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

Percentage Accurate: 99.9% → 99.9%

Time: 6.4s

Alternatives: 11

Speedup: 1.0×

• 26.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, 5, x \cdot \left(t + \left(y + z\right) \cdot 2\right)\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma y 5.0 (* x (+ t (* (+ y z) 2.0)))))

C

double code(double x, double y, double z, double t) {
	return fma(y, 5.0, (x * (t + ((y + z) * 2.0))));
}

Julia

function code(x, y, z, t)
	return fma(y, 5.0, Float64(x * Float64(t + Float64(Float64(y + z) * 2.0))))
end

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0 + N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

   3. associate-+l+ 100.0%

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

   4. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

   5. +-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

   6. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

   7. distribute-rgt-out 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

   8. metadata-eval 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(t + \left(y + z\right) \cdot 2\right)\right) \]

Alternative 2: 88.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-35} \lor \neg \left(x \leq 3.75 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(z \cdot 2 + \left(t + y \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(z \cdot 2 + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.5e-35) (not (<= x 3.75e-7)))
   (* x (+ (* z 2.0) (+ t (* y 2.0))))
   (+ (* y 5.0) (* x (+ (* z 2.0) (* y 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.5e-35) || !(x <= 3.75e-7)) {
		tmp = x * ((z * 2.0) + (t + (y * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * ((z * 2.0) + (y * 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.5d-35)) .or. (.not. (x <= 3.75d-7))) then
        tmp = x * ((z * 2.0d0) + (t + (y * 2.0d0)))
    else
        tmp = (y * 5.0d0) + (x * ((z * 2.0d0) + (y * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.5e-35) || !(x <= 3.75e-7)) {
		tmp = x * ((z * 2.0) + (t + (y * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * ((z * 2.0) + (y * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.5e-35) or not (x <= 3.75e-7):
		tmp = x * ((z * 2.0) + (t + (y * 2.0)))
	else:
		tmp = (y * 5.0) + (x * ((z * 2.0) + (y * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.5e-35) || !(x <= 3.75e-7))
		tmp = Float64(x * Float64(Float64(z * 2.0) + Float64(t + Float64(y * 2.0))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(Float64(z * 2.0) + Float64(y * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.5e-35) || ~((x <= 3.75e-7)))
		tmp = x * ((z * 2.0) + (t + (y * 2.0)));
	else
		tmp = (y * 5.0) + (x * ((z * 2.0) + (y * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.5e-35], N[Not[LessEqual[x, 3.75e-7]], $MachinePrecision]], N[(x * N[(N[(z * 2.0), $MachinePrecision] + N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(N[(z * 2.0), $MachinePrecision] + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5e-35 or 3.7500000000000001e-7 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around inf 99.5%

      \[\leadsto \color{blue}{\left(2 \cdot z + \left(2 \cdot y + t\right)\right) \cdot x} \]

   if -7.5e-35 < x < 3.7500000000000001e-7

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around 0 83.4%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-35} \lor \neg \left(x \leq 3.75 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(z \cdot 2 + \left(t + y \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(z \cdot 2 + y \cdot 2\right)\\ \end{array} \]

Alternative 3: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -9.4 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+162} \lor \neg \left(x \leq 6 \cdot 10^{+253}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* (+ y z) 2.0))))
   (if (<= x -9.4e-39)
     t_1
     (if (<= x 1.15e-84)
       (* y 5.0)
       (if (or (<= x 3.1e+162) (not (<= x 6e+253))) t_1 (* x t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -9.4e-39) {
		tmp = t_1;
	} else if (x <= 1.15e-84) {
		tmp = y * 5.0;
	} else if ((x <= 3.1e+162) || !(x <= 6e+253)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + z) * 2.0d0)
    if (x <= (-9.4d-39)) then
        tmp = t_1
    else if (x <= 1.15d-84) then
        tmp = y * 5.0d0
    else if ((x <= 3.1d+162) .or. (.not. (x <= 6d+253))) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -9.4e-39) {
		tmp = t_1;
	} else if (x <= 1.15e-84) {
		tmp = y * 5.0;
	} else if ((x <= 3.1e+162) || !(x <= 6e+253)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + z) * 2.0)
	tmp = 0
	if x <= -9.4e-39:
		tmp = t_1
	elif x <= 1.15e-84:
		tmp = y * 5.0
	elif (x <= 3.1e+162) or not (x <= 6e+253):
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + z) * 2.0))
	tmp = 0.0
	if (x <= -9.4e-39)
		tmp = t_1;
	elseif (x <= 1.15e-84)
		tmp = Float64(y * 5.0);
	elseif ((x <= 3.1e+162) || !(x <= 6e+253))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + z) * 2.0);
	tmp = 0.0;
	if (x <= -9.4e-39)
		tmp = t_1;
	elseif (x <= 1.15e-84)
		tmp = y * 5.0;
	elseif ((x <= 3.1e+162) || ~((x <= 6e+253)))
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.4e-39], t$95$1, If[LessEqual[x, 1.15e-84], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 3.1e+162], N[Not[LessEqual[x, 6e+253]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.4000000000000005e-39 or 1.1499999999999999e-84 < x < 3.1e162 or 5.9999999999999996e253 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around inf 96.7%

