4. Taylor expanded in y around 0 2.0%

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

5. Final simplification 2.0%

   \[\leadsto z \]

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 2023182 
(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))