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

Percentage Accurate: 99.9% → 100.0%

Time: 5.9s

Alternatives: 8

Speedup: 1.0×

• 20.7% 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-def 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: 60.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 0.084:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+64}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9e-37)
   (* x y)
   (if (<= x 5.4e-120)
     (* z 5.0)
     (if (<= x 8.5e-37)
       (* x y)
       (if (<= x 0.084) (* z 5.0) (if (<= x 7.8e+64) (* x y) (* z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e-37) {
		tmp = x * y;
	} else if (x <= 5.4e-120) {
		tmp = z * 5.0;
	} else if (x <= 8.5e-37) {
		tmp = x * y;
	} else if (x <= 0.084) {
		tmp = z * 5.0;
	} else if (x <= 7.8e+64) {
		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 <= (-9d-37)) then
        tmp = x * y
    else if (x <= 5.4d-120) then
        tmp = z * 5.0d0
    else if (x <= 8.5d-37) then
        tmp = x * y
    else if (x <= 0.084d0) then
        tmp = z * 5.0d0
    else if (x <= 7.8d+64) 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 <= -9e-37) {
		tmp = x * y;
	} else if (x <= 5.4e-120) {
		tmp = z * 5.0;
	} else if (x <= 8.5e-37) {
		tmp = x * y;
	} else if (x <= 0.084) {
		tmp = z * 5.0;
	} else if (x <= 7.8e+64) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9e-37:
		tmp = x * y
	elif x <= 5.4e-120:
		tmp = z * 5.0
	elif x <= 8.5e-37:
		tmp = x * y
	elif x <= 0.084:
		tmp = z * 5.0
	elif x <= 7.8e+64:
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9e-37)
		tmp = Float64(x * y);
	elseif (x <= 5.4e-120)
		tmp = Float64(z * 5.0);
	elseif (x <= 8.5e-37)
		tmp = Float64(x * y);
	elseif (x <= 0.084)
		tmp = Float64(z * 5.0);
	elseif (x <= 7.8e+64)
		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 <= -9e-37)
		tmp = x * y;
	elseif (x <= 5.4e-120)
		tmp = z * 5.0;
	elseif (x <= 8.5e-37)
		tmp = x * y;
	elseif (x <= 0.084)
		tmp = z * 5.0;
	elseif (x <= 7.8e+64)
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9e-37], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.4e-120], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 8.5e-37], N[(x * y), $MachinePrecision], If[LessEqual[x, 0.084], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 7.8e+64], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.00000000000000081e-37 or 5.3999999999999997e-120 < x < 8.5000000000000007e-37 or 0.0840000000000000052 < x < 7.7999999999999996e64

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 60.8%

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

   if -9.00000000000000081e-37 < x < 5.3999999999999997e-120 or 8.5000000000000007e-37 < x < 0.0840000000000000052

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.2%

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

   if 7.7999999999999996e64 < 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 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 66.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 0.084:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+64}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-36} \lor \neg \left(x \leq 3.3 \cdot 10^{-123}\right) \land \left(x \leq 1.35 \cdot 10^{-36} \lor \neg \left(x \leq 0.084\right)\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.5e-36)
         (and (not (<= x 3.3e-123)) (or (<= x 1.35e-36) (not (<= x 0.084)))))
   (* x (+ z y))
   (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.5e-36) || (!(x <= 3.3e-123) && ((x <= 1.35e-36) || !(x <= 0.084)))) {
		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 <= (-4.5d-36)) .or. (.not. (x <= 3.3d-123)) .and. (x <= 1.35d-36) .or. (.not. (x <= 0.084d0))) 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 <= -4.5e-36) || (!(x <= 3.3e-123) && ((x <= 1.35e-36) || !(x <= 0.084)))) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.5e-36) or (not (x <= 3.3e-123) and ((x <= 1.35e-36) or not (x <= 0.084))):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.5e-36) || (!(x <= 3.3e-123) && ((x <= 1.35e-36) || !(x <= 0.084))))
		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 <= -4.5e-36) || (~((x <= 3.3e-123)) && ((x <= 1.35e-36) || ~((x <= 0.084)))))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.5e-36], And[N[Not[LessEqual[x, 3.3e-123]], $MachinePrecision], Or[LessEqual[x, 1.35e-36], N[Not[LessEqual[x, 0.084]], $MachinePrecision]]]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.50000000000000024e-36 or 3.3000000000000003e-123 < x < 1.35000000000000004e-36 or 0.0840000000000000052 < 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 95.2%