      \[\leadsto \color{blue}{\left(2 \cdot z + \left(2 \cdot y + t\right)\right) \cdot x} \]

   3. Taylor expanded in t around 0 73.2%

      \[\leadsto \color{blue}{\left(2 \cdot z + 2 \cdot y\right) \cdot x} \]
   4. Step-by-step derivation

      1. distribute-lft-in 73.2%

         \[\leadsto \color{blue}{\left(2 \cdot \left(z + y\right)\right)} \cdot x \]

      2. *-commutative 73.2%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \left(z + y\right)\right)} \]

      3. +-commutative 73.2%

         \[\leadsto x \cdot \left(2 \cdot \color{blue}{\left(y + z\right)}\right) \]

   5. Simplified 73.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \left(y + z\right)\right)} \]

   if -9.4000000000000005e-39 < x < 1.1499999999999999e-84

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 64.0%

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

   if 3.1e162 < x < 5.9999999999999996e253

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 64.9%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+162} \lor \neg \left(x \leq 6 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 4: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+162} \lor \neg \left(x \leq 6 \cdot 10^{+253}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* (+ y z) 2.0))))
   (if (<= x -1.25e-38)
     t_1
     (if (<= x 1.2e-84)
       (* y (+ 5.0 (* x 2.0)))
       (if (or (<= x 3.1e+162) (not (<= x 6e+253))) t_1 (* x t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -1.25e-38) {
		tmp = t_1;
	} else if (x <= 1.2e-84) {
		tmp = y * (5.0 + (x * 2.0));
	} else if ((x <= 3.1e+162) || !(x <= 6e+253)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + z) * 2.0d0)
    if (x <= (-1.25d-38)) then
        tmp = t_1
    else if (x <= 1.2d-84) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else if ((x <= 3.1d+162) .or. (.not. (x <= 6d+253))) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -1.25e-38) {
		tmp = t_1;
	} else if (x <= 1.2e-84) {
		tmp = y * (5.0 + (x * 2.0));
	} else if ((x <= 3.1e+162) || !(x <= 6e+253)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + z) * 2.0)
	tmp = 0
	if x <= -1.25e-38:
		tmp = t_1
	elif x <= 1.2e-84:
		tmp = y * (5.0 + (x * 2.0))
	elif (x <= 3.1e+162) or not (x <= 6e+253):
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + z) * 2.0))
	tmp = 0.0
	if (x <= -1.25e-38)
		tmp = t_1;
	elseif (x <= 1.2e-84)
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	elseif ((x <= 3.1e+162) || !(x <= 6e+253))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + z) * 2.0);
	tmp = 0.0;
	if (x <= -1.25e-38)
		tmp = t_1;
	elseif (x <= 1.2e-84)
		tmp = y * (5.0 + (x * 2.0));
	elseif ((x <= 3.1e+162) || ~((x <= 6e+253)))
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e-38], t$95$1, If[LessEqual[x, 1.2e-84], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.1e+162], N[Not[LessEqual[x, 6e+253]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25000000000000008e-38 or 1.20000000000000009e-84 < x < 3.1e162 or 5.9999999999999996e253 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around inf 96.7%

      \[\leadsto \color{blue}{\left(2 \cdot z + \left(2 \cdot y + t\right)\right) \cdot x} \]

   3. Taylor expanded in t around 0 73.2%

      \[\leadsto \color{blue}{\left(2 \cdot z + 2 \cdot y\right) \cdot x} \]
   4. Step-by-step derivation

      1. distribute-lft-in 73.2%

         \[\leadsto \color{blue}{\left(2 \cdot \left(z + y\right)\right)} \cdot x \]

      2. *-commutative 73.2%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \left(z + y\right)\right)} \]

      3. +-commutative 73.2%

         \[\leadsto x \cdot \left(2 \cdot \color{blue}{\left(y + z\right)}\right) \]

