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

Percentage Accurate: 99.9% → 100.0%

Time: 5.7s

Alternatives: 8

Speedup: 1.0×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma z 5.0 (* x (+ z y))))

C

double code(double x, double y, double z) {
	return fma(z, 5.0, (x * (z + y)));
}

Julia

function code(x, y, z)
	return fma(z, 5.0, Float64(x * Float64(z + y)))
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, z + y, z \cdot 5\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma x (+ z y) (* z 5.0)))

C

double code(double x, double y, double z) {
	return fma(x, (z + y), (z * 5.0));
}

Julia

function code(x, y, z)
	return fma(x, Float64(z + y), Float64(z * 5.0))
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-def 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 3: 60.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-137}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-23}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 3800000 \lor \neg \left(x \leq 1.15 \cdot 10^{+275}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.25e-95)
   (* x y)
   (if (<= x 2.05e-137)
     (* z 5.0)
     (if (<= x 6.2e-124)
       (* x y)
       (if (<= x 6e-23)
         (* z 5.0)
         (if (or (<= x 3800000.0) (not (<= x 1.15e+275))) (* x y) (* z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e-95) {
		tmp = x * y;
	} else if (x <= 2.05e-137) {
		tmp = z * 5.0;
	} else if (x <= 6.2e-124) {
		tmp = x * y;
	} else if (x <= 6e-23) {
		tmp = z * 5.0;
	} else if ((x <= 3800000.0) || !(x <= 1.15e+275)) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.25d-95)) then
        tmp = x * y
    else if (x <= 2.05d-137) then
        tmp = z * 5.0d0
    else if (x <= 6.2d-124) then
        tmp = x * y
    else if (x <= 6d-23) then
        tmp = z * 5.0d0
    else if ((x <= 3800000.0d0) .or. (.not. (x <= 1.15d+275))) then
        tmp = x * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e-95) {
		tmp = x * y;
	} else if (x <= 2.05e-137) {
		tmp = z * 5.0;
	} else if (x <= 6.2e-124) {
		tmp = x * y;
	} else if (x <= 6e-23) {
		tmp = z * 5.0;
	} else if ((x <= 3800000.0) || !(x <= 1.15e+275)) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.25e-95:
		tmp = x * y
	elif x <= 2.05e-137:
		tmp = z * 5.0
	elif x <= 6.2e-124:
		tmp = x * y
	elif x <= 6e-23:
		tmp = z * 5.0
	elif (x <= 3800000.0) or not (x <= 1.15e+275):
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.25e-95)
		tmp = Float64(x * y);
	elseif (x <= 2.05e-137)
		tmp = Float64(z * 5.0);
	elseif (x <= 6.2e-124)
		tmp = Float64(x * y);
	elseif (x <= 6e-23)
		tmp = Float64(z * 5.0);
	elseif ((x <= 3800000.0) || !(x <= 1.15e+275))
		tmp = Float64(x * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.25e-95)
		tmp = x * y;
	elseif (x <= 2.05e-137)
		tmp = z * 5.0;
	elseif (x <= 6.2e-124)
		tmp = x * y;
	elseif (x <= 6e-23)
		tmp = z * 5.0;
	elseif ((x <= 3800000.0) || ~((x <= 1.15e+275)))
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.25e-95], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.05e-137], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 6.2e-124], N[(x * y), $MachinePrecision], If[LessEqual[x, 6e-23], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 3800000.0], N[Not[LessEqual[x, 1.15e+275]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e-95 or 2.0499999999999999e-137 < x < 6.1999999999999996e-124 or 6.00000000000000006e-23 < x < 3.8e6 or 1.15000000000000005e275 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 67.0%

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

   if -2.25e-95 < x < 2.0499999999999999e-137 or 6.1999999999999996e-124 < x < 6.00000000000000006e-23

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.8%

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

   if 3.8e6 < x < 1.15000000000000005e275

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. +-commutative 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around inf 70.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-137}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-23}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 3800000 \lor \neg \left(x \leq 1.15 \cdot 10^{+275}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{-95}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-16}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -2.25e-95)
     t_0
     (if (<= x 1.85e-137)
       (* z 5.0)
       (if (<= x 6.1e-124) (* x y) (if (<= x 4.8e-16) (* z 5.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -2.25e-95) {
		tmp = t_0;
	} else if (x <= 1.85e-137) {
		tmp = z * 5.0;
	} else if (x <= 6.1e-124) {
		tmp = x * y;
	} else if (x <= 4.8e-16) {
		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 <= (-2.25d-95)) then
        tmp = t_0
    else if (x <= 1.85d-137) then
        tmp = z * 5.0d0
    else if (x <= 6.1d-124) then
        tmp = x * y
    else if (x <= 4.8d-16) 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 <= -2.25e-95) {
		tmp = t_0;
	} else if (x <= 1.85e-137) {
		tmp = z * 5.0;
	} else if (x <= 6.1e-124) {
		tmp = x * y;
	} else if (x <= 4.8e-16) {
		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 <= -2.25e-95:
		tmp = t_0
	elif x <= 1.85e-137:
		tmp = z * 5.0
	elif x <= 6.1e-124:
		tmp = x * y
	elif x <= 4.8e-16:
		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 <= -2.25e-95)
		tmp = t_0;
	elseif (x <= 1.85e-137)
		tmp = Float64(z * 5.0);
	elseif (x <= 6.1e-124)
		tmp = Float64(x * y);
	elseif (x <= 4.8e-16)
		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 <= -2.25e-95)
		tmp = t_0;
	elseif (x <= 1.85e-137)
		tmp = z * 5.0;
	elseif (x <= 6.1e-124)
		tmp = x * y;
	elseif (x <= 4.8e-16)
		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, -2.25e-95], t$95$0, If[LessEqual[x, 1.85e-137], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 6.1e-124], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.8e-16], N[(z * 5.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e-95 or 4.8000000000000001e-16 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 94.9%

