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

Percentage Accurate: 99.8% → 99.8%

Time: 5.8s

Alternatives: 8

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+47} \lor \neg \left(z \leq -3.7 \cdot 10^{-134}\right) \land \left(z \leq -4.2 \cdot 10^{-158} \lor \neg \left(z \leq 1.46 \cdot 10^{+99}\right)\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.36e+47)
         (and (not (<= z -3.7e-134))
              (or (<= z -4.2e-158) (not (<= z 1.46e+99)))))
   (- z)
   (* 3.0 (* x y))))

C

assert(x < y);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.36e+47) || (!(z <= -3.7e-134) && ((z <= -4.2e-158) || !(z <= 1.46e+99)))) {
		tmp = -z;
	} else {
		tmp = 3.0 * (x * y);
	}
	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 <= (-1.36d+47)) .or. (.not. (z <= (-3.7d-134))) .and. (z <= (-4.2d-158)) .or. (.not. (z <= 1.46d+99))) then
        tmp = -z
    else
        tmp = 3.0d0 * (x * y)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.36e+47) || (!(z <= -3.7e-134) && ((z <= -4.2e-158) || !(z <= 1.46e+99)))) {
		tmp = -z;
	} else {
		tmp = 3.0 * (x * y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	tmp = 0
	if (z <= -1.36e+47) or (not (z <= -3.7e-134) and ((z <= -4.2e-158) or not (z <= 1.46e+99))):
		tmp = -z
	else:
		tmp = 3.0 * (x * y)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.36e+47) || (!(z <= -3.7e-134) && ((z <= -4.2e-158) || !(z <= 1.46e+99))))
		tmp = Float64(-z);
	else
		tmp = Float64(3.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.36e+47) || (~((z <= -3.7e-134)) && ((z <= -4.2e-158) || ~((z <= 1.46e+99)))))
		tmp = -z;
	else
		tmp = 3.0 * (x * y);
	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[Or[LessEqual[z, -1.36e+47], And[N[Not[LessEqual[z, -3.7e-134]], $MachinePrecision], Or[LessEqual[z, -4.2e-158], N[Not[LessEqual[z, 1.46e+99]], $MachinePrecision]]]], (-z), N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3599999999999999e47 or -3.7e-134 < z < -4.19999999999999983e-158 or 1.4600000000000001e99 < z

   1. Initial program 99.9%

      \[\left(x \cdot 3\right) \cdot y - z \]
   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 79.2%

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

      1. mul-1-neg 79.2%

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

   6. Simplified 79.2%

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

   if -1.3599999999999999e47 < z < -3.7e-134 or -4.19999999999999983e-158 < z < 1.4600000000000001e99

   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. Step-by-step derivation

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. fma-neg 99.7%

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

      5. add-sqr-sqrt 44.0%

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

      6. sqrt-unprod 83.0%

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

      7. sqr-neg 83.0%

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

      8. sqrt-unprod 41.9%

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

      9. add-sqr-sqrt 75.4%

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

   5. Applied egg-rr 75.4%

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

   6. Taylor expanded in y around inf 76.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+47} \lor \neg \left(z \leq -3.7 \cdot 10^{-134}\right) \land \left(z \leq -4.2 \cdot 10^{-158} \lor \neg \left(z \leq 1.46 \cdot 10^{+99}\right)\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 3: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+48}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-134}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-158} \lor \neg \left(z \leq 1.46 \cdot 10^{+99}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -2.55e+48)
   (- z)
   (if (<= z -3.7e-134)
     (* 3.0 (* x y))
     (if (or (<= z -4.2e-158) (not (<= z 1.46e+99))) (- z) (* x (* 3.0 y))))))

