Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4

Percentage Accurate: 99.9% → 99.9%

Time: 8.9s

Alternatives: 9

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

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) + y) + x) + z) + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + y) + x) + z) + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(2, x + y, x + z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma 2.0 (+ x y) (+ x z)))

C

double code(double x, double y, double z) {
	return fma(2.0, (x + y), (x + z));
}

Julia

function code(x, y, z)
	return fma(2.0, Float64(x + y), Float64(x + z))
end

Wolfram

code[x_, y_, z_] := N[(2.0 * N[(x + y), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. +-commutative N/A

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

   5. count-2 N/A

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right)} + \left(x + z\right) \]

   6. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x + y, x + z\right)} \]

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

      \[\leadsto \mathsf{fma}\left(2, \color{blue}{x + y}, x + z\right) \]

   8. +-lowering-+.f64 99.9

      \[\leadsto \mathsf{fma}\left(2, x + y, \color{blue}{x + z}\right) \]

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2, x + y, x + z\right)} \]
5. Add Preprocessing

Alternative 2: 52.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+159}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-196}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-144}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+83}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e+159)
   (* x 3.0)
   (if (<= x -2.9e-196)
     (+ x z)
     (if (<= x 4.1e-144) (* 2.0 y) (if (<= x 8.5e+83) (+ x z) (* x 3.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e+159) {
		tmp = x * 3.0;
	} else if (x <= -2.9e-196) {
		tmp = x + z;
	} else if (x <= 4.1e-144) {
		tmp = 2.0 * y;
	} else if (x <= 8.5e+83) {
		tmp = x + z;
	} else {
		tmp = x * 3.0;
	}
	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 <= (-1.9d+159)) then
        tmp = x * 3.0d0
    else if (x <= (-2.9d-196)) then
        tmp = x + z
    else if (x <= 4.1d-144) then
        tmp = 2.0d0 * y
    else if (x <= 8.5d+83) then
        tmp = x + z
    else
        tmp = x * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e+159) {
		tmp = x * 3.0;
	} else if (x <= -2.9e-196) {
		tmp = x + z;
	} else if (x <= 4.1e-144) {
		tmp = 2.0 * y;
	} else if (x <= 8.5e+83) {
		tmp = x + z;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.9e+159:
		tmp = x * 3.0
	elif x <= -2.9e-196:
		tmp = x + z
	elif x <= 4.1e-144:
		tmp = 2.0 * y
	elif x <= 8.5e+83:
		tmp = x + z
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e+159)
		tmp = Float64(x * 3.0);
	elseif (x <= -2.9e-196)
		tmp = Float64(x + z);
	elseif (x <= 4.1e-144)
		tmp = Float64(2.0 * y);
	elseif (x <= 8.5e+83)
		tmp = Float64(x + z);
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.9e+159)
		tmp = x * 3.0;
	elseif (x <= -2.9e-196)
		tmp = x + z;
	elseif (x <= 4.1e-144)
		tmp = 2.0 * y;
	elseif (x <= 8.5e+83)
		tmp = x + z;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e+159], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, -2.9e-196], N[(x + z), $MachinePrecision], If[LessEqual[x, 4.1e-144], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, 8.5e+83], N[(x + z), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.89999999999999983e159 or 8.4999999999999995e83 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot 3} \]

      2. *-lowering-*.f64 74.3

         \[\leadsto \color{blue}{x \cdot 3} \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot 3} \]

   if -1.89999999999999983e159 < x < -2.89999999999999987e-196 or 4.1e-144 < x < 8.4999999999999995e83

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 52.8%

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

   if -2.89999999999999987e-196 < x < 4.1e-144

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 61.4

         \[\leadsto \color{blue}{2 \cdot y} \]

   5. Simplified 61.4%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+159}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-196}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-144}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+83}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x + y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.2e+98)
   (fma x 3.0 z)
   (if (<= x 1.3e+85) (fma 2.0 y z) (fma 2.0 (+ x y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e+98) {
		tmp = fma(x, 3.0, z);
	} else if (x <= 1.3e+85) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = fma(2.0, (x + y), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.2e+98)
		tmp = fma(x, 3.0, z);
	elseif (x <= 1.3e+85)
		tmp = fma(2.0, y, z);
	else
		tmp = fma(2.0, Float64(x + y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.2e+98], N[(x * 3.0 + z), $MachinePrecision], If[LessEqual[x, 1.3e+85], N[(2.0 * y + z), $MachinePrecision], N[(2.0 * N[(x + y), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.2000000000000001e98

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + 2 \cdot x\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \color{blue}{\left(2 \cdot x + z\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + 2 \cdot x\right) + z} \]

      3. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(2 + 1\right) \cdot x} + z \]

      4. metadata-eval N/A

         \[\leadsto \color{blue}{3} \cdot x + z \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot 3} + z \]

      6. accelerator-lowering-fma.f64 85.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3, z\right)} \]

