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

Percentage Accurate: 99.8% → 99.8%

Time: 7.1s

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 99.5%

   \[\left(x \cdot 3\right) \cdot y - z \]
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 99.7%

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

6. Final simplification 99.7%

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

Alternative 2: 69.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+91} \lor \neg \left(z \leq -0.78\right) \land \left(z \leq -5 \cdot 10^{-71} \lor \neg \left(z \leq 880000000000\right)\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.3e+91)
         (and (not (<= z -0.78))
              (or (<= z -5e-71) (not (<= z 880000000000.0)))))
   (- z)
   (* 3.0 (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.3e+91) || (!(z <= -0.78) && ((z <= -5e-71) || !(z <= 880000000000.0)))) {
		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 ((z <= (-4.3d+91)) .or. (.not. (z <= (-0.78d0))) .and. (z <= (-5d-71)) .or. (.not. (z <= 880000000000.0d0))) 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 ((z <= -4.3e+91) || (!(z <= -0.78) && ((z <= -5e-71) || !(z <= 880000000000.0)))) {
		tmp = -z;
	} else {
		tmp = 3.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.3e+91) or (not (z <= -0.78) and ((z <= -5e-71) or not (z <= 880000000000.0))):
		tmp = -z
	else:
		tmp = 3.0 * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.3e+91) || (!(z <= -0.78) && ((z <= -5e-71) || !(z <= 880000000000.0))))
		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 ((z <= -4.3e+91) || (~((z <= -0.78)) && ((z <= -5e-71) || ~((z <= 880000000000.0)))))
		tmp = -z;
	else
		tmp = 3.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.3e+91], And[N[Not[LessEqual[z, -0.78]], $MachinePrecision], Or[LessEqual[z, -5e-71], N[Not[LessEqual[z, 880000000000.0]], $MachinePrecision]]]], (-z), N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000001e91 or -0.78000000000000003 < z < -4.99999999999999998e-71 or 8.8e11 < z

   1. Initial program 99.2%

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

      1. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 75.1%

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

      1. mul-1-neg 75.1%

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

   7. Simplified 75.1%

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

   if -4.3000000000000001e91 < z < -0.78000000000000003 or -4.99999999999999998e-71 < z < 8.8e11

   1. Initial program 99.7%

      \[\left(x \cdot 3\right) \cdot y - z \]
   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 99.6%

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

   6. Taylor expanded in x around inf 78.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+91} \lor \neg \left(z \leq -0.78\right) \land \left(z \leq -5 \cdot 10^{-71} \lor \neg \left(z \leq 880000000000\right)\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+91} \lor \neg \left(z \leq -0.00365 \lor \neg \left(z \leq -2.7 \cdot 10^{-71}\right) \land z \leq 4300000000000\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e+91)
         (not
          (or (<= z -0.00365)
              (and (not (<= z -2.7e-71)) (<= z 4300000000000.0)))))
   (- z)
   (* y (* 3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+91) || !((z <= -0.00365) || (!(z <= -2.7e-71) && (z <= 4300000000000.0)))) {
		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 ((z <= (-6d+91)) .or. (.not. (z <= (-0.00365d0)) .or. (.not. (z <= (-2.7d-71))) .and. (z <= 4300000000000.0d0))) 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 ((z <= -6e+91) || !((z <= -0.00365) || (!(z <= -2.7e-71) && (z <= 4300000000000.0)))) {
		tmp = -z;
	} else {
		tmp = y * (3.0 * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6e+91) or not ((z <= -0.00365) or (not (z <= -2.7e-71) and (z <= 4300000000000.0))):
		tmp = -z
	else:
		tmp = y * (3.0 * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6e+91) || !((z <= -0.00365) || (!(z <= -2.7e-71) && (z <= 4300000000000.0))))
		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 ((z <= -6e+91) || ~(((z <= -0.00365) || (~((z <= -2.7e-71)) && (z <= 4300000000000.0)))))
		tmp = -z;
	else
		tmp = y * (3.0 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e+91], N[Not[Or[LessEqual[z, -0.00365], And[N[Not[LessEqual[z, -2.7e-71]], $MachinePrecision], LessEqual[z, 4300000000000.0]]]], $MachinePrecision]], (-z), N[(y * N[(3.0 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000012e91 or -0.00365000000000000003 < z < -2.7000000000000001e-71 or 4.3e12 < z

   1. Initial program 99.2%

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

      1. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 75.1%

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

      1. mul-1-neg 75.1%

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

   7. Simplified 75.1%

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

   if -6.00000000000000012e91 < z < -0.00365000000000000003 or -2.7000000000000001e-71 < z < 4.3e12

   1. Initial program 99.7%

      \[\left(x \cdot 3\right) \cdot y - z \]
   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 y around inf 99.0%

