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

Percentage Accurate: 99.9% → 100.0%

Time: 6.3s

Alternatives: 8

Speedup: 1.0×

• 20.3% 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. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. fma-define 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -0.0078:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-101}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-153}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-55}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -0.0078)
     t_0
     (if (<= x -2.6e-101)
       (* z 5.0)
       (if (<= x -4.1e-153) (* x y) (if (<= x 3.2e-55) (* z 5.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -0.0078) {
		tmp = t_0;
	} else if (x <= -2.6e-101) {
		tmp = z * 5.0;
	} else if (x <= -4.1e-153) {
		tmp = x * y;
	} else if (x <= 3.2e-55) {
		tmp = z * 5.0;
	} else {
		tmp = t_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 = x * (z + y)
    if (x <= (-0.0078d0)) then
        tmp = t_0
    else if (x <= (-2.6d-101)) then
        tmp = z * 5.0d0
    else if (x <= (-4.1d-153)) then
        tmp = x * y
    else if (x <= 3.2d-55) then
        tmp = z * 5.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -0.0078) {
		tmp = t_0;
	} else if (x <= -2.6e-101) {
		tmp = z * 5.0;
	} else if (x <= -4.1e-153) {
		tmp = x * y;
	} else if (x <= 3.2e-55) {
		tmp = z * 5.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -0.0078:
		tmp = t_0
	elif x <= -2.6e-101:
		tmp = z * 5.0
	elif x <= -4.1e-153:
		tmp = x * y
	elif x <= 3.2e-55:
		tmp = z * 5.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -0.0078)
		tmp = t_0;
	elseif (x <= -2.6e-101)
		tmp = Float64(z * 5.0);
	elseif (x <= -4.1e-153)
		tmp = Float64(x * y);
	elseif (x <= 3.2e-55)
		tmp = Float64(z * 5.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -0.0078)
		tmp = t_0;
	elseif (x <= -2.6e-101)
		tmp = z * 5.0;
	elseif (x <= -4.1e-153)
		tmp = x * y;
	elseif (x <= 3.2e-55)
		tmp = z * 5.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.0078], t$95$0, If[LessEqual[x, -2.6e-101], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, -4.1e-153], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.2e-55], N[(z * 5.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0077999999999999996 or 3.2000000000000001e-55 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.4%

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

      1. +-commutative 97.4%

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

   5. Simplified 97.4%

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

   if -0.0077999999999999996 < x < -2.6000000000000001e-101 or -4.1e-153 < x < 3.2000000000000001e-55

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.9%

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

   if -2.6000000000000001e-101 < x < -4.1e-153

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 70.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0078:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-101}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-153}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-55}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-101}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-153}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-56}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -6e+24)
     t_0
     (if (<= x -4.2e-101)
       (* z (+ 5.0 x))
       (if (<= x -4.1e-153) (* x y) (if (<= x 2.7e-56) (* z 5.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -6e+24) {
		tmp = t_0;
	} else if (x <= -4.2e-101) {
		tmp = z * (5.0 + x);
	} else if (x <= -4.1e-153) {
		tmp = x * y;
	} else if (x <= 2.7e-56) {
		tmp = z * 5.0;
	} else {
		tmp = t_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 = x * (z + y)
    if (x <= (-6d+24)) then
        tmp = t_0
    else if (x <= (-4.2d-101)) then
        tmp = z * (5.0d0 + x)
    else if (x <= (-4.1d-153)) then
        tmp = x * y
    else if (x <= 2.7d-56) then
        tmp = z * 5.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -6e+24) {
		tmp = t_0;
	} else if (x <= -4.2e-101) {
		tmp = z * (5.0 + x);
	} else if (x <= -4.1e-153) {
		tmp = x * y;
	} else if (x <= 2.7e-56) {
		tmp = z * 5.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -6e+24:
		tmp = t_0
	elif x <= -4.2e-101:
		tmp = z * (5.0 + x)
	elif x <= -4.1e-153:
		tmp = x * y
	elif x <= 2.7e-56:
		tmp = z * 5.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -6e+24)
		tmp = t_0;
	elseif (x <= -4.2e-101)
		tmp = Float64(z * Float64(5.0 + x));
	elseif (x <= -4.1e-153)
		tmp = Float64(x * y);
	elseif (x <= 2.7e-56)
		tmp = Float64(z * 5.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -6e+24)
		tmp = t_0;
	elseif (x <= -4.2e-101)
		tmp = z * (5.0 + x);
	elseif (x <= -4.1e-153)
		tmp = x * y;
	elseif (x <= 2.7e-56)
		tmp = z * 5.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+24], t$95$0, If[LessEqual[x, -4.2e-101], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.1e-153], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.7e-56], N[(z * 5.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.9999999999999999e24 or 2.69999999999999995e-56 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.3%

