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

Percentage Accurate: 99.9% → 99.9%

Time: 7.2s

Alternatives: 8

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: 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]

Derivation

1. Initial program 99.9%

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

Alternative 2: 62.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-69}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+135}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5e-8)
   (* x y)
   (if (<= x 3.7e-69)
     (* z 5.0)
     (if (<= x 2.4e+85) (* x y) (if (<= x 1.12e+135) (* x z) (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e-8) {
		tmp = x * y;
	} else if (x <= 3.7e-69) {
		tmp = z * 5.0;
	} else if (x <= 2.4e+85) {
		tmp = x * y;
	} else if (x <= 1.12e+135) {
		tmp = x * z;
	} 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 <= (-5.5d-8)) then
        tmp = x * y
    else if (x <= 3.7d-69) then
        tmp = z * 5.0d0
    else if (x <= 2.4d+85) then
        tmp = x * y
    else if (x <= 1.12d+135) then
        tmp = x * z
    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 <= -5.5e-8) {
		tmp = x * y;
	} else if (x <= 3.7e-69) {
		tmp = z * 5.0;
	} else if (x <= 2.4e+85) {
		tmp = x * y;
	} else if (x <= 1.12e+135) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5e-8:
		tmp = x * y
	elif x <= 3.7e-69:
		tmp = z * 5.0
	elif x <= 2.4e+85:
		tmp = x * y
	elif x <= 1.12e+135:
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5e-8)
		tmp = Float64(x * y);
	elseif (x <= 3.7e-69)
		tmp = Float64(z * 5.0);
	elseif (x <= 2.4e+85)
		tmp = Float64(x * y);
	elseif (x <= 1.12e+135)
		tmp = Float64(x * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5e-8)
		tmp = x * y;
	elseif (x <= 3.7e-69)
		tmp = z * 5.0;
	elseif (x <= 2.4e+85)
		tmp = x * y;
	elseif (x <= 1.12e+135)
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5e-8], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.7e-69], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 2.4e+85], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.12e+135], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5000000000000003e-8 or 3.7000000000000002e-69 < x < 2.39999999999999997e85 or 1.1199999999999999e135 < x

   1. Initial program 100.0%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 93.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 64.0%

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

   7. Simplified 64.0%

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

   if -5.5000000000000003e-8 < x < 3.7000000000000002e-69

   1. Initial program 99.8%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 78.9%

         \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{z}\right) \]

   7. Simplified 78.9%

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

   if 2.39999999999999997e85 < x < 1.1199999999999999e135

   1. Initial program 100.0%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 91.0%

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

   10. Simplified 91.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-69}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+135}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.00031:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -5.0) t_0 (if (<= x 0.00031) (+ (* x y) (* z 5.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -5.0) {
		tmp = t_0;
	} else if (x <= 0.00031) {
		tmp = (x * y) + (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 * (y + z)
    if (x <= (-5.0d0)) then
        tmp = t_0
    else if (x <= 0.00031d0) then
        tmp = (x * y) + (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 * (y + z);
	double tmp;
	if (x <= -5.0) {
		tmp = t_0;
	} else if (x <= 0.00031) {
		tmp = (x * y) + (z * 5.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -5.0:
		tmp = t_0
	elif x <= 0.00031:
		tmp = (x * y) + (z * 5.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -5.0)
		tmp = t_0;
	elseif (x <= 0.00031)
		tmp = Float64(Float64(x * y) + Float64(z * 5.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	tmp = 0.0;
	if (x <= -5.0)
		tmp = t_0;
	elseif (x <= 0.00031)
		tmp = (x * y) + (z * 5.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.0], t$95$0, If[LessEqual[x, 0.00031], N[(N[(x * y), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5 or 3.1e-4 < x

   1. Initial program 100.0%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 94.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 94.0%

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

   5. Taylor expanded in x around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 98.9%

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

   7. Simplified 98.9%

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

   if -5 < x < 3.1e-4

   1. Initial program 99.8%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{5}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 99.1%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 0.00031:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -240000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -240000000.0) t_0 (if (<= x 2.05e-78) (* z (+ x 5.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -240000000.0) {
		tmp = t_0;
	} else if (x <= 2.05e-78) {
		tmp = z * (x + 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 * (y + z)
    if (x <= (-240000000.0d0)) then
        tmp = t_0
    else if (x <= 2.05d-78) then
        tmp = z * (x + 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 * (y + z);
	double tmp;
	if (x <= -240000000.0) {
		tmp = t_0;
	} else if (x <= 2.05e-78) {
		tmp = z * (x + 5.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -240000000.0:
		tmp = t_0
	elif x <= 2.05e-78:
		tmp = z * (x + 5.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -240000000.0)
		tmp = t_0;
	elseif (x <= 2.05e-78)
		tmp = Float64(z * Float64(x + 5.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	tmp = 0.0;
	if (x <= -240000000.0)
		tmp = t_0;
	elseif (x <= 2.05e-78)
		tmp = z * (x + 5.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -240000000.0], t$95$0, If[LessEqual[x, 2.05e-78], N[(z * N[(x + 5.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4e8 or 2.0499999999999999e-78 < x

