Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C

Percentage Accurate: 99.9% → 100.0%

Time: 4.7s

Alternatives: 7

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

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 * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

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 * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma z 5.0 (* x (+ z y))))

C

double code(double x, double y, double z) {
	return fma(z, 5.0, (x * (z + y)));
}

Julia

function code(x, y, z)
	return fma(z, 5.0, Float64(x * Float64(z + y)))
end

Wolfram

code[x_, y_, z_] := N[(z * 5.0 + N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto \color{blue}{z \cdot 5 + x \cdot \left(y + z\right)} \]

   2. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, 5, x \cdot \left(y + z\right)\right)} \]

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, 5, x \cdot \left(y + z\right)\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right) \]

Alternative 2: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+73}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-40} \lor \neg \left(y \leq 2.95 \cdot 10^{-6}\right) \land y \leq 4.2 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.6e+73)
   (* x y)
   (if (or (<= y 4.5e-40) (and (not (<= y 2.95e-6)) (<= y 4.2e+112)))
     (* z (+ 5.0 x))
     (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.6e+73) {
		tmp = x * y;
	} else if ((y <= 4.5e-40) || (!(y <= 2.95e-6) && (y <= 4.2e+112))) {
		tmp = z * (5.0 + x);
	} else {
		tmp = 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 (y <= (-1.6d+73)) then
        tmp = x * y
    else if ((y <= 4.5d-40) .or. (.not. (y <= 2.95d-6)) .and. (y <= 4.2d+112)) then
        tmp = z * (5.0d0 + x)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.6e+73) {
		tmp = x * y;
	} else if ((y <= 4.5e-40) || (!(y <= 2.95e-6) && (y <= 4.2e+112))) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.6e+73:
		tmp = x * y
	elif (y <= 4.5e-40) or (not (y <= 2.95e-6) and (y <= 4.2e+112)):
		tmp = z * (5.0 + x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.6e+73)
		tmp = Float64(x * y);
	elseif ((y <= 4.5e-40) || (!(y <= 2.95e-6) && (y <= 4.2e+112)))
		tmp = Float64(z * Float64(5.0 + x));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.6e+73)
		tmp = x * y;
	elseif ((y <= 4.5e-40) || (~((y <= 2.95e-6)) && (y <= 4.2e+112)))
		tmp = z * (5.0 + x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.6e+73], N[(x * y), $MachinePrecision], If[Or[LessEqual[y, 4.5e-40], And[N[Not[LessEqual[y, 2.95e-6]], $MachinePrecision], LessEqual[y, 4.2e+112]]], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999991e73 or 4.5000000000000001e-40 < y < 2.95000000000000013e-6 or 4.1999999999999998e112 < y

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around inf 78.2%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -1.59999999999999991e73 < y < 4.5000000000000001e-40 or 2.95000000000000013e-6 < y < 4.1999999999999998e112

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around 0 87.2%

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

      1. +-commutative 87.2%

         \[\leadsto \color{blue}{5 \cdot z + z \cdot x} \]

      2. *-commutative 87.2%

         \[\leadsto 5 \cdot z + \color{blue}{x \cdot z} \]

      3. distribute-rgt-in 87.2%

         \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]

   4. Simplified 87.2%

      \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+73}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-40} \lor \neg \left(y \leq 2.95 \cdot 10^{-6}\right) \land y \leq 4.2 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 60.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -200000000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-79}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-12}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+152}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -200000000000.0)
   (* z x)
   (if (<= x -3.2e-79)
     (* x y)
     (if (<= x 5.4e-12) (* z 5.0) (if (<= x 5.5e+152) (* x y) (* z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -200000000000.0) {
		tmp = z * x;
	} else if (x <= -3.2e-79) {
		tmp = x * y;
	} else if (x <= 5.4e-12) {
		tmp = z * 5.0;
	} else if (x <= 5.5e+152) {
		tmp = x * y;
	} else {
		tmp = z * 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 (x <= (-200000000000.0d0)) then
        tmp = z * x
    else if (x <= (-3.2d-79)) then
        tmp = x * y
    else if (x <= 5.4d-12) then
        tmp = z * 5.0d0
    else if (x <= 5.5d+152) then
        tmp = x * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -200000000000.0) {
		tmp = z * x;
	} else if (x <= -3.2e-79) {
		tmp = x * y;
	} else if (x <= 5.4e-12) {
		tmp = z * 5.0;
	} else if (x <= 5.5e+152) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -200000000000.0:
		tmp = z * x
	elif x <= -3.2e-79:
		tmp = x * y
	elif x <= 5.4e-12:
		tmp = z * 5.0
	elif x <= 5.5e+152:
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -200000000000.0)
		tmp = Float64(z * x);
	elseif (x <= -3.2e-79)
		tmp = Float64(x * y);
	elseif (x <= 5.4e-12)
		tmp = Float64(z * 5.0);
	elseif (x <= 5.5e+152)
		tmp = Float64(x * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -200000000000.0)
		tmp = z * x;
	elseif (x <= -3.2e-79)
		tmp = x * y;
	elseif (x <= 5.4e-12)
		tmp = z * 5.0;
	elseif (x <= 5.5e+152)
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -200000000000.0], N[(z * x), $MachinePrecision], If[LessEqual[x, -3.2e-79], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.4e-12], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 5.5e+152], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e11 or 5.4999999999999999e152 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around 0 66.9%

