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

Percentage Accurate: 99.8% → 99.8%

Time: 9.0s

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, 0.1× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (fma (* x 3.0) y (- z)))

C

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

Julia

x, y = sort([x, y])
function code(x, y, z)
	return fma(Float64(x * 3.0), y, Float64(-z))
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-39}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-32} \lor \neg \left(z \leq 11600000\right) \land z \leq 1.9 \cdot 10^{+74}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e-39)
   (- z)
   (if (or (<= z 3.9e-32) (and (not (<= z 11600000.0)) (<= z 1.9e+74)))
     (* 3.0 (* x y))
     (- z))))

C

assert(x < y);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e-39) {
		tmp = -z;
	} else if ((z <= 3.9e-32) || (!(z <= 11600000.0) && (z <= 1.9e+74))) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-1.8d-39)) then
        tmp = -z
    else if ((z <= 3.9d-32) .or. (.not. (z <= 11600000.0d0)) .and. (z <= 1.9d+74)) then
        tmp = 3.0d0 * (x * y)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e-39) {
		tmp = -z;
	} else if ((z <= 3.9e-32) || (!(z <= 11600000.0) && (z <= 1.9e+74))) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	tmp = 0
	if z <= -1.8e-39:
		tmp = -z
	elif (z <= 3.9e-32) or (not (z <= 11600000.0) and (z <= 1.9e+74)):
		tmp = 3.0 * (x * y)
	else:
		tmp = -z
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e-39)
		tmp = Float64(-z);
	elseif ((z <= 3.9e-32) || (!(z <= 11600000.0) && (z <= 1.9e+74)))
		tmp = Float64(3.0 * Float64(x * y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.8e-39)
		tmp = -z;
	elseif ((z <= 3.9e-32) || (~((z <= 11600000.0)) && (z <= 1.9e+74)))
		tmp = 3.0 * (x * y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -1.8e-39], (-z), If[Or[LessEqual[z, 3.9e-32], And[N[Not[LessEqual[z, 11600000.0]], $MachinePrecision], LessEqual[z, 1.9e+74]]], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e-39 or 3.9000000000000001e-32 < z < 1.16e7 or 1.8999999999999999e74 < 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 74.1%

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

      1. mul-1-neg 74.1%

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

   6. Simplified 74.1%

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

   if -1.8e-39 < z < 3.9000000000000001e-32 or 1.16e7 < z < 1.8999999999999999e74

   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. Taylor expanded in x around 0 99.8%

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

   5. Taylor expanded in x around inf 79.3%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-39}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-32} \lor \neg \left(z \leq 11600000\right) \land z \leq 1.9 \cdot 10^{+74}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-36}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-32}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 30500:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+74}:\\ \;\;\;\;\frac{y}{\frac{0.3333333333333333}{x}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -2.65e-36)
   (- z)
   (if (<= z 2e-32)
     (* 3.0 (* x y))
     (if (<= z 30500.0)
       (- z)
       (if (<= z 1.56e+74) (/ y (/ 0.3333333333333333 x)) (- z))))))

C

assert(x < y);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.65e-36) {
		tmp = -z;
	} else if (z <= 2e-32) {
		tmp = 3.0 * (x * y);
	} else if (z <= 30500.0) {
		tmp = -z;
	} else if (z <= 1.56e+74) {
		tmp = y / (0.3333333333333333 / x);
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-2.65d-36)) then
        tmp = -z
    else if (z <= 2d-32) then
        tmp = 3.0d0 * (x * y)
    else if (z <= 30500.0d0) then
        tmp = -z
    else if (z <= 1.56d+74) then
        tmp = y / (0.3333333333333333d0 / x)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.65e-36) {
		tmp = -z;
	} else if (z <= 2e-32) {
		tmp = 3.0 * (x * y);
	} else if (z <= 30500.0) {
		tmp = -z;
	} else if (z <= 1.56e+74) {
		tmp = y / (0.3333333333333333 / x);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	tmp = 0
	if z <= -2.65e-36:
		tmp = -z
	elif z <= 2e-32:
		tmp = 3.0 * (x * y)
	elif z <= 30500.0:
		tmp = -z
	elif z <= 1.56e+74:
		tmp = y / (0.3333333333333333 / x)
	else:
		tmp = -z
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	tmp = 0.0
	if (z <= -2.65e-36)
		tmp = Float64(-z);
	elseif (z <= 2e-32)
		tmp = Float64(3.0 * Float64(x * y));
	elseif (z <= 30500.0)
		tmp = Float64(-z);
	elseif (z <= 1.56e+74)
		tmp = Float64(y / Float64(0.3333333333333333 / x));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.65e-36)
		tmp = -z;
	elseif (z <= 2e-32)
		tmp = 3.0 * (x * y);
	elseif (z <= 30500.0)
		tmp = -z;
	elseif (z <= 1.56e+74)
		tmp = y / (0.3333333333333333 / x);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -2.65e-36], (-z), If[LessEqual[z, 2e-32], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 30500.0], (-z), If[LessEqual[z, 1.56e+74], N[(y / N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6499999999999999e-36 or 2.00000000000000011e-32 < z < 30500 or 1.56e74 < 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 74.1%

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

      1. mul-1-neg 74.1%

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

   6. Simplified 74.1%

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

   if -2.6499999999999999e-36 < z < 2.00000000000000011e-32

   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. Taylor expanded in x around 0 99.8%

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

   5. Taylor expanded in x around inf 80.8%

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

   if 30500 < z < 1.56e74

   1. Initial program 99.6%

      \[\left(x \cdot 3\right) \cdot y - z \]
   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. Taylor expanded in x around inf 68.6%

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

      1. metadata-eval 68.6%

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

      2. *-inverses 55.3%

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

      3. associate-/l* 55.3%

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

      4. *-commutative 55.3%

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

      5. associate-/l* 55.3%

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

      6. metadata-eval 55.3%

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

      7. associate-/l* 55.2%

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

      8. *-commutative 55.2%

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

      9. associate-*r* 54.8%

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

      10. *-commutative 54.8%

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

      11. associate-*r* 55.0%

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

      12. remove-double-neg 55.0%

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

      13. distribute-lft-neg-out 55.0%

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

      14. metadata-eval 55.0%

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

      15. frac-2neg 55.0%

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

      16. associate-/r/ 54.8%

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

      17. *-commutative 54.8%

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

      18. associate-/l* 55.0%

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

   7. Applied egg-rr 68.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{0.3333333333333333}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-36}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-32}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 30500:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+74}:\\ \;\;\;\;\frac{y}{\frac{0.3333333333333333}{x}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (* 3.0 (* x y)) z))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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

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

Python

[x, y] = sort([x, y])
def code(x, y, z):
	return (3.0 * (x * y)) - z

Julia

x, y = sort([x, y])
function code(x, y, z)
	return Float64(Float64(3.0 * Float64(x * y)) - z)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z)
	tmp = (3.0 * (x * y)) - z;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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* 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 99.9%

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

5. Final simplification 99.9%

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

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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

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

Python

[x, y] = sort([x, y])
def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

x, y = sort([x, y])
function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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: 51.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ -z \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- z))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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

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

Python

[x, y] = sort([x, y])
def code(x, y, z):
	return -z

Julia

x, y = sort([x, y])
function code(x, y, z)
	return Float64(-z)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z)
	tmp = -z;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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. Taylor expanded in x around 0 49.2%

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

   1. mul-1-neg 49.2%

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

6. Simplified 49.2%

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

7. Final simplification 49.2%

   \[\leadsto -z \]

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 2023297 
(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))