   5. Simplified 73.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \left(y + z\right)\right)} \]

   if -1.25000000000000008e-38 < x < 1.20000000000000009e-84

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around inf 64.0%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   if 3.1e162 < x < 5.9999999999999996e253

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 64.9%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+162} \lor \neg \left(x \leq 6 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 5: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-35} \lor \neg \left(x \leq 7.4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(z \cdot 2 + \left(t + y \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.2e-35) (not (<= x 7.4e-7)))
   (* x (+ (* z 2.0) (+ t (* y 2.0))))
   (+ (* y 5.0) (* 2.0 (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e-35) || !(x <= 7.4e-7)) {
		tmp = x * ((z * 2.0) + (t + (y * 2.0)));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.2d-35)) .or. (.not. (x <= 7.4d-7))) then
        tmp = x * ((z * 2.0d0) + (t + (y * 2.0d0)))
    else
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e-35) || !(x <= 7.4e-7)) {
		tmp = x * ((z * 2.0) + (t + (y * 2.0)));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.2e-35) or not (x <= 7.4e-7):
		tmp = x * ((z * 2.0) + (t + (y * 2.0)))
	else:
		tmp = (y * 5.0) + (2.0 * (x * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.2e-35) || !(x <= 7.4e-7))
		tmp = Float64(x * Float64(Float64(z * 2.0) + Float64(t + Float64(y * 2.0))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.2e-35) || ~((x <= 7.4e-7)))
		tmp = x * ((z * 2.0) + (t + (y * 2.0)));
	else
		tmp = (y * 5.0) + (2.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.2e-35], N[Not[LessEqual[x, 7.4e-7]], $MachinePrecision]], N[(x * N[(N[(z * 2.0), $MachinePrecision] + N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.20000000000000038e-35 or 7.40000000000000009e-7 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around inf 99.5%

      \[\leadsto \color{blue}{\left(2 \cdot z + \left(2 \cdot y + t\right)\right) \cdot x} \]

   if -7.20000000000000038e-35 < x < 7.40000000000000009e-7

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      5. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      7. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      8. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

   3. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

   4. Taylor expanded in z around inf 83.0%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{2 \cdot \left(z \cdot x\right)}\right) \]
   5. Step-by-step derivation

      1. fma-udef 83.0%

         \[\leadsto \color{blue}{y \cdot 5 + 2 \cdot \left(z \cdot x\right)} \]

   6. Applied egg-rr 83.0%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-35} \lor \neg \left(x \leq 7.4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(z \cdot 2 + \left(t + y \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

2. Final simplification 100.0%

   \[\leadsto x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) + y \cdot 5 \]

Alternative 7: 46.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-84}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -1.2e+139)
     (* x (* y 2.0))
     (if (<= x -7.4e-39)
       t_1
       (if (<= x 1.2e-84) (* y 5.0) (if (<= x 1.5e+55) t_1 (* x t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -1.2e+139) {
		tmp = x * (y * 2.0);
	} else if (x <= -7.4e-39) {
		tmp = t_1;
	} else if (x <= 1.2e-84) {
		tmp = y * 5.0;
	} else if (x <= 1.5e+55) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-1.2d+139)) then
        tmp = x * (y * 2.0d0)
    else if (x <= (-7.4d-39)) then
        tmp = t_1
    else if (x <= 1.2d-84) then
        tmp = y * 5.0d0
    else if (x <= 1.5d+55) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -1.2e+139) {
		tmp = x * (y * 2.0);
	} else if (x <= -7.4e-39) {
		tmp = t_1;
	} else if (x <= 1.2e-84) {
		tmp = y * 5.0;
	} else if (x <= 1.5e+55) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -1.2e+139:
		tmp = x * (y * 2.0)
	elif x <= -7.4e-39:
		tmp = t_1
	elif x <= 1.2e-84:
		tmp = y * 5.0
	elif x <= 1.5e+55:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -1.2e+139)
		tmp = Float64(x * Float64(y * 2.0));
	elseif (x <= -7.4e-39)
		tmp = t_1;
	elseif (x <= 1.2e-84)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.5e+55)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -1.2e+139)
		tmp = x * (y * 2.0);
	elseif (x <= -7.4e-39)
		tmp = t_1;
	elseif (x <= 1.2e-84)
		tmp = y * 5.0;
	elseif (x <= 1.5e+55)
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+139], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.4e-39], t$95$1, If[LessEqual[x, 1.2e-84], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.5e+55], t$95$1, N[(x * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.20000000000000004e139

