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

Percentage Accurate: 99.9% → 100.0%

Time: 8.0s

Alternatives: 8

Speedup: 1.0×

• 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, 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: 61.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+96}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-16}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+98}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+96)
   (* z x)
   (if (<= x -3.1e-9)
     (* x y)
     (if (<= x 2.5e-16) (* z 5.0) (if (<= x 7e+98) (* x y) (* z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+96) {
		tmp = z * x;
	} else if (x <= -3.1e-9) {
		tmp = x * y;
	} else if (x <= 2.5e-16) {
		tmp = z * 5.0;
	} else if (x <= 7e+98) {
		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 <= (-1.55d+96)) then
        tmp = z * x
    else if (x <= (-3.1d-9)) then
        tmp = x * y
    else if (x <= 2.5d-16) then
        tmp = z * 5.0d0
    else if (x <= 7d+98) 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 <= -1.55e+96) {
		tmp = z * x;
	} else if (x <= -3.1e-9) {
		tmp = x * y;
	} else if (x <= 2.5e-16) {
		tmp = z * 5.0;
	} else if (x <= 7e+98) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.55e+96:
		tmp = z * x
	elif x <= -3.1e-9:
		tmp = x * y
	elif x <= 2.5e-16:
		tmp = z * 5.0
	elif x <= 7e+98:
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+96)
		tmp = Float64(z * x);
	elseif (x <= -3.1e-9)
		tmp = Float64(x * y);
	elseif (x <= 2.5e-16)
		tmp = Float64(z * 5.0);
	elseif (x <= 7e+98)
		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 <= -1.55e+96)
		tmp = z * x;
	elseif (x <= -3.1e-9)
		tmp = x * y;
	elseif (x <= 2.5e-16)
		tmp = z * 5.0;
	elseif (x <= 7e+98)
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+96], N[(z * x), $MachinePrecision], If[LessEqual[x, -3.1e-9], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.5e-16], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 7e+98], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5499999999999999e96 or 7e98 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 62.5%

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

   if -1.5499999999999999e96 < x < -3.10000000000000005e-9 or 2.5000000000000002e-16 < x < 7e98

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 62.9%

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

   if -3.10000000000000005e-9 < x < 2.5000000000000002e-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 70.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+96}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-16}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+98}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.0) || !(x <= 5.0)) {
		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 <= (-5.0d0)) .or. (.not. (x <= 5.0d0))) 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 <= -5.0) || !(x <= 5.0)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * y) + (z * 5.0);
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.0) || !(x <= 5.0))
		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 <= -5.0) || ~((x <= 5.0)))
		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, -5.0], N[Not[LessEqual[x, 5.0]], $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 or 5 < 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 99.5%

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

      1. +-commutative 99.5%

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

   5. Simplified 99.5%

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

   if -5 < x < 5

   1. Initial program 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. associate-+l+ 99.9%

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

      3. *-commutative 99.9%

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

      4. fma-def 99.9%

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

      5. distribute-lft-out 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-+ 99.9%

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

      3. associate-*l/ 99.7%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, -\color{blue}{25}\right) \cdot z}{x - 5}\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, \color{blue}{-25}\right) \cdot z}{x - 5}\right) \]

      7. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, -25\right) \cdot z}{\color{blue}{x + \left(-5\right)}}\right) \]

      8. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, -25\right) \cdot z}{x + \color{blue}{-5}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{\mathsf{fma}\left(x, x, -25\right) \cdot z}{x + -5}}\right) \]

   7. Taylor expanded in x around 0 99.6%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{\color{blue}{-25 \cdot z}}{x + -5}\right) \]
   8. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{\color{blue}{z \cdot -25}}{x + -5}\right) \]

   9. Simplified 99.6%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{\color{blue}{z \cdot -25}}{x + -5}\right) \]
   10. Step-by-step derivation

       1. fma-udef 99.6%

          \[\leadsto \color{blue}{x \cdot y + \frac{z \cdot -25}{x + -5}} \]

       2. *-commutative 99.6%

          \[\leadsto x \cdot y + \frac{\color{blue}{-25 \cdot z}}{x + -5} \]

       3. *-un-lft-identity 99.6%

          \[\leadsto x \cdot y + \frac{-25 \cdot z}{\color{blue}{1 \cdot \left(x + -5\right)}} \]

       4. times-frac 99.7%

          \[\leadsto x \cdot y + \color{blue}{\frac{-25}{1} \cdot \frac{z}{x + -5}} \]

       5. metadata-eval 99.7%

          \[\leadsto x \cdot y + \color{blue}{-25} \cdot \frac{z}{x + -5} \]

   11. Applied egg-rr 99.7%

       \[\leadsto \color{blue}{x \cdot y + -25 \cdot \frac{z}{x + -5}} \]

   12. Taylor expanded in x around 0 99.1%

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

       1. *-commutative 99.1%

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

   14. Simplified 99.1%

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

4. Final simplification 99.3%

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

Alternative 4: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-8} \lor \neg \left(x \leq 1.65 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.8e-8) (not (<= x 1.65e-15))) (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.8e-8) || !(x <= 1.65e-15)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.8d-8)) .or. (.not. (x <= 1.65d-15))) then
        tmp = x * (z + y)
    else
        tmp = z * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.8e-8) || !(x <= 1.65e-15)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.8e-8) or not (x <= 1.65e-15):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.8e-8) || !(x <= 1.65e-15))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(z * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.8e-8) || ~((x <= 1.65e-15)))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.8e-8], N[Not[LessEqual[x, 1.65e-15]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.79999999999999991e-8 or 1.65e-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 98.2%

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

      1. +-commutative 98.2%

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

   5. Simplified 98.2%

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

   if -1.79999999999999991e-8 < x < 1.65e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 70.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-8} \lor \neg \left(x \leq 1.65 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-6} \lor \neg \left(x \leq 370000\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e-6) (not (<= x 370000.0))) (* x (+ z y)) (* z (+ 5.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-6) || !(x <= 370000.0)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8.5d-6)) .or. (.not. (x <= 370000.0d0))) then
        tmp = x * (z + y)
    else
        tmp = z * (5.0d0 + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-6) || !(x <= 370000.0)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e-6) or not (x <= 370000.0):
		tmp = x * (z + y)
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e-6) || !(x <= 370000.0))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(z * Float64(5.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.5e-6) || ~((x <= 370000.0)))
		tmp = x * (z + y);
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-6], N[Not[LessEqual[x, 370000.0]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.4999999999999999e-6 or 3.7e5 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -8.4999999999999999e-6 < x < 3.7e5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.2%

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

      1. distribute-rgt-in 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-6} \lor \neg \left(x \leq 370000\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-8} \lor \neg \left(x \leq 1.35 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.3e-8) (not (<= x 1.35e-15))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.3e-8) || !(x <= 1.35e-15)) {
		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 <= (-1.3d-8)) .or. (.not. (x <= 1.35d-15))) 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 <= -1.3e-8) || !(x <= 1.35e-15)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.3e-8) or not (x <= 1.35e-15):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.3e-8) || !(x <= 1.35e-15))
		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 <= -1.3e-8) || ~((x <= 1.35e-15)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.3e-8], N[Not[LessEqual[x, 1.35e-15]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3000000000000001e-8 or 1.35000000000000005e-15 < 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 48.4%

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

   if -1.3000000000000001e-8 < x < 1.35000000000000005e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 70.4%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-8} \lor \neg \left(x \leq 1.35 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
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: 36.5% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 35.7%

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

4. Final simplification 35.7%

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

Developer target: 97.9% 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 2024096 
(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)))