   1. Initial program 100.0%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 94.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 98.0%

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

   7. Simplified 98.0%

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

   if -2.4e8 < x < 2.0499999999999999e-78

   1. Initial program 99.8%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0

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

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

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(5 + x\right)}\right) \]

      2. +-lowering-+.f64 80.3%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(5, \color{blue}{x}\right)\right) \]

   7. Simplified 80.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -240000000:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-78}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -5.5e-8) t_0 (if (<= x 1.4e-78) (* z 5.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -5.5e-8) {
		tmp = t_0;
	} else if (x <= 1.4e-78) {
		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 * (y + z)
    if (x <= (-5.5d-8)) then
        tmp = t_0
    else if (x <= 1.4d-78) 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 * (y + z);
	double tmp;
	if (x <= -5.5e-8) {
		tmp = t_0;
	} else if (x <= 1.4e-78) {
		tmp = z * 5.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -5.5e-8:
		tmp = t_0
	elif x <= 1.4e-78:
		tmp = z * 5.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -5.5e-8)
		tmp = t_0;
	elseif (x <= 1.4e-78)
		tmp = Float64(z * 5.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	tmp = 0.0;
	if (x <= -5.5e-8)
		tmp = t_0;
	elseif (x <= 1.4e-78)
		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[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e-8], t$95$0, If[LessEqual[x, 1.4e-78], N[(z * 5.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000003e-8 or 1.40000000000000012e-78 < x

   1. Initial program 100.0%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 94.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 97.7%

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

   7. Simplified 97.7%

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

   if -5.5000000000000003e-8 < x < 1.40000000000000012e-78

   1. Initial program 99.8%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{z}\right) \]

   7. Simplified 79.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-78}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y + z \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5e+37) (+ (* x y) (* z (+ x 5.0))) (* x (+ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5e+37) {
		tmp = (x * y) + (z * (x + 5.0));
	} else {
		tmp = x * (y + z);
	}
	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 <= 5d+37) then
        tmp = (x * y) + (z * (x + 5.0d0))
    else
        tmp = x * (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 5e+37) {
		tmp = (x * y) + (z * (x + 5.0));
	} else {
		tmp = x * (y + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5e+37:
		tmp = (x * y) + (z * (x + 5.0))
	else:
		tmp = x * (y + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5e+37)
		tmp = Float64(Float64(x * y) + Float64(z * Float64(x + 5.0)));
	else
		tmp = Float64(x * Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 5e+37)
		tmp = (x * y) + (z * (x + 5.0));
	else
		tmp = x * (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5e+37], N[(N[(x * y), $MachinePrecision] + N[(z * N[(x + 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.99999999999999989e37

   1. Initial program 99.9%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 98.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 98.4%

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

   if 4.99999999999999989e37 < x

   1. Initial program 100.0%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 90.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 90.7%

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

   5. Taylor expanded in x around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y + z \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-69}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.2e-7) (* x y) (if (<= x 7.5e-69) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e-7) {
		tmp = x * y;
	} else if (x <= 7.5e-69) {
		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 <= (-5.2d-7)) then
        tmp = x * y
    else if (x <= 7.5d-69) 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 <= -5.2e-7) {
		tmp = x * y;
	} else if (x <= 7.5e-69) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.2e-7:
		tmp = x * y
	elif x <= 7.5e-69:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.2e-7)
		tmp = Float64(x * y);
	elseif (x <= 7.5e-69)
		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 <= -5.2e-7)
		tmp = x * y;
	elseif (x <= 7.5e-69)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.2e-7], N[(x * y), $MachinePrecision], If[LessEqual[x, 7.5e-69], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.19999999999999998e-7 or 7.5e-69 < x

   1. Initial program 100.0%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 94.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 94.2%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 59.6%

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

   7. Simplified 59.6%

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

   if -5.19999999999999998e-7 < x < 7.5e-69

   1. Initial program 99.8%

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

      1. distribute-lft-in N/A

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

      2. associate-+l+ N/A

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

      3. *-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 78.9%

         \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{z}\right) \]

   7. Simplified 78.9%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-69}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.2% 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. Step-by-step derivation

   1. distribute-lft-in N/A

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

   2. associate-+l+ N/A

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

   3. *-commutative N/A

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

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

   6. distribute-lft-out N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

   8. +-lowering-+.f64 96.8%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

3. Simplified 96.8%

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

5. Taylor expanded in x around 0

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

   1. *-lowering-*.f64 37.9%

      \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{z}\right) \]

7. Simplified 37.9%

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

8. Final simplification 37.9%

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

Developer Target 1: 98.0% 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 2024191 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (* (+ x 5) z) (* x y)))

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