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

      1. +-commutative 95.2%

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

   5. Simplified 95.2%

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

   if -4.50000000000000024e-36 < x < 3.3000000000000003e-123 or 1.35000000000000004e-36 < x < 0.0840000000000000052

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-36} \lor \neg \left(x \leq 3.3 \cdot 10^{-123}\right) \land \left(x \leq 1.35 \cdot 10^{-36} \lor \neg \left(x \leq 0.084\right)\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{-38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-39} \lor \neg \left(x \leq 11600\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -7e-38)
     t_0
     (if (<= x 5.4e-120)
       (* z 5.0)
       (if (or (<= x 9e-39) (not (<= x 11600.0))) t_0 (* z (+ 5.0 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -7e-38) {
		tmp = t_0;
	} else if (x <= 5.4e-120) {
		tmp = z * 5.0;
	} else if ((x <= 9e-39) || !(x <= 11600.0)) {
		tmp = t_0;
	} else {
		tmp = z * (5.0 + 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) :: t_0
    real(8) :: tmp
    t_0 = x * (z + y)
    if (x <= (-7d-38)) then
        tmp = t_0
    else if (x <= 5.4d-120) then
        tmp = z * 5.0d0
    else if ((x <= 9d-39) .or. (.not. (x <= 11600.0d0))) then
        tmp = t_0
    else
        tmp = z * (5.0d0 + x)
    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 <= -7e-38) {
		tmp = t_0;
	} else if (x <= 5.4e-120) {
		tmp = z * 5.0;
	} else if ((x <= 9e-39) || !(x <= 11600.0)) {
		tmp = t_0;
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -7e-38:
		tmp = t_0
	elif x <= 5.4e-120:
		tmp = z * 5.0
	elif (x <= 9e-39) or not (x <= 11600.0):
		tmp = t_0
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -7e-38)
		tmp = t_0;
	elseif (x <= 5.4e-120)
		tmp = Float64(z * 5.0);
	elseif ((x <= 9e-39) || !(x <= 11600.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(5.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -7e-38)
		tmp = t_0;
	elseif (x <= 5.4e-120)
		tmp = z * 5.0;
	elseif ((x <= 9e-39) || ~((x <= 11600.0)))
		tmp = t_0;
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e-38], t$95$0, If[LessEqual[x, 5.4e-120], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 9e-39], N[Not[LessEqual[x, 11600.0]], $MachinePrecision]], t$95$0, N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.0000000000000003e-38 or 5.3999999999999997e-120 < x < 9.0000000000000002e-39 or 11600 < 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 96.0%

