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×

• 20.5% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 100.0

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 100.0

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

4. Applied rewrites 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 61.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+186}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-48}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-36}:\\ \;\;\;\;5 \cdot z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+180}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e+186)
   (* x y)
   (if (<= x -1.4e+24)
     (* x z)
     (if (<= x -1.1e-48)
       (* x y)
       (if (<= x 1.18e-36) (* 5.0 z) (if (<= x 1.65e+180) (* x y) (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+186) {
		tmp = x * y;
	} else if (x <= -1.4e+24) {
		tmp = x * z;
	} else if (x <= -1.1e-48) {
		tmp = x * y;
	} else if (x <= 1.18e-36) {
		tmp = 5.0 * z;
	} else if (x <= 1.65e+180) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.1d+186)) then
        tmp = x * y
    else if (x <= (-1.4d+24)) then
        tmp = x * z
    else if (x <= (-1.1d-48)) then
        tmp = x * y
    else if (x <= 1.18d-36) then
        tmp = 5.0d0 * z
    else if (x <= 1.65d+180) then
        tmp = x * y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+186) {
		tmp = x * y;
	} else if (x <= -1.4e+24) {
		tmp = x * z;
	} else if (x <= -1.1e-48) {
		tmp = x * y;
	} else if (x <= 1.18e-36) {
		tmp = 5.0 * z;
	} else if (x <= 1.65e+180) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e+186:
		tmp = x * y
	elif x <= -1.4e+24:
		tmp = x * z
	elif x <= -1.1e-48:
		tmp = x * y
	elif x <= 1.18e-36:
		tmp = 5.0 * z
	elif x <= 1.65e+180:
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e+186)
		tmp = Float64(x * y);
	elseif (x <= -1.4e+24)
		tmp = Float64(x * z);
	elseif (x <= -1.1e-48)
		tmp = Float64(x * y);
	elseif (x <= 1.18e-36)
		tmp = Float64(5.0 * z);
	elseif (x <= 1.65e+180)
		tmp = Float64(x * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e+186)
		tmp = x * y;
	elseif (x <= -1.4e+24)
		tmp = x * z;
	elseif (x <= -1.1e-48)
		tmp = x * y;
	elseif (x <= 1.18e-36)
		tmp = 5.0 * z;
	elseif (x <= 1.65e+180)
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e+186], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.4e+24], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.1e-48], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.18e-36], N[(5.0 * z), $MachinePrecision], If[LessEqual[x, 1.65e+180], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1e186 or -1.4000000000000001e24 < x < -1.10000000000000006e-48 or 1.1799999999999999e-36 < x < 1.64999999999999995e180

   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. *-commutative N/A

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

      2. lower-*.f64 64.8

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

   5. Applied rewrites 64.8%

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

   if -2.1e186 < x < -1.4000000000000001e24 or 1.64999999999999995e180 < 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. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. metadata-eval N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 66.1

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 66.1%

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

   if -1.10000000000000006e-48 < x < 1.1799999999999999e-36

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 74.9

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

   5. Applied rewrites 74.9%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+186}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-48}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-36}:\\ \;\;\;\;5 \cdot z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+180}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y + z\right) \cdot x\\ \mathbf{if}\;x \leq -1.18 \cdot 10^{-48}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ y z) x)))
   (if (<= x -1.18e-48) t_0 (if (<= x 1.18e-36) (fma z 5.0 (* x z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y + z) * x;
	double tmp;
	if (x <= -1.18e-48) {
		tmp = t_0;
	} else if (x <= 1.18e-36) {
		tmp = fma(z, 5.0, (x * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y + z) * x)
	tmp = 0.0
	if (x <= -1.18e-48)
		tmp = t_0;
	elseif (x <= 1.18e-36)
		tmp = fma(z, 5.0, Float64(x * z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.18e-48], t$95$0, If[LessEqual[x, 1.18e-36], N[(z * 5.0 + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.18000000000000007e-48 or 1.1799999999999999e-36 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   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. lift-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. associate--l+ N/A

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

      8. lower-fma.f64 N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. distribute-lft-out N/A

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

      11. lower-*.f64 N/A

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

      12. lower-+.f64 95.8

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

   4. Applied rewrites 95.8%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 96.2

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

   7. Applied rewrites 96.2%

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

   if -1.18000000000000007e-48 < x < 1.1799999999999999e-36

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   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. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. metadata-eval N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 74.9