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

      1. +-commutative 94.9%

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

   5. Simplified 94.9%

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

   if -2.25e-95 < x < 1.85e-137 or 6.0999999999999998e-124 < x < 4.8000000000000001e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.8%

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

   if 1.85e-137 < x < 6.0999999999999998e-124

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 81.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-16}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-95} \lor \neg \left(x \leq 2.05 \cdot 10^{-137}\right) \land \left(x \leq 6.1 \cdot 10^{-124} \lor \neg \left(x \leq 1.75 \cdot 10^{-16}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.15e-95)
         (and (not (<= x 2.05e-137))
              (or (<= x 6.1e-124) (not (<= x 1.75e-16)))))
   (* x y)
   (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.15e-95) || (!(x <= 2.05e-137) && ((x <= 6.1e-124) || !(x <= 1.75e-16)))) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.15d-95)) .or. (.not. (x <= 2.05d-137)) .and. (x <= 6.1d-124) .or. (.not. (x <= 1.75d-16))) then
        tmp = x * y
    else
        tmp = z * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.15e-95) || (!(x <= 2.05e-137) && ((x <= 6.1e-124) || !(x <= 1.75e-16)))) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.15e-95) or (not (x <= 2.05e-137) and ((x <= 6.1e-124) or not (x <= 1.75e-16))):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.15e-95) || (!(x <= 2.05e-137) && ((x <= 6.1e-124) || !(x <= 1.75e-16))))
		tmp = Float64(x * y);
	else
		tmp = Float64(z * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.15e-95) || (~((x <= 2.05e-137)) && ((x <= 6.1e-124) || ~((x <= 1.75e-16)))))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.15e-95], And[N[Not[LessEqual[x, 2.05e-137]], $MachinePrecision], Or[LessEqual[x, 6.1e-124], N[Not[LessEqual[x, 1.75e-16]], $MachinePrecision]]]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.14999999999999999e-95 or 2.0499999999999999e-137 < x < 6.0999999999999998e-124 or 1.75000000000000009e-16 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 52.8%

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

   if -2.14999999999999999e-95 < x < 2.0499999999999999e-137 or 6.0999999999999998e-124 < x < 1.75000000000000009e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.8%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-95} \lor \neg \left(x \leq 2.05 \cdot 10^{-137}\right) \land \left(x \leq 6.1 \cdot 10^{-124} \lor \neg \left(x \leq 1.75 \cdot 10^{-16}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+15} \lor \neg \left(x \leq 3 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z \cdot -5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.6e+15) (not (<= x 3e-15)))
   (* x (+ z y))
   (- (* x y) (* z -5.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.6e+15) || !(x <= 3e-15)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * y) - (z * -5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.6d+15)) .or. (.not. (x <= 3d-15))) then
        tmp = x * (z + y)
    else
        tmp = (x * y) - (z * (-5.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.6e+15) || !(x <= 3e-15)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * y) - (z * -5.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.6e+15) or not (x <= 3e-15):
		tmp = x * (z + y)
	else:
		tmp = (x * y) - (z * -5.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.6e+15) || !(x <= 3e-15))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(x * y) - Float64(z * -5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.6e+15) || ~((x <= 3e-15)))
		tmp = x * (z + y);
	else
		tmp = (x * y) - (z * -5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.6e+15], N[Not[LessEqual[x, 3e-15]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(z * -5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.6e15 or 3e-15 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

   if -5.6e15 < x < 3e-15

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around -inf 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. mul-1-neg 99.9%

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

      7. unsub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 99.8%

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

      1. *-commutative 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+15} \lor \neg \left(x \leq 3 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z \cdot -5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(z + y\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (z + y)) + (z * 5.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (z + y)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (z + y)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (z + y)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(z + y)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (z + y)) + (z * 5.0);
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 8: 36.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* z 5.0))

C

double code(double x, double y, double z) {
	return z * 5.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z * 5.0d0
end function

Java

public static double code(double x, double y, double z) {
	return z * 5.0;
}

Python

def code(x, y, z):
	return z * 5.0

Julia

function code(x, y, z)
	return Float64(z * 5.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = z * 5.0;
end

Wolfram

code[x_, y_, z_] := N[(z * 5.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 34.5%

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

4. Final simplification 34.5%

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

Developer target: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 5\right) \cdot z + x \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (+ x 5.0) z) (* x y)))

C

double code(double x, double y, double z) {
	return ((x + 5.0) * z) + (x * y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x + 5.0d0) * z) + (x * y)
end function

Java

public static double code(double x, double y, double z) {
	return ((x + 5.0) * z) + (x * y);
}

Python

def code(x, y, z):
	return ((x + 5.0) * z) + (x * y)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x + 5.0) * z) + Float64(x * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x + 5.0) * z) + (x * y);
end

Wolfram

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

Reproduce

herbie shell --seed 2024026 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

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