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

      1. +-commutative 97.3%

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

   5. Simplified 97.3%

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

   if -5.9999999999999999e24 < x < -4.20000000000000031e-101

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.4%

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

      1. distribute-rgt-in 83.4%

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

   5. Simplified 83.4%

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

   if -4.20000000000000031e-101 < x < -4.1e-153

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 70.1%

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

   if -4.1e-153 < x < 2.69999999999999995e-56

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.1%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-101}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-153}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-56}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00155 \lor \neg \left(x \leq -6.5 \cdot 10^{-101} \lor \neg \left(x \leq -4.1 \cdot 10^{-153}\right) \land x \leq 3.5 \cdot 10^{-54}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.00155)
         (not
          (or (<= x -6.5e-101) (and (not (<= x -4.1e-153)) (<= x 3.5e-54)))))
   (* x y)
   (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.00155) || !((x <= -6.5e-101) || (!(x <= -4.1e-153) && (x <= 3.5e-54)))) {
		tmp = x * 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 <= (-0.00155d0)) .or. (.not. (x <= (-6.5d-101)) .or. (.not. (x <= (-4.1d-153))) .and. (x <= 3.5d-54))) then
        tmp = x * 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 <= -0.00155) || !((x <= -6.5e-101) || (!(x <= -4.1e-153) && (x <= 3.5e-54)))) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.00155) or not ((x <= -6.5e-101) or (not (x <= -4.1e-153) and (x <= 3.5e-54))):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.00155) || !((x <= -6.5e-101) || (!(x <= -4.1e-153) && (x <= 3.5e-54))))
		tmp = Float64(x * y);
	else
		tmp = Float64(z * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.00155) || ~(((x <= -6.5e-101) || (~((x <= -4.1e-153)) && (x <= 3.5e-54)))))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.00155], N[Not[Or[LessEqual[x, -6.5e-101], And[N[Not[LessEqual[x, -4.1e-153]], $MachinePrecision], LessEqual[x, 3.5e-54]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00154999999999999995 or -6.4999999999999996e-101 < x < -4.1e-153 or 3.49999999999999982e-54 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 51.8%

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

   if -0.00154999999999999995 < x < -6.4999999999999996e-101 or -4.1e-153 < x < 3.49999999999999982e-54

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.9%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00155 \lor \neg \left(x \leq -6.5 \cdot 10^{-101} \lor \neg \left(x \leq -4.1 \cdot 10^{-153}\right) \land x \leq 3.5 \cdot 10^{-54}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-101} \lor \neg \left(x \leq -4.1 \cdot 10^{-153}\right) \land x \leq 4 \cdot 10^{-54}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.0)
   (* z x)
   (if (or (<= x -2.6e-101) (and (not (<= x -4.1e-153)) (<= x 4e-54)))
     (* z 5.0)
     (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.0) {
		tmp = z * x;
	} else if ((x <= -2.6e-101) || (!(x <= -4.1e-153) && (x <= 4e-54))) {
		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 <= (-5.0d0)) then
        tmp = z * x
    else if ((x <= (-2.6d-101)) .or. (.not. (x <= (-4.1d-153))) .and. (x <= 4d-54)) 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 <= -5.0) {
		tmp = z * x;
	} else if ((x <= -2.6e-101) || (!(x <= -4.1e-153) && (x <= 4e-54))) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.0:
		tmp = z * x
	elif (x <= -2.6e-101) or (not (x <= -4.1e-153) and (x <= 4e-54)):
		tmp = z * 5.0
	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 <= -2.6e-101) || (!(x <= -4.1e-153) && (x <= 4e-54)))
		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 <= -5.0)
		tmp = z * x;
	elseif ((x <= -2.6e-101) || (~((x <= -4.1e-153)) && (x <= 4e-54)))
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.0], N[(z * x), $MachinePrecision], If[Or[LessEqual[x, -2.6e-101], And[N[Not[LessEqual[x, -4.1e-153]], $MachinePrecision], LessEqual[x, 4e-54]]], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 63.5%

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

   if -5 < x < -2.6000000000000001e-101 or -4.1e-153 < x < 4.0000000000000001e-54

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.9%

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

   if -2.6000000000000001e-101 < x < -4.1e-153 or 4.0000000000000001e-54 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 57.1%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-101} \lor \neg \left(x \leq -4.1 \cdot 10^{-153}\right) \land x \leq 4 \cdot 10^{-54}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.0) (not (<= x 5e-9))) (* x (+ z y)) (+ (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.0) || !(x <= 5e-9)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (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)) .or. (.not. (x <= 5d-9))) then
        tmp = x * (z + y)
    else
        tmp = (z * 5.0d0) + (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) || !(x <= 5e-9)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.0) or not (x <= 5e-9):
		tmp = x * (z + y)
	else:
		tmp = (z * 5.0) + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.0) || !(x <= 5e-9))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(z * 5.0) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.0) || ~((x <= 5e-9)))
		tmp = x * (z + y);
	else
		tmp = (z * 5.0) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.0], N[Not[LessEqual[x, 5e-9]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(z * 5.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5 or 5.0000000000000001e-9 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

   if -5 < x < 5.0000000000000001e-9

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 84.3%

      \[\leadsto \color{blue}{y \cdot \left(x + \left(5 \cdot \frac{z}{y} + \frac{x \cdot z}{y}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-/l* 84.0%

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

      2. distribute-rgt-out 84.6%

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

      3. +-commutative 84.6%

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

   7. Simplified 84.6%

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

   8. Taylor expanded in x around 0 83.3%

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

   9. Taylor expanded in y around 0 97.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto x \cdot \left(z + y\right) + z \cdot 5 \]
4. Add Preprocessing

Alternative 8: 36.3% 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. Add Preprocessing

3. Taylor expanded in x around 0 38.5%

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

4. Final simplification 38.5%

   \[\leadsto z \cdot 5 \]
5. Add Preprocessing

Developer target: 97.7% 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 2024079 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

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

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