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

Percentage Accurate: 99.8% → 99.8%

Time: 10.6s

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

\[\begin{array}{l} \\ \mathsf{fma}\left(x \cdot y, 3, 0 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (* x y) 3.0 (- 0.0 z)))

C

double code(double x, double y, double z) {
	return fma((x * y), 3.0, (0.0 - z));
}

Julia

function code(x, y, z)
	return fma(Float64(x * y), 3.0, Float64(0.0 - z))
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] * 3.0 + N[(0.0 - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. sub-neg N/A

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

   2. associate-*l* N/A

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

   3. *-commutative N/A

      \[\leadsto x \cdot \left(y \cdot 3\right) + \left(\mathsf{neg}\left(z\right)\right) \]

   4. associate-*r* N/A

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

   5. accelerator-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(x \cdot y\right), \color{blue}{3}, \left(\mathsf{neg}\left(z\right)\right)\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(x, y\right), 3, \left(\mathsf{neg}\left(z\right)\right)\right) \]

   7. neg-sub0 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(x, y\right), 3, \left(0 - z\right)\right) \]

   8. --lowering--.f64 99.8%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(x, y\right), 3, \mathsf{\_.f64}\left(0, z\right)\right) \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot y, 3, 0 - z\right)} \]
5. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(x, y\right), 3, \left(\mathsf{neg}\left(z\right)\right)\right) \]

   2. neg-lowering-neg.f64 99.8%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(x, y\right), 3, \mathsf{neg.f64}\left(z\right)\right) \]

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(x \cdot y, 3, 0 - z\right) \]
8. Add Preprocessing

Alternative 2: 78.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot 3\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+71}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x 3.0))))
   (if (<= t_0 -1e+52)
     (* (* x y) 3.0)
     (if (<= t_0 2e+71) (- 0.0 z) (* x (* y 3.0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * 3.0);
	double tmp;
	if (t_0 <= -1e+52) {
		tmp = (x * y) * 3.0;
	} else if (t_0 <= 2e+71) {
		tmp = 0.0 - z;
	} else {
		tmp = x * (y * 3.0);
	}
	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 (t_0 <= (-1d+52)) then
        tmp = (x * y) * 3.0d0
    else if (t_0 <= 2d+71) then
        tmp = 0.0d0 - z
    else
        tmp = x * (y * 3.0d0)
    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 (t_0 <= -1e+52) {
		tmp = (x * y) * 3.0;
	} else if (t_0 <= 2e+71) {
		tmp = 0.0 - z;
	} else {
		tmp = x * (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * 3.0)
	tmp = 0
	if t_0 <= -1e+52:
		tmp = (x * y) * 3.0
	elif t_0 <= 2e+71:
		tmp = 0.0 - z
	else:
		tmp = x * (y * 3.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * 3.0))
	tmp = 0.0
	if (t_0 <= -1e+52)
		tmp = Float64(Float64(x * y) * 3.0);
	elseif (t_0 <= 2e+71)
		tmp = Float64(0.0 - z);
	else
		tmp = Float64(x * Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * 3.0);
	tmp = 0.0;
	if (t_0 <= -1e+52)
		tmp = (x * y) * 3.0;
	elseif (t_0 <= 2e+71)
		tmp = 0.0 - z;
	else
		tmp = x * (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+52], N[(N[(x * y), $MachinePrecision] * 3.0), $MachinePrecision], If[LessEqual[t$95$0, 2e+71], N[(0.0 - z), $MachinePrecision], N[(x * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 3 binary64)) y) < -9.9999999999999999e51

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-neg-in N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(-3 \cdot y\right)\right)}\right) \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(-3\right)\right) \cdot \color{blue}{y}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right) \]

      9. *-lowering-*.f64 88.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, \color{blue}{y}\right)\right) \]

   5. Simplified 88.1%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot y\right), \color{blue}{3}\right) \]

      4. *-lowering-*.f64 88.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, y\right), 3\right) \]

   7. Applied egg-rr 88.2%

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

   if -9.9999999999999999e51 < (*.f64 (*.f64 x #s(literal 3 binary64)) y) < 2.0000000000000001e71

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 79.8%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 79.8%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 79.8%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 79.8%

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

   if 2.0000000000000001e71 < (*.f64 (*.f64 x #s(literal 3 binary64)) y)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-neg-in N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(-3 \cdot y\right)\right)}\right) \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(-3\right)\right) \cdot \color{blue}{y}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right) \]

      9. *-lowering-*.f64 94.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, \color{blue}{y}\right)\right) \]