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

      1. +-commutative 96.0%

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

   5. Simplified 96.0%

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

   if -7.0000000000000003e-38 < x < 5.3999999999999997e-120

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.8%

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

   if 9.0000000000000002e-39 < x < 11600

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 87.7%

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

      1. distribute-rgt-in 87.8%

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

   5. Simplified 87.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-39} \lor \neg \left(x \leq 11600\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-36} \lor \neg \left(x \leq 5.4 \cdot 10^{-120} \lor \neg \left(x \leq 8 \cdot 10^{-39}\right) \land x \leq 0.084\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.65e-36)
         (not (or (<= x 5.4e-120) (and (not (<= x 8e-39)) (<= x 0.084)))))
   (* x y)
   (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.65e-36) || !((x <= 5.4e-120) || (!(x <= 8e-39) && (x <= 0.084)))) {
		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 <= (-2.65d-36)) .or. (.not. (x <= 5.4d-120) .or. (.not. (x <= 8d-39)) .and. (x <= 0.084d0))) 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 <= -2.65e-36) || !((x <= 5.4e-120) || (!(x <= 8e-39) && (x <= 0.084)))) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.65e-36) or not ((x <= 5.4e-120) or (not (x <= 8e-39) and (x <= 0.084))):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.65e-36) || !((x <= 5.4e-120) || (!(x <= 8e-39) && (x <= 0.084))))
		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 <= -2.65e-36) || ~(((x <= 5.4e-120) || (~((x <= 8e-39)) && (x <= 0.084)))))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.65e-36], N[Not[Or[LessEqual[x, 5.4e-120], And[N[Not[LessEqual[x, 8e-39]], $MachinePrecision], LessEqual[x, 0.084]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6499999999999999e-36 or 5.3999999999999997e-120 < x < 7.99999999999999943e-39 or 0.0840000000000000052 < 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 54.7%

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

   if -2.6499999999999999e-36 < x < 5.3999999999999997e-120 or 7.99999999999999943e-39 < x < 0.0840000000000000052

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-36} \lor \neg \left(x \leq 5.4 \cdot 10^{-120} \lor \neg \left(x \leq 8 \cdot 10^{-39}\right) \land x \leq 0.084\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+34} \lor \neg \left(x \leq 0.35\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z \cdot -5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.6e+34) (not (<= x 0.35)))
   (* x (+ z y))
   (- (* x y) (* z -5.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.6e+34) || !(x <= 0.35)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * y) - (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 <= (-6.6d+34)) .or. (.not. (x <= 0.35d0))) then
        tmp = x * (z + y)
    else
        tmp = (x * y) - (z * (-5.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.6e+34) || !(x <= 0.35)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * y) - (z * -5.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.6e+34) or not (x <= 0.35):
		tmp = x * (z + y)
	else:
		tmp = (x * y) - (z * -5.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.6e+34) || !(x <= 0.35))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(x * y) - Float64(z * -5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.6e+34) || ~((x <= 0.35)))
		tmp = x * (z + y);
	else
		tmp = (x * y) - (z * -5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.6e+34], N[Not[LessEqual[x, 0.35]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(z * -5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.59999999999999976e34 or 0.34999999999999998 < 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 98.2%

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

      1. +-commutative 98.2%

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

   5. Simplified 98.2%

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

   if -6.59999999999999976e34 < x < 0.34999999999999998

   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-def 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 z around -inf 99.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot x - 5\right)\right) + x \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{x \cdot y + -1 \cdot \left(z \cdot \left(-1 \cdot x - 5\right)\right)} \]

      2. mul-1-neg 99.9%

         \[\leadsto x \cdot y + \color{blue}{\left(-z \cdot \left(-1 \cdot x - 5\right)\right)} \]

      3. unsub-neg 99.9%

         \[\leadsto \color{blue}{x \cdot y - z \cdot \left(-1 \cdot x - 5\right)} \]

      4. sub-neg 99.9%

         \[\leadsto x \cdot y - z \cdot \color{blue}{\left(-1 \cdot x + \left(-5\right)\right)} \]

      5. +-commutative 99.9%

         \[\leadsto x \cdot y - z \cdot \color{blue}{\left(\left(-5\right) + -1 \cdot x\right)} \]

      6. mul-1-neg 99.9%

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

      7. unsub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 99.0%

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

      1. *-commutative 99.0%

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

   10. Simplified 99.0%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+34} \lor \neg \left(x \leq 0.35\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z \cdot -5\\ \end{array} \]
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: 36.8% 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 35.6%

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

4. Final simplification 35.6%

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

Developer target: 97.8% 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 2024031 
(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)))