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

Percentage Accurate: 99.9% → 100.0%

Time: 5.6s

Alternatives: 8

Speedup: 1.1×

• 20.8% 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, 1.1× 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. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 100.0

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

4. Applied rewrites 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: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.5)
   (* x (+ z y))
   (if (<= x 5.1e-20) (fma z 5.0 (* x y)) (fma z x (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5) {
		tmp = x * (z + y);
	} else if (x <= 5.1e-20) {
		tmp = fma(z, 5.0, (x * y));
	} else {
		tmp = fma(z, x, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.5)
		tmp = Float64(x * Float64(z + y));
	elseif (x <= 5.1e-20)
		tmp = fma(z, 5.0, Float64(x * y));
	else
		tmp = fma(z, x, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.5], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.1e-20], N[(z * 5.0 + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 97.0

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

   5. Applied rewrites 97.0%

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

   if -6.5 < x < 5.10000000000000019e-20

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 98.9

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

   7. Applied rewrites 98.9%

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

   if 5.10000000000000019e-20 < 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

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 98.8

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

   5. Applied rewrites 98.8%

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

   7. Applied rewrites 98.8%

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

Alternative 3: 83.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5e+26)
   (* x (+ z y))
   (if (<= x 4.7e-55) (* z (+ 5.0 x)) (fma z x (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e+26) {
		tmp = x * (z + y);
	} else if (x <= 4.7e-55) {
		tmp = z * (5.0 + x);
	} else {
		tmp = fma(z, x, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5e+26)
		tmp = Float64(x * Float64(z + y));
	elseif (x <= 4.7e-55)
		tmp = Float64(z * Float64(5.0 + x));
	else
		tmp = fma(z, x, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5e+26], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.7e-55], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4999999999999997e26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -5.4999999999999997e26 < x < 4.7e-55

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 80.1

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

   5. Applied rewrites 80.1%

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

   if 4.7e-55 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 95.4

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

   5. Applied rewrites 95.4%

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

   7. Applied rewrites 95.5%

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

Alternative 4: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -5.5e+26) t_0 (if (<= x 4.7e-55) (* z (+ 5.0 x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -5.5e+26) {
		tmp = t_0;
	} else if (x <= 4.7e-55) {
		tmp = z * (5.0 + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z + y)
    if (x <= (-5.5d+26)) then
        tmp = t_0
    else if (x <= 4.7d-55) then
        tmp = z * (5.0d0 + x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -5.5e+26) {
		tmp = t_0;
	} else if (x <= 4.7e-55) {
		tmp = z * (5.0 + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -5.5e+26:
		tmp = t_0
	elif x <= 4.7e-55:
		tmp = z * (5.0 + x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -5.5e+26)
		tmp = t_0;
	elseif (x <= 4.7e-55)
		tmp = Float64(z * Float64(5.0 + x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -5.5e+26)
		tmp = t_0;
	elseif (x <= 4.7e-55)
		tmp = z * (5.0 + x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e+26], t$95$0, If[LessEqual[x, 4.7e-55], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4999999999999997e26 or 4.7e-55 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 97.1

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

   5. Applied rewrites 97.1%

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

   if -5.4999999999999997e26 < x < 4.7e-55

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 80.1

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

   5. Applied rewrites 80.1%

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

Alternative 5: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -0.022:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-55}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -0.022) t_0 (if (<= x 4.7e-55) (* z 5.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -0.022) {
		tmp = t_0;
	} else if (x <= 4.7e-55) {
		tmp = z * 5.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z + y)
    if (x <= (-0.022d0)) then
        tmp = t_0
    else if (x <= 4.7d-55) then
        tmp = z * 5.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -0.022) {
		tmp = t_0;
	} else if (x <= 4.7e-55) {
		tmp = z * 5.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -0.022:
		tmp = t_0
	elif x <= 4.7e-55:
		tmp = z * 5.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -0.022)
		tmp = t_0;
	elseif (x <= 4.7e-55)
		tmp = Float64(z * 5.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -0.022)
		tmp = t_0;
	elseif (x <= 4.7e-55)
		tmp = z * 5.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.022], t$95$0, If[LessEqual[x, 4.7e-55], N[(z * 5.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.021999999999999999 or 4.7e-55 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 96.1

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

   5. Applied rewrites 96.1%

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

   if -0.021999999999999999 < x < 4.7e-55

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 79.0

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

   5. Applied rewrites 79.0%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.022:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-55}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.022:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-54}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.022) (* x y) (if (<= x 4.3e-54) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.022) {
		tmp = x * y;
	} else if (x <= 4.3e-54) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.022d0)) then
        tmp = x * y
    else if (x <= 4.3d-54) then
        tmp = z * 5.0d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.022) {
		tmp = x * y;
	} else if (x <= 4.3e-54) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.022:
		tmp = x * y
	elif x <= 4.3e-54:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.022)
		tmp = Float64(x * y);
	elseif (x <= 4.3e-54)
		tmp = Float64(z * 5.0);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.022)
		tmp = x * y;
	elseif (x <= 4.3e-54)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.022], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.3e-54], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.021999999999999999 or 4.3e-54 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

   if -0.021999999999999999 < x < 4.3e-54

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 79.0

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

   5. Applied rewrites 79.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.022:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-54}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 4.2:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.0) (* z x) (if (<= x 4.2) (* z 5.0) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.0) {
		tmp = z * x;
	} else if (x <= 4.2) {
		tmp = z * 5.0;
	} 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 <= (-5.0d0)) then
        tmp = z * x
    else if (x <= 4.2d0) then
        tmp = z * 5.0d0
    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 <= -5.0) {
		tmp = z * x;
	} else if (x <= 4.2) {
		tmp = z * 5.0;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.0:
		tmp = z * x
	elif x <= 4.2:
		tmp = z * 5.0
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.0)
		tmp = Float64(z * x);
	elseif (x <= 4.2)
		tmp = Float64(z * 5.0);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.0)
		tmp = z * x;
	elseif (x <= 4.2)
		tmp = z * 5.0;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.0], N[(z * x), $MachinePrecision], If[LessEqual[x, 4.2], N[(z * 5.0), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5 or 4.20000000000000018 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 46.8

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

   5. Applied rewrites 46.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.8%

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

   if -5 < x < 4.20000000000000018

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 73.6

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

   5. Applied rewrites 73.6%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 4.2:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 28.1% accurate, 2.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = z * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. distribute-rgt-in N/A

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

   2. lower-*.f64 N/A

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

   3. lower-+.f64 62.2

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

5. Applied rewrites 62.2%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 22.0%

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

9. Final simplification 22.0%

   \[\leadsto z \cdot x \]
10. Add Preprocessing

Developer Target 1: 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 2024221 
(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)))