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

Percentage Accurate: 99.9% → 100.0%

Time: 4.5s

Alternatives: 7

Speedup: 1.0×

• 20.4% 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: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-100}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{+19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+62} \lor \neg \left(x \leq 6.2 \cdot 10^{+111}\right) \land x \leq 8 \cdot 10^{+214}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.0)
   (* z x)
   (if (<= x 4e-100)
     (* z 5.0)
     (if (<= x 1.76e+19)
       (* x y)
       (if (or (<= x 1.55e+62) (and (not (<= x 6.2e+111)) (<= x 8e+214)))
         (* z x)
         (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.0) {
		tmp = z * x;
	} else if (x <= 4e-100) {
		tmp = z * 5.0;
	} else if (x <= 1.76e+19) {
		tmp = x * y;
	} else if ((x <= 1.55e+62) || (!(x <= 6.2e+111) && (x <= 8e+214))) {
		tmp = z * 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 (x <= (-5.0d0)) then
        tmp = z * x
    else if (x <= 4d-100) then
        tmp = z * 5.0d0
    else if (x <= 1.76d+19) then
        tmp = x * y
    else if ((x <= 1.55d+62) .or. (.not. (x <= 6.2d+111)) .and. (x <= 8d+214)) then
        tmp = z * 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 (x <= -5.0) {
		tmp = z * x;
	} else if (x <= 4e-100) {
		tmp = z * 5.0;
	} else if (x <= 1.76e+19) {
		tmp = x * y;
	} else if ((x <= 1.55e+62) || (!(x <= 6.2e+111) && (x <= 8e+214))) {
		tmp = z * x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.0:
		tmp = z * x
	elif x <= 4e-100:
		tmp = z * 5.0
	elif x <= 1.76e+19:
		tmp = x * y
	elif (x <= 1.55e+62) or (not (x <= 6.2e+111) and (x <= 8e+214)):
		tmp = z * x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.0)
		tmp = Float64(z * x);
	elseif (x <= 4e-100)
		tmp = Float64(z * 5.0);
	elseif (x <= 1.76e+19)
		tmp = Float64(x * y);
	elseif ((x <= 1.55e+62) || (!(x <= 6.2e+111) && (x <= 8e+214)))
		tmp = Float64(z * x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.0)
		tmp = z * x;
	elseif (x <= 4e-100)
		tmp = z * 5.0;
	elseif (x <= 1.76e+19)
		tmp = x * y;
	elseif ((x <= 1.55e+62) || (~((x <= 6.2e+111)) && (x <= 8e+214)))
		tmp = z * x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.0], N[(z * x), $MachinePrecision], If[LessEqual[x, 4e-100], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 1.76e+19], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, 1.55e+62], And[N[Not[LessEqual[x, 6.2e+111]], $MachinePrecision], LessEqual[x, 8e+214]]], N[(z * x), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5 or 1.76e19 < x < 1.55000000000000007e62 or 6.2000000000000001e111 < x < 7.9999999999999996e214

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 64.5%

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

      1. +-commutative 64.5%

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

      2. *-commutative 64.5%

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

      3. distribute-rgt-in 64.5%

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

   4. Simplified 64.5%

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

   5. Taylor expanded in x around inf 64.5%

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

   if -5 < x < 4.0000000000000001e-100

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 71.9%

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

   if 4.0000000000000001e-100 < x < 1.76e19 or 1.55000000000000007e62 < x < 6.2000000000000001e111 or 7.9999999999999996e214 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 67.8%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-100}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{+19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+62} \lor \neg \left(x \leq 6.2 \cdot 10^{+111}\right) \land x \leq 8 \cdot 10^{+214}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 75.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-119} \lor \neg \left(z \leq 1.05 \cdot 10^{-62}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e-119) (not (<= z 1.05e-62))) (* z (+ 5.0 x)) (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e-119) || !(z <= 1.05e-62)) {
		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 ((z <= (-4d-119)) .or. (.not. (z <= 1.05d-62))) 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 ((z <= -4e-119) || !(z <= 1.05e-62)) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e-119) or not (z <= 1.05e-62):
		tmp = z * (5.0 + x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e-119) || !(z <= 1.05e-62))
		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 ((z <= -4e-119) || ~((z <= 1.05e-62)))
		tmp = z * (5.0 + x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e-119], N[Not[LessEqual[z, 1.05e-62]], $MachinePrecision]], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000005e-119 or 1.05e-62 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.1%

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

      1. +-commutative 83.1%

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

      2. *-commutative 83.1%

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

      3. distribute-rgt-in 83.2%

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

   4. Simplified 83.2%

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

   if -4.00000000000000005e-119 < z < 1.05e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 75.5%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-119} \lor \neg \left(z \leq 1.05 \cdot 10^{-62}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 79.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-118} \lor \neg \left(z \leq 2.15 \cdot 10^{-61}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e-118) (not (<= z 2.15e-61)))
   (* z (+ 5.0 x))
   (* x (+ z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e-118) || !(z <= 2.15e-61)) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * (z + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.8d-118)) .or. (.not. (z <= 2.15d-61))) then
        tmp = z * (5.0d0 + x)
    else
        tmp = x * (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e-118) || !(z <= 2.15e-61)) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * (z + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e-118) or not (z <= 2.15e-61):
		tmp = z * (5.0 + x)
	else:
		tmp = x * (z + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e-118) || !(z <= 2.15e-61))
		tmp = Float64(z * Float64(5.0 + x));
	else
		tmp = Float64(x * Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.8e-118) || ~((z <= 2.15e-61)))
		tmp = z * (5.0 + x);
	else
		tmp = x * (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e-118], N[Not[LessEqual[z, 2.15e-61]], $MachinePrecision]], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999961e-118 or 2.1500000000000002e-61 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.1%

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

      1. +-commutative 83.1%

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

      2. *-commutative 83.1%

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

      3. distribute-rgt-in 83.2%

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

   4. Simplified 83.2%

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

   if -5.79999999999999961e-118 < z < 2.1500000000000002e-61

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.9%

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

      1. +-commutative 83.9%

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

   4. Simplified 83.9%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-118} \lor \neg \left(z \leq 2.15 \cdot 10^{-61}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]

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: 61.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-101}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e-11) (* x y) (if (<= x 7.5e-101) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-11) {
		tmp = x * y;
	} else if (x <= 7.5e-101) {
		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 <= (-1.4d-11)) then
        tmp = x * y
    else if (x <= 7.5d-101) 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 <= -1.4e-11) {
		tmp = x * y;
	} else if (x <= 7.5e-101) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e-11:
		tmp = x * y
	elif x <= 7.5e-101:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e-11)
		tmp = Float64(x * y);
	elseif (x <= 7.5e-101)
		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 <= -1.4e-11)
		tmp = x * y;
	elseif (x <= 7.5e-101)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e-11], N[(x * y), $MachinePrecision], If[LessEqual[x, 7.5e-101], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e-11 or 7.5000000000000001e-101 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 51.4%

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

   if -1.4e-11 < x < 7.5000000000000001e-101

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 72.4%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-101}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 36.9% 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 37.2%

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

3. Final simplification 37.2%

   \[\leadsto z \cdot 5 \]

Developer target: 98.1% 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 2023192 
(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)))