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{\left(2 \cdot z + \left(2 \cdot y + t\right)\right) \cdot x} \]

   3. Taylor expanded in y around inf 50.4%

      \[\leadsto \color{blue}{2 \cdot \left(y \cdot x\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 50.4%

         \[\leadsto \color{blue}{\left(2 \cdot y\right) \cdot x} \]

   5. Simplified 50.4%

      \[\leadsto \color{blue}{\left(2 \cdot y\right) \cdot x} \]

   if -1.20000000000000004e139 < x < -7.40000000000000029e-39 or 1.20000000000000009e-84 < x < 1.50000000000000008e55

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around inf 54.4%

      \[\leadsto \color{blue}{2 \cdot \left(z \cdot x\right)} \]

   if -7.40000000000000029e-39 < x < 1.20000000000000009e-84

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 64.0%

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

   if 1.50000000000000008e55 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 51.8%

      \[\leadsto \color{blue}{t \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-39}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-84}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 8: 46.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-84}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -8.5e-39)
     t_1
     (if (<= x 1.05e-84) (* y 5.0) (if (<= x 3.6e+55) t_1 (* x t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -8.5e-39) {
		tmp = t_1;
	} else if (x <= 1.05e-84) {
		tmp = y * 5.0;
	} else if (x <= 3.6e+55) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-8.5d-39)) then
        tmp = t_1
    else if (x <= 1.05d-84) then
        tmp = y * 5.0d0
    else if (x <= 3.6d+55) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -8.5e-39) {
		tmp = t_1;
	} else if (x <= 1.05e-84) {
		tmp = y * 5.0;
	} else if (x <= 3.6e+55) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -8.5e-39:
		tmp = t_1
	elif x <= 1.05e-84:
		tmp = y * 5.0
	elif x <= 3.6e+55:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -8.5e-39)
		tmp = t_1;
	elseif (x <= 1.05e-84)
		tmp = Float64(y * 5.0);
	elseif (x <= 3.6e+55)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -8.5e-39)
		tmp = t_1;
	elseif (x <= 1.05e-84)
		tmp = y * 5.0;
	elseif (x <= 3.6e+55)
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e-39], t$95$1, If[LessEqual[x, 1.05e-84], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 3.6e+55], t$95$1, N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5000000000000005e-39 or 1.04999999999999999e-84 < x < 3.59999999999999987e55

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around inf 48.1%

      \[\leadsto \color{blue}{2 \cdot \left(z \cdot x\right)} \]

   if -8.5000000000000005e-39 < x < 1.04999999999999999e-84

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 64.0%

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

   if 3.59999999999999987e55 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 51.8%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-39}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-84}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 9: 78.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+21} \lor \neg \left(y \leq 6.4 \cdot 10^{+99}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.2e+21) (not (<= y 6.4e+99)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.2e+21) || !(y <= 6.4e+99)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.2d+21)) .or. (.not. (y <= 6.4d+99))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.2e+21) || !(y <= 6.4e+99)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.2e+21) or not (y <= 6.4e+99):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.2e+21) || !(y <= 6.4e+99))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.2e+21) || ~((y <= 6.4e+99)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.2e+21], N[Not[LessEqual[y, 6.4e+99]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e21 or 6.39999999999999999e99 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around inf 79.4%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   if -2.2e21 < y < 6.39999999999999999e99

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 82.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+21} \lor \neg \left(y \leq 6.4 \cdot 10^{+99}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 10: 47.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-35}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 0.00039:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.4e-35) (* x t) (if (<= x 0.00039) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.4e-35) {
		tmp = x * t;
	} else if (x <= 0.00039) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-7.4d-35)) then
        tmp = x * t
    else if (x <= 0.00039d0) then
        tmp = y * 5.0d0
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.4e-35) {
		tmp = x * t;
	} else if (x <= 0.00039) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.4e-35:
		tmp = x * t
	elif x <= 0.00039:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.4e-35)
		tmp = Float64(x * t);
	elseif (x <= 0.00039)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.4e-35)
		tmp = x * t;
	elseif (x <= 0.00039)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.4e-35], N[(x * t), $MachinePrecision], If[LessEqual[x, 0.00039], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.3999999999999998e-35 or 3.89999999999999993e-4 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 37.7%

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

   if -7.3999999999999998e-35 < x < 3.89999999999999993e-4

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 58.8%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-35}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 0.00039:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 11: 30.0% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

2. Taylor expanded in x around 0 26.9%

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

3. Final simplification 26.9%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))