C

assert(x < y);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.55e+48) {
		tmp = -z;
	} else if (z <= -3.7e-134) {
		tmp = 3.0 * (x * y);
	} else if ((z <= -4.2e-158) || !(z <= 1.46e+99)) {
		tmp = -z;
	} else {
		tmp = x * (3.0 * y);
	}
	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 <= (-2.55d+48)) then
        tmp = -z
    else if (z <= (-3.7d-134)) then
        tmp = 3.0d0 * (x * y)
    else if ((z <= (-4.2d-158)) .or. (.not. (z <= 1.46d+99))) then
        tmp = -z
    else
        tmp = x * (3.0d0 * y)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.55e+48) {
		tmp = -z;
	} else if (z <= -3.7e-134) {
		tmp = 3.0 * (x * y);
	} else if ((z <= -4.2e-158) || !(z <= 1.46e+99)) {
		tmp = -z;
	} else {
		tmp = x * (3.0 * y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	tmp = 0
	if z <= -2.55e+48:
		tmp = -z
	elif z <= -3.7e-134:
		tmp = 3.0 * (x * y)
	elif (z <= -4.2e-158) or not (z <= 1.46e+99):
		tmp = -z
	else:
		tmp = x * (3.0 * y)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	tmp = 0.0
	if (z <= -2.55e+48)
		tmp = Float64(-z);
	elseif (z <= -3.7e-134)
		tmp = Float64(3.0 * Float64(x * y));
	elseif ((z <= -4.2e-158) || !(z <= 1.46e+99))
		tmp = Float64(-z);
	else
		tmp = Float64(x * Float64(3.0 * y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.55e+48)
		tmp = -z;
	elseif (z <= -3.7e-134)
		tmp = 3.0 * (x * y);
	elseif ((z <= -4.2e-158) || ~((z <= 1.46e+99)))
		tmp = -z;
	else
		tmp = x * (3.0 * y);
	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, -2.55e+48], (-z), If[LessEqual[z, -3.7e-134], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.2e-158], N[Not[LessEqual[z, 1.46e+99]], $MachinePrecision]], (-z), N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5499999999999999e48 or -3.7e-134 < z < -4.19999999999999983e-158 or 1.4600000000000001e99 < z

   1. Initial program 99.9%

      \[\left(x \cdot 3\right) \cdot y - z \]
   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 79.2%

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

      1. mul-1-neg 79.2%

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

   6. Simplified 79.2%

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

   if -2.5499999999999999e48 < z < -3.7e-134

   1. Initial program 99.8%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. fma-neg 99.8%

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

      5. add-sqr-sqrt 99.6%

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

      6. sqrt-unprod 99.8%

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

      7. sqr-neg 99.8%

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

      8. sqrt-unprod 0.0%

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

      9. add-sqr-sqrt 61.8%

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

   5. Applied egg-rr 61.8%

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

   6. Taylor expanded in y around inf 63.0%

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

   if -4.19999999999999983e-158 < z < 1.4600000000000001e99

   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. Step-by-step derivation

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. fma-neg 99.6%

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

      5. add-sqr-sqrt 30.2%

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

      6. sqrt-unprod 78.8%

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

      7. sqr-neg 78.8%

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

      8. sqrt-unprod 52.3%

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

      9. add-sqr-sqrt 78.7%

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

   5. Applied egg-rr 78.7%

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

   6. Taylor expanded in y around inf 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*l* 79.4%

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

      3. *-commutative 79.4%

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

   8. Simplified 79.4%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+48}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-134}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-158} \lor \neg \left(z \leq 1.46 \cdot 10^{+99}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \]

Alternative 4: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+48}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-158} \lor \neg \left(z \leq 1.5 \cdot 10^{+99}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -1.45e+48)
   (- z)
   (if (<= z -3.7e-134)
     (* y (* x 3.0))
     (if (or (<= z -4.2e-158) (not (<= z 1.5e+99))) (- z) (* x (* 3.0 y))))))