   5. Simplified 85.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3, z\right)} \]

   if -8.2000000000000001e98 < x < 1.30000000000000005e85

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot y + z} \]

      2. accelerator-lowering-fma.f64 89.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]

   5. Simplified 89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]

   if 1.30000000000000005e85 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(2 \cdot x + 2 \cdot y\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot x + 2 \cdot y\right) + x} \]

      2. distribute-lft-out N/A

         \[\leadsto \color{blue}{2 \cdot \left(x + y\right)} + x \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, x + y, x\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{y + x}, x\right) \]

      5. +-lowering-+.f64 87.6

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{y + x}, x\right) \]

   5. Simplified 87.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x + y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.5e+101)
   (fma x 3.0 z)
   (if (<= x 3.4e+86) (fma 2.0 y z) (fma x 3.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.5e+101) {
		tmp = fma(x, 3.0, z);
	} else if (x <= 3.4e+86) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = fma(x, 3.0, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.5e+101)
		tmp = fma(x, 3.0, z);
	elseif (x <= 3.4e+86)
		tmp = fma(2.0, y, z);
	else
		tmp = fma(x, 3.0, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.5e+101], N[(x * 3.0 + z), $MachinePrecision], If[LessEqual[x, 3.4e+86], N[(2.0 * y + z), $MachinePrecision], N[(x * 3.0 + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000002e101 or 3.3999999999999998e86 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + 2 \cdot x\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \color{blue}{\left(2 \cdot x + z\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + 2 \cdot x\right) + z} \]

      3. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(2 + 1\right) \cdot x} + z \]

      4. metadata-eval N/A

         \[\leadsto \color{blue}{3} \cdot x + z \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot 3} + z \]

      6. accelerator-lowering-fma.f64 86.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3, z\right)} \]

   5. Simplified 86.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3, z\right)} \]

   if -4.5000000000000002e101 < x < 3.3999999999999998e86

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot y + z} \]

      2. accelerator-lowering-fma.f64 89.3

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]

   5. Simplified 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+179}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.5e+179) (* x 3.0) (if (<= x 7.5e+113) (fma 2.0 y z) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e+179) {
		tmp = x * 3.0;
	} else if (x <= 7.5e+113) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.5e+179)
		tmp = Float64(x * 3.0);
	elseif (x <= 7.5e+113)
		tmp = fma(2.0, y, z);
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.5e+179], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 7.5e+113], N[(2.0 * y + z), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5e179 or 7.5000000000000001e113 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot 3} \]

      2. *-lowering-*.f64 80.4

         \[\leadsto \color{blue}{x \cdot 3} \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{x \cdot 3} \]

   if -9.5e179 < x < 7.5000000000000001e113

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot y + z} \]

      2. accelerator-lowering-fma.f64 84.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]

   5. Simplified 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 54.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-62}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+118}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.4e-62) (* 2.0 y) (if (<= y 1.05e+118) (+ x z) (* 2.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.4e-62) {
		tmp = 2.0 * y;
	} else if (y <= 1.05e+118) {
		tmp = x + z;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-7.4d-62)) then
        tmp = 2.0d0 * y
    else if (y <= 1.05d+118) then
        tmp = x + z
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.4e-62) {
		tmp = 2.0 * y;
	} else if (y <= 1.05e+118) {
		tmp = x + z;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.4e-62:
		tmp = 2.0 * y
	elif y <= 1.05e+118:
		tmp = x + z
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.4e-62)
		tmp = Float64(2.0 * y);
	elseif (y <= 1.05e+118)
		tmp = Float64(x + z);
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.4e-62)
		tmp = 2.0 * y;
	elseif (y <= 1.05e+118)
		tmp = x + z;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.4e-62], N[(2.0 * y), $MachinePrecision], If[LessEqual[y, 1.05e+118], N[(x + z), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.3999999999999996e-62 or 1.05e118 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 60.3

         \[\leadsto \color{blue}{2 \cdot y} \]

   5. Simplified 60.3%

      \[\leadsto \color{blue}{2 \cdot y} \]

   if -7.3999999999999996e-62 < y < 1.05e118

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 52.1%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-62}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+118}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.9% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ x + z \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around inf

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

5. Simplified 38.7%

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

6. Final simplification 38.7%

   \[\leadsto x + z \]
7. Add Preprocessing

Alternative 8: 34.9% accurate, 16.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around inf

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

5. Simplified 33.4%

   \[\leadsto \color{blue}{z} \]
6. Add Preprocessing

Alternative 9: 7.8% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{2 \cdot y} + x \]
4. Step-by-step derivation

   1. *-lowering-*.f64 38.5

      \[\leadsto \color{blue}{2 \cdot y} + x \]

5. Simplified 38.5%

   \[\leadsto \color{blue}{2 \cdot y} + x \]

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
7. Step-by-step derivation

8. Simplified 8.2%

   \[\leadsto \color{blue}{x} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024199 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  :precision binary64
  (+ (+ (+ (+ (+ x y) y) x) z) x))