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

Percentage Accurate: 99.9% → 100.0%

Time: 5.4s

Alternatives: 6

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(z * 5.0 + N[(N[(z + y), $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. Add Preprocessing

Alternative 2: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+16}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-23} \lor \neg \left(x \leq 3.2 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.4e+16)
   (* x z)
   (if (or (<= x -3.2e-23) (not (<= x 3.2e-29))) (* y x) (* 5.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e+16) {
		tmp = x * z;
	} else if ((x <= -3.2e-23) || !(x <= 3.2e-29)) {
		tmp = y * x;
	} else {
		tmp = 5.0 * 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 <= (-5.4d+16)) then
        tmp = x * z
    else if ((x <= (-3.2d-23)) .or. (.not. (x <= 3.2d-29))) then
        tmp = y * x
    else
        tmp = 5.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e+16) {
		tmp = x * z;
	} else if ((x <= -3.2e-23) || !(x <= 3.2e-29)) {
		tmp = y * x;
	} else {
		tmp = 5.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.4e+16:
		tmp = x * z
	elif (x <= -3.2e-23) or not (x <= 3.2e-29):
		tmp = y * x
	else:
		tmp = 5.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.4e+16)
		tmp = Float64(x * z);
	elseif ((x <= -3.2e-23) || !(x <= 3.2e-29))
		tmp = Float64(y * x);
	else
		tmp = Float64(5.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.4e+16)
		tmp = x * z;
	elseif ((x <= -3.2e-23) || ~((x <= 3.2e-29)))
		tmp = y * x;
	else
		tmp = 5.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.4e+16], N[(x * z), $MachinePrecision], If[Or[LessEqual[x, -3.2e-23], N[Not[LessEqual[x, 3.2e-29]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(5.0 * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4e16

   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 64.4

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

   5. Applied rewrites 64.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 64.4%

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

   if -5.4e16 < x < -3.19999999999999976e-23 or 3.2e-29 < 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. *-commutative N/A

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

      2. lower-*.f64 62.5

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

   5. Applied rewrites 62.5%

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

   if -3.19999999999999976e-23 < x < 3.2e-29

   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 76.8

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

   5. Applied rewrites 76.8%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+16}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-23} \lor \neg \left(x \leq 3.2 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-23} \lor \neg \left(x \leq 3.2 \cdot 10^{-62}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.2e-23) (not (<= x 3.2e-62)))
   (* (+ y z) x)
   (fma z 5.0 (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.2e-23) || !(x <= 3.2e-62)) {
		tmp = (y + z) * x;
	} else {
		tmp = fma(z, 5.0, (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.2e-23) || !(x <= 3.2e-62))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = fma(z, 5.0, Float64(x * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.2e-23], N[Not[LessEqual[x, 3.2e-62]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(z * 5.0 + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999976e-23 or 3.20000000000000021e-62 < 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 53.0

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

   5. Applied rewrites 53.0%

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

   7. Applied rewrites 53.0%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 95.2

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

   10. Applied rewrites 95.2%

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

   if -3.19999999999999976e-23 < x < 3.20000000000000021e-62

   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 78.1

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

   5. Applied rewrites 78.1%

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

   7. Applied rewrites 78.2%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-23} \lor \neg \left(x \leq 3.2 \cdot 10^{-62}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-23} \lor \neg \left(x \leq 3.2 \cdot 10^{-62}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.2e-23) (not (<= x 3.2e-62))) (* (+ y z) x) (* 5.0 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.2e-23) || !(x <= 3.2e-62)) {
		tmp = (y + z) * x;
	} else {
		tmp = 5.0 * 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 <= (-3.2d-23)) .or. (.not. (x <= 3.2d-62))) then
        tmp = (y + z) * x
    else
        tmp = 5.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.2e-23) || !(x <= 3.2e-62)) {
		tmp = (y + z) * x;
	} else {
		tmp = 5.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.2e-23) or not (x <= 3.2e-62):
		tmp = (y + z) * x
	else:
		tmp = 5.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.2e-23) || !(x <= 3.2e-62))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = Float64(5.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.2e-23) || ~((x <= 3.2e-62)))
		tmp = (y + z) * x;
	else
		tmp = 5.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.2e-23], N[Not[LessEqual[x, 3.2e-62]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(5.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999976e-23 or 3.20000000000000021e-62 < 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 53.0

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

   5. Applied rewrites 53.0%

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

   7. Applied rewrites 53.0%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 95.2

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

   10. Applied rewrites 95.2%

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

   if -3.19999999999999976e-23 < x < 3.20000000000000021e-62

   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 78.1

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

   5. Applied rewrites 78.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-23} \lor \neg \left(x \leq 3.2 \cdot 10^{-62}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.23 \lor \neg \left(x \leq 0.92\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.23) (not (<= x 0.92))) (* x z) (* 5.0 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.23) || !(x <= 0.92)) {
		tmp = x * z;
	} else {
		tmp = 5.0 * 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 <= (-0.23d0)) .or. (.not. (x <= 0.92d0))) then
        tmp = x * z
    else
        tmp = 5.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.23) || !(x <= 0.92)) {
		tmp = x * z;
	} else {
		tmp = 5.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.23) or not (x <= 0.92):
		tmp = x * z
	else:
		tmp = 5.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.23) || !(x <= 0.92))
		tmp = Float64(x * z);
	else
		tmp = Float64(5.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.23) || ~((x <= 0.92)))
		tmp = x * z;
	else
		tmp = 5.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.23], N[Not[LessEqual[x, 0.92]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(5.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.23000000000000001 or 0.92000000000000004 < 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 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 55.1%

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

   if -0.23000000000000001 < x < 0.92000000000000004

   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 71.0

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

   5. Applied rewrites 71.0%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.23 \lor \neg \left(x \leq 0.92\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 28.2% 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 63.8

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

5. Applied rewrites 63.8%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 29.1%

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

Developer Target 1: 97.5% 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 2024324 
(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)))