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

      1. +-commutative 66.9%

         \[\leadsto \color{blue}{5 \cdot z + z \cdot x} \]

      2. *-commutative 66.9%

         \[\leadsto 5 \cdot z + \color{blue}{x \cdot z} \]

      3. distribute-rgt-in 66.9%

         \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]

   4. Simplified 66.9%

      \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]

   5. Taylor expanded in x around inf 66.5%

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

   if -2e11 < x < -3.19999999999999988e-79 or 5.39999999999999961e-12 < x < 5.4999999999999999e152

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around inf 67.8%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -3.19999999999999988e-79 < x < 5.39999999999999961e-12

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around 0 77.3%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -200000000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-79}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-12}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+152}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 4: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-80} \lor \neg \left(x \leq 1.1 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.8e-80) (not (<= x 1.1e-17))) (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e-80) || !(x <= 1.1e-17)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	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) :: tmp
    if ((x <= (-6.8d-80)) .or. (.not. (x <= 1.1d-17))) then
        tmp = x * (z + y)
    else
        tmp = z * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e-80) || !(x <= 1.1e-17)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.8e-80) or not (x <= 1.1e-17):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.8e-80) || !(x <= 1.1e-17))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(z * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.8e-80) || ~((x <= 1.1e-17)))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.8e-80], N[Not[LessEqual[x, 1.1e-17]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.8000000000000001e-80 or 1.1e-17 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around inf 94.9%

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

      1. +-commutative 94.9%

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

   4. Simplified 94.9%

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

   if -6.8000000000000001e-80 < x < 1.1e-17

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around 0 77.3%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-80} \lor \neg \left(x \leq 1.1 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(z + y\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (z + y)) + (z * 5.0);
}

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 * (z + y)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (z + y)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (z + y)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(z + y)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (z + y)) + (z * 5.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]

2. Final simplification 99.9%

   \[\leadsto x \cdot \left(z + y\right) + z \cdot 5 \]

Alternative 6: 61.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-18}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e-80) (* x y) (if (<= x 6.2e-18) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e-80) {
		tmp = x * y;
	} else if (x <= 6.2e-18) {
		tmp = z * 5.0;
	} else {
		tmp = 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 (x <= (-1.25d-80)) then
        tmp = x * y
    else if (x <= 6.2d-18) then
        tmp = z * 5.0d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e-80) {
		tmp = x * y;
	} else if (x <= 6.2e-18) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e-80:
		tmp = x * y
	elif x <= 6.2e-18:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e-80)
		tmp = Float64(x * y);
	elseif (x <= 6.2e-18)
		tmp = Float64(z * 5.0);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.25e-80)
		tmp = x * y;
	elseif (x <= 6.2e-18)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e-80], N[(x * y), $MachinePrecision], If[LessEqual[x, 6.2e-18], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e-80 or 6.20000000000000014e-18 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around inf 49.6%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -1.25e-80 < x < 6.20000000000000014e-18

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around 0 77.3%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-18}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 36.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* z 5.0))

C

double code(double x, double y, double z) {
	return z * 5.0;
}

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 * 5.0d0
end function

Java

public static double code(double x, double y, double z) {
	return z * 5.0;
}

Python

def code(x, y, z):
	return z * 5.0

Julia

function code(x, y, z)
	return Float64(z * 5.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = z * 5.0;
end

Wolfram

code[x_, y_, z_] := N[(z * 5.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]

2. Taylor expanded in x around 0 35.8%

   \[\leadsto \color{blue}{5 \cdot z} \]

3. Final simplification 35.8%

   \[\leadsto z \cdot 5 \]

Developer target: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 5\right) \cdot z + x \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (+ x 5.0) z) (* x y)))

C

double code(double x, double y, double z) {
	return ((x + 5.0) * z) + (x * y);
}

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 + 5.0d0) * z) + (x * y)
end function

Java

public static double code(double x, double y, double z) {
	return ((x + 5.0) * z) + (x * y);
}

Python

def code(x, y, z):
	return ((x + 5.0) * z) + (x * y)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x + 5.0) * z) + Float64(x * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x + 5.0) * z) + (x * y);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x + 5.0), $MachinePrecision] * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

  (+ (* x (+ y z)) (* z 5.0)))