   5. Simplified 94.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 3\right) \leq -1 \cdot 10^{+52}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 3\\ \mathbf{elif}\;y \cdot \left(x \cdot 3\right) \leq 2 \cdot 10^{+71}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot 3\right)\\ t_1 := x \cdot \left(y \cdot 3\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+71}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x 3.0))) (t_1 (* x (* y 3.0))))
   (if (<= t_0 -1e+52) t_1 (if (<= t_0 2e+71) (- 0.0 z) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * 3.0);
	double t_1 = x * (y * 3.0);
	double tmp;
	if (t_0 <= -1e+52) {
		tmp = t_1;
	} else if (t_0 <= 2e+71) {
		tmp = 0.0 - z;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = y * (x * 3.0d0)
    t_1 = x * (y * 3.0d0)
    if (t_0 <= (-1d+52)) then
        tmp = t_1
    else if (t_0 <= 2d+71) then
        tmp = 0.0d0 - z
    else
        tmp = t_1
    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 t_1 = x * (y * 3.0);
	double tmp;
	if (t_0 <= -1e+52) {
		tmp = t_1;
	} else if (t_0 <= 2e+71) {
		tmp = 0.0 - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * 3.0)
	t_1 = x * (y * 3.0)
	tmp = 0
	if t_0 <= -1e+52:
		tmp = t_1
	elif t_0 <= 2e+71:
		tmp = 0.0 - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * 3.0))
	t_1 = Float64(x * Float64(y * 3.0))
	tmp = 0.0
	if (t_0 <= -1e+52)
		tmp = t_1;
	elseif (t_0 <= 2e+71)
		tmp = Float64(0.0 - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * 3.0);
	t_1 = x * (y * 3.0);
	tmp = 0.0;
	if (t_0 <= -1e+52)
		tmp = t_1;
	elseif (t_0 <= 2e+71)
		tmp = 0.0 - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+52], t$95$1, If[LessEqual[t$95$0, 2e+71], N[(0.0 - z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 3 binary64)) y) < -9.9999999999999999e51 or 2.0000000000000001e71 < (*.f64 (*.f64 x #s(literal 3 binary64)) y)

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-neg-in N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(-3 \cdot y\right)\right)}\right) \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(-3\right)\right) \cdot \color{blue}{y}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right) \]

      9. *-lowering-*.f64 90.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, \color{blue}{y}\right)\right) \]

   5. Simplified 90.8%

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

   if -9.9999999999999999e51 < (*.f64 (*.f64 x #s(literal 3 binary64)) y) < 2.0000000000000001e71

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 79.8%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 79.8%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 79.8%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 79.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 3\right) \leq -1 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 3\right) \leq 2 \cdot 10^{+71}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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 99.8%

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

3. Final simplification 99.8%

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

Alternative 5: 51.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ 0 - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- 0.0 z))

C

double code(double x, double y, double z) {
	return 0.0 - 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 = 0.0d0 - z
end function

Java

public static double code(double x, double y, double z) {
	return 0.0 - z;
}

Python

def code(x, y, z):
	return 0.0 - z

Julia

function code(x, y, z)
	return Float64(0.0 - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0 - z;
end

Wolfram

code[x_, y_, z_] := N[(0.0 - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(z\right) \]

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{z} \]

   3. --lowering--.f64 51.0%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

5. Simplified 51.0%

   \[\leadsto \color{blue}{0 - z} \]
6. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{neg}\left(z\right) \]

   2. neg-lowering-neg.f64 51.0%

      \[\leadsto \mathsf{neg.f64}\left(z\right) \]

7. Applied egg-rr 51.0%

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

8. Final simplification 51.0%

   \[\leadsto 0 - z \]
9. Add Preprocessing

Alternative 6: 2.2% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

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

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

function tmp = code(x, y, z)
	tmp = z;
end

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(z\right) \]

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{z} \]

   3. --lowering--.f64 51.0%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

5. Simplified 51.0%

   \[\leadsto \color{blue}{0 - z} \]
6. Step-by-step derivation

   1. flip3-- N/A

      \[\leadsto \frac{{0}^{3} - {z}^{3}}{\color{blue}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}} \]

   2. metadata-eval N/A

      \[\leadsto \frac{0 - {z}^{3}}{\color{blue}{0} \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   3. sub0-neg N/A

      \[\leadsto \frac{\mathsf{neg}\left({z}^{3}\right)}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   4. cube-neg N/A

      \[\leadsto \frac{{\left(\mathsf{neg}\left(z\right)\right)}^{3}}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   5. sub0-neg N/A

      \[\leadsto \frac{{\left(0 - z\right)}^{3}}{\color{blue}{0} \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   6. sqr-pow N/A

      \[\leadsto \frac{{\left(0 - z\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(0 - z\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   7. unpow-prod-down N/A

      \[\leadsto \frac{{\left(\left(0 - z\right) \cdot \left(0 - z\right)\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   8. sub0-neg N/A

      \[\leadsto \frac{{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(0 - z\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   9. sub0-neg N/A

      \[\leadsto \frac{{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   10. sqr-neg N/A

       \[\leadsto \frac{{\left(z \cdot z\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0} \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   11. unpow-prod-down N/A

       \[\leadsto \frac{{z}^{\left(\frac{3}{2}\right)} \cdot {z}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   12. sqr-pow N/A

       \[\leadsto \frac{{z}^{3}}{\color{blue}{0 \cdot 0} + \left(z \cdot z + 0 \cdot z\right)} \]

   13. metadata-eval N/A

       \[\leadsto \frac{{z}^{3}}{0 + \left(\color{blue}{z \cdot z} + 0 \cdot z\right)} \]

   14. +-lft-identity N/A

       \[\leadsto \frac{{z}^{3}}{z \cdot z + \color{blue}{0 \cdot z}} \]

   15. mul0-lft N/A

       \[\leadsto \frac{{z}^{3}}{z \cdot z + 0} \]

   16. +-rgt-identity N/A

       \[\leadsto \frac{{z}^{3}}{z \cdot \color{blue}{z}} \]

   17. pow2 N/A

       \[\leadsto \frac{{z}^{3}}{{z}^{\color{blue}{2}}} \]

   18. pow-div N/A

       \[\leadsto {z}^{\color{blue}{\left(3 - 2\right)}} \]

   19. metadata-eval N/A

       \[\leadsto {z}^{1} \]

   20. unpow1 2.0%

       \[\leadsto z \]

7. Applied egg-rr 2.0%

   \[\leadsto \color{blue}{z} \]
8. Add Preprocessing

Developer Target 1: 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 2024191 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* x (* 3 y)) z))

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