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

      1. +-commutative 99.0%

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

      2. fma-define 99.0%

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

      3. mul-1-neg 99.0%

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

      4. fma-neg 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in x around inf 78.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+91} \lor \neg \left(z \leq -0.00365 \lor \neg \left(z \leq -2.7 \cdot 10^{-71}\right) \land z \leq 4300000000000\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+91}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -0.34:\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-71} \lor \neg \left(z \leq 650000000000\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.45e+91)
   (- z)
   (if (<= z -0.34)
     (* y (* 3.0 x))
     (if (or (<= z -3.1e-71) (not (<= z 650000000000.0)))
       (- z)
       (* x (* 3.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.45e+91) {
		tmp = -z;
	} else if (z <= -0.34) {
		tmp = y * (3.0 * x);
	} else if ((z <= -3.1e-71) || !(z <= 650000000000.0)) {
		tmp = -z;
	} else {
		tmp = x * (3.0 * 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 (z <= (-2.45d+91)) then
        tmp = -z
    else if (z <= (-0.34d0)) then
        tmp = y * (3.0d0 * x)
    else if ((z <= (-3.1d-71)) .or. (.not. (z <= 650000000000.0d0))) then
        tmp = -z
    else
        tmp = x * (3.0d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.45e+91) {
		tmp = -z;
	} else if (z <= -0.34) {
		tmp = y * (3.0 * x);
	} else if ((z <= -3.1e-71) || !(z <= 650000000000.0)) {
		tmp = -z;
	} else {
		tmp = x * (3.0 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.45e+91:
		tmp = -z
	elif z <= -0.34:
		tmp = y * (3.0 * x)
	elif (z <= -3.1e-71) or not (z <= 650000000000.0):
		tmp = -z
	else:
		tmp = x * (3.0 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.45e+91)
		tmp = Float64(-z);
	elseif (z <= -0.34)
		tmp = Float64(y * Float64(3.0 * x));
	elseif ((z <= -3.1e-71) || !(z <= 650000000000.0))
		tmp = Float64(-z);
	else
		tmp = Float64(x * Float64(3.0 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.45e+91)
		tmp = -z;
	elseif (z <= -0.34)
		tmp = y * (3.0 * x);
	elseif ((z <= -3.1e-71) || ~((z <= 650000000000.0)))
		tmp = -z;
	else
		tmp = x * (3.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.45e+91], (-z), If[LessEqual[z, -0.34], N[(y * N[(3.0 * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.1e-71], N[Not[LessEqual[z, 650000000000.0]], $MachinePrecision]], (-z), N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45000000000000015e91 or -0.340000000000000024 < z < -3.10000000000000002e-71 or 6.5e11 < z

   1. Initial program 99.2%

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

      1. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 75.1%

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

      1. mul-1-neg 75.1%

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

   7. Simplified 75.1%

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

   if -2.45000000000000015e91 < z < -0.340000000000000024

   1. Initial program 99.7%

      \[\left(x \cdot 3\right) \cdot y - z \]
   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 y around inf 94.0%

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

      1. +-commutative 94.0%

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

      2. fma-define 94.0%

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

      3. mul-1-neg 94.0%

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

      4. fma-neg 94.0%

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

   7. Simplified 94.0%

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

   8. Taylor expanded in x around inf 93.8%

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

   if -3.10000000000000002e-71 < z < 6.5e11

   1. Initial program 99.7%

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

      1. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 99.6%

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

   6. Taylor expanded in x around inf 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-*r* 76.6%

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

   8. Simplified 76.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+91}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -0.34:\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-71} \lor \neg \left(z \leq 650000000000\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.6% 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 99.5%

   \[\left(x \cdot 3\right) \cdot y - z \]
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 45.8%

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

   1. mul-1-neg 45.8%

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

7. Simplified 45.8%

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

8. Final simplification 45.8%

   \[\leadsto -z \]
9. 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 99.5%

   \[\left(x \cdot 3\right) \cdot y - z \]
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 y around inf 87.1%

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

   1. +-commutative 87.1%

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

   2. fma-define 87.1%

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

   3. mul-1-neg 87.1%

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

   4. fma-neg 87.1%

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

7. Simplified 87.1%

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

8. Taylor expanded in x around 0 33.5%

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

   1. mul-1-neg 33.5%

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

   2. distribute-neg-frac2 33.5%

      \[\leadsto y \cdot \color{blue}{\frac{z}{-y}} \]

10. Simplified 33.5%

    \[\leadsto y \cdot \color{blue}{\frac{z}{-y}} \]
11. Step-by-step derivation

    1. clear-num 33.4%

       \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{-y}{z}}} \]

    2. un-div-inv 33.8%

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

    3. add-sqr-sqrt 15.6%

       \[\leadsto \frac{y}{\frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{z}} \]

    4. sqrt-unprod 11.2%

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

    5. sqr-neg 11.2%

       \[\leadsto \frac{y}{\frac{\sqrt{\color{blue}{y \cdot y}}}{z}} \]

    6. sqrt-unprod 1.1%

       \[\leadsto \frac{y}{\frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{z}} \]

    7. add-sqr-sqrt 2.4%

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

12. Applied egg-rr 2.4%

    \[\leadsto \color{blue}{\frac{y}{\frac{y}{z}}} \]
13. Step-by-step derivation

    1. associate-/r/ 2.5%

       \[\leadsto \color{blue}{\frac{y}{y} \cdot z} \]

    2. *-inverses 2.5%

       \[\leadsto \color{blue}{1} \cdot z \]

    3. *-lft-identity 2.5%

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

14. Simplified 2.5%

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

15. Final simplification 2.5%

    \[\leadsto z \]
16. 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 2024059 
(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))