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

   5. Applied rewrites 74.9%

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

   7. Applied rewrites 75.0%

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

Alternative 4: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y + z\right) \cdot x\\ \mathbf{if}\;x \leq -1.18 \cdot 10^{-48}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-36}:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ y z) x)))
   (if (<= x -1.18e-48) t_0 (if (<= x 1.18e-36) (* 5.0 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y + z) * x;
	double tmp;
	if (x <= -1.18e-48) {
		tmp = t_0;
	} else if (x <= 1.18e-36) {
		tmp = 5.0 * z;
	} 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 = (y + z) * x
    if (x <= (-1.18d-48)) then
        tmp = t_0
    else if (x <= 1.18d-36) then
        tmp = 5.0d0 * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y + z) * x;
	double tmp;
	if (x <= -1.18e-48) {
		tmp = t_0;
	} else if (x <= 1.18e-36) {
		tmp = 5.0 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y + z) * x
	tmp = 0
	if x <= -1.18e-48:
		tmp = t_0
	elif x <= 1.18e-36:
		tmp = 5.0 * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y + z) * x)
	tmp = 0.0
	if (x <= -1.18e-48)
		tmp = t_0;
	elseif (x <= 1.18e-36)
		tmp = Float64(5.0 * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y + z) * x;
	tmp = 0.0;
	if (x <= -1.18e-48)
		tmp = t_0;
	elseif (x <= 1.18e-36)
		tmp = 5.0 * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.18e-48], t$95$0, If[LessEqual[x, 1.18e-36], N[(5.0 * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.18000000000000007e-48 or 1.1799999999999999e-36 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   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. lift-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. associate--l+ N/A

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

      8. lower-fma.f64 N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. distribute-lft-out N/A

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

      11. lower-*.f64 N/A

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

      12. lower-+.f64 95.8

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

   4. Applied rewrites 95.8%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 96.2

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

   7. Applied rewrites 96.2%

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

   if -1.18000000000000007e-48 < x < 1.1799999999999999e-36

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 74.9

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

   5. Applied rewrites 74.9%

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

Alternative 5: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - -5\right) \cdot z\\ \mathbf{if}\;z \leq -4 \cdot 10^{-80}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-76}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x -5.0) z)))
   (if (<= z -4e-80) t_0 (if (<= z 2.8e-76) (* x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - -5.0) * z;
	double tmp;
	if (z <= -4e-80) {
		tmp = t_0;
	} else if (z <= 2.8e-76) {
		tmp = x * y;
	} 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 - (-5.0d0)) * z
    if (z <= (-4d-80)) then
        tmp = t_0
    else if (z <= 2.8d-76) then
        tmp = x * y
    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 - -5.0) * z;
	double tmp;
	if (z <= -4e-80) {
		tmp = t_0;
	} else if (z <= 2.8e-76) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - -5.0) * z
	tmp = 0
	if z <= -4e-80:
		tmp = t_0
	elif z <= 2.8e-76:
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - -5.0) * z)
	tmp = 0.0
	if (z <= -4e-80)
		tmp = t_0;
	elseif (z <= 2.8e-76)
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - -5.0) * z;
	tmp = 0.0;
	if (z <= -4e-80)
		tmp = t_0;
	elseif (z <= 2.8e-76)
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - -5.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4e-80], t$95$0, If[LessEqual[z, 2.8e-76], N[(x * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999985e-80 or 2.8000000000000001e-76 < z

   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. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. metadata-eval N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 82.3

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

   5. Applied rewrites 82.3%

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

   if -3.99999999999999985e-80 < z < 2.8000000000000001e-76

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-80}:\\ \;\;\;\;\left(x - -5\right) \cdot z\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-76}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x - -5\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+185}:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(x + 5\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4e+185) (* (+ y z) x) (fma y x (* (+ x 5.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4e+185) {
		tmp = (y + z) * x;
	} else {
		tmp = fma(y, x, ((x + 5.0) * z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4e+185)
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = fma(y, x, Float64(Float64(x + 5.0) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4e+185], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(y * x + N[(N[(x + 5.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9999999999999999e185

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   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. lift-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. associate--l+ N/A

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

      8. lower-fma.f64 N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. distribute-lft-out N/A

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

      11. lower-*.f64 N/A

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

      12. lower-+.f64 76.2

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

   4. Applied rewrites 76.2%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 100.0

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

   7. Applied rewrites 100.0%

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

   if -3.9999999999999999e185 < x

   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. lift-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. associate--l+ N/A

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

      8. lower-fma.f64 N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. distribute-lft-out N/A

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

      11. lower-*.f64 N/A

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

      12. lower-+.f64 99.5

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

   4. Applied rewrites 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+185}:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(x + 5\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. metadata-eval N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 54.4

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

   5. Applied rewrites 54.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 53.6%

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

   if -5 < x < 5

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 68.5

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

   5. Applied rewrites 68.5%

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

Alternative 8: 27.6% accurate, 2.8× speedup

Math

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

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%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
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. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. +-commutative N/A

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

   5. metadata-eval N/A

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

   6. sub-neg N/A

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

   7. lower--.f64 61.5

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

5. Applied rewrites 61.5%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 28.6%

   \[\leadsto x \cdot \color{blue}{z} \]
9. 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 2024298 
(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)))