C

assert(x < y);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.45e+48) {
		tmp = -z;
	} else if (z <= -3.7e-134) {
		tmp = y * (x * 3.0);
	} else if ((z <= -4.2e-158) || !(z <= 1.5e+99)) {
		tmp = -z;
	} else {
		tmp = x * (3.0 * y);
	}
	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 <= (-1.45d+48)) then
        tmp = -z
    else if (z <= (-3.7d-134)) then
        tmp = y * (x * 3.0d0)
    else if ((z <= (-4.2d-158)) .or. (.not. (z <= 1.5d+99))) then
        tmp = -z
    else
        tmp = x * (3.0d0 * y)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.45e+48) {
		tmp = -z;
	} else if (z <= -3.7e-134) {
		tmp = y * (x * 3.0);
	} else if ((z <= -4.2e-158) || !(z <= 1.5e+99)) {
		tmp = -z;
	} else {
		tmp = x * (3.0 * y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	tmp = 0
	if z <= -1.45e+48:
		tmp = -z
	elif z <= -3.7e-134:
		tmp = y * (x * 3.0)
	elif (z <= -4.2e-158) or not (z <= 1.5e+99):
		tmp = -z
	else:
		tmp = x * (3.0 * y)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	tmp = 0.0
	if (z <= -1.45e+48)
		tmp = Float64(-z);
	elseif (z <= -3.7e-134)
		tmp = Float64(y * Float64(x * 3.0));
	elseif ((z <= -4.2e-158) || !(z <= 1.5e+99))
		tmp = Float64(-z);
	else
		tmp = Float64(x * Float64(3.0 * y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.45e+48)
		tmp = -z;
	elseif (z <= -3.7e-134)
		tmp = y * (x * 3.0);
	elseif ((z <= -4.2e-158) || ~((z <= 1.5e+99)))
		tmp = -z;
	else
		tmp = x * (3.0 * y);
	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, -1.45e+48], (-z), If[LessEqual[z, -3.7e-134], N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.2e-158], N[Not[LessEqual[z, 1.5e+99]], $MachinePrecision]], (-z), N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e48 or -3.7e-134 < z < -4.19999999999999983e-158 or 1.50000000000000007e99 < z

   1. Initial program 99.9%

      \[\left(x \cdot 3\right) \cdot y - z \]
   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 79.2%

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

      1. mul-1-neg 79.2%

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

   6. Simplified 79.2%

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

   if -1.4499999999999999e48 < z < -3.7e-134

   1. Initial program 99.8%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. fma-neg 99.8%

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

      5. add-sqr-sqrt 99.6%

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

      6. sqrt-unprod 99.8%

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

      7. sqr-neg 99.8%

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

      8. sqrt-unprod 0.0%

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

      9. add-sqr-sqrt 61.8%

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

   5. Applied egg-rr 61.8%

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

   6. Taylor expanded in y around inf 63.0%

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

      1. add-cube-cbrt 62.5%

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

      2. pow3 62.6%

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

      3. associate-*r* 62.9%

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

      4. *-commutative 62.9%

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

   8. Applied egg-rr 62.9%

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

      1. rem-cube-cbrt 63.1%

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

      2. *-commutative 63.1%

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

   10. Applied egg-rr 63.1%

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

   if -4.19999999999999983e-158 < z < 1.50000000000000007e99

   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. Step-by-step derivation

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. fma-neg 99.6%

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

      5. add-sqr-sqrt 30.2%

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

      6. sqrt-unprod 78.8%

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

      7. sqr-neg 78.8%

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

      8. sqrt-unprod 52.3%

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

      9. add-sqr-sqrt 78.7%

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

   5. Applied egg-rr 78.7%

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

   6. Taylor expanded in y around inf 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*l* 79.4%

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

      3. *-commutative 79.4%

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

   8. Simplified 79.4%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+48}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-158} \lor \neg \left(z \leq 1.5 \cdot 10^{+99}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \end{array} \]

Alternative 5: 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* 99.8%

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

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 6: 99.8% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (* 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(x * Float64(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[(x * N[(3.0 * 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. Final simplification 99.8%

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

Alternative 7: 50.8% 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* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around 0 46.2%

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

   1. mul-1-neg 46.2%

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

6. Simplified 46.2%

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

7. Final simplification 46.2%

   \[\leadsto -z \]

Alternative 8: 2.2% accurate, 7.0× 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 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* 99.8%

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

3. Simplified 99.8%

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

   1. associate-*r* 99.8%

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

   2. *-commutative 99.8%

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

   3. associate-*r* 99.8%

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

   4. fma-neg 99.8%

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

   5. add-sqr-sqrt 52.4%

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

   6. sqrt-unprod 65.6%

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

   7. sqr-neg 65.6%

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

   8. sqrt-unprod 29.0%

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

   9. add-sqr-sqrt 53.7%

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

5. Applied egg-rr 53.7%

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

6. Taylor expanded in y around 0 2.1%

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

7. Final simplification 2.1%

   \[\leadsto z \]

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 2023318 
(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))