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

Percentage Accurate: 99.8% → 99.8%

Time: 9.8s

Alternatives: 15

Speedup: 1.0×

• 27.7% 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: 99.8% 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: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. fma-def 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 47.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+163}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -0.00072:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 0.11:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 7.3 \cdot 10^{+211} \lor \neg \left(x \leq 7.4 \cdot 10^{+281}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7e+163)
   (* x y)
   (if (<= x -0.00072)
     (* x t)
     (if (<= x 0.11)
       (* y 5.0)
       (if (or (<= x 7.3e+211) (not (<= x 7.4e+281)))
         (* x t)
         (* 2.0 (* x z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e+163) {
		tmp = x * y;
	} else if (x <= -0.00072) {
		tmp = x * t;
	} else if (x <= 0.11) {
		tmp = y * 5.0;
	} else if ((x <= 7.3e+211) || !(x <= 7.4e+281)) {
		tmp = x * t;
	} else {
		tmp = 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 <= (-7d+163)) then
        tmp = x * y
    else if (x <= (-0.00072d0)) then
        tmp = x * t
    else if (x <= 0.11d0) then
        tmp = y * 5.0d0
    else if ((x <= 7.3d+211) .or. (.not. (x <= 7.4d+281))) then
        tmp = x * t
    else
        tmp = 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 <= -7e+163) {
		tmp = x * y;
	} else if (x <= -0.00072) {
		tmp = x * t;
	} else if (x <= 0.11) {
		tmp = y * 5.0;
	} else if ((x <= 7.3e+211) || !(x <= 7.4e+281)) {
		tmp = x * t;
	} else {
		tmp = 2.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7e+163:
		tmp = x * y
	elif x <= -0.00072:
		tmp = x * t
	elif x <= 0.11:
		tmp = y * 5.0
	elif (x <= 7.3e+211) or not (x <= 7.4e+281):
		tmp = x * t
	else:
		tmp = 2.0 * (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7e+163)
		tmp = Float64(x * y);
	elseif (x <= -0.00072)
		tmp = Float64(x * t);
	elseif (x <= 0.11)
		tmp = Float64(y * 5.0);
	elseif ((x <= 7.3e+211) || !(x <= 7.4e+281))
		tmp = Float64(x * t);
	else
		tmp = Float64(2.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7e+163)
		tmp = x * y;
	elseif (x <= -0.00072)
		tmp = x * t;
	elseif (x <= 0.11)
		tmp = y * 5.0;
	elseif ((x <= 7.3e+211) || ~((x <= 7.4e+281)))
		tmp = x * t;
	else
		tmp = 2.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7e+163], N[(x * y), $MachinePrecision], If[LessEqual[x, -0.00072], N[(x * t), $MachinePrecision], If[LessEqual[x, 0.11], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 7.3e+211], N[Not[LessEqual[x, 7.4e+281]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.0000000000000005e163

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.9%

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

   4. Taylor expanded in z around 0 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in y around inf 59.2%

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

      1. +-commutative 59.2%

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

   9. Simplified 59.2%

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

   10. Taylor expanded in x around inf 59.2%

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

       1. *-commutative 59.2%

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

   12. Simplified 59.2%

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

   if -7.0000000000000005e163 < x < -7.20000000000000045e-4 or 0.110000000000000001 < x < 7.3000000000000001e211 or 7.3999999999999996e281 < 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. Add Preprocessing

   3. Taylor expanded in t around inf 42.1%

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

   5. Simplified 42.1%

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

   if -7.20000000000000045e-4 < x < 0.110000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.0%

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

   if 7.3000000000000001e211 < x < 7.3999999999999996e281

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 67.5%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+163}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -0.00072:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 0.11:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 7.3 \cdot 10^{+211} \lor \neg \left(x \leq 7.4 \cdot 10^{+281}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x + 5\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-173}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-12}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ x 5.0))))
   (if (<= y -3e-84)
     t_1
     (if (<= y 4.1e-173)
       (* x t)
       (if (<= y 6.2e-82) (* 2.0 (* x z)) (if (<= y 1.7e-12) (* x t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x + 5.0);
	double tmp;
	if (y <= -3e-84) {
		tmp = t_1;
	} else if (y <= 4.1e-173) {
		tmp = x * t;
	} else if (y <= 6.2e-82) {
		tmp = 2.0 * (x * z);
	} else if (y <= 1.7e-12) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	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 = y * (x + 5.0d0)
    if (y <= (-3d-84)) then
        tmp = t_1
    else if (y <= 4.1d-173) then
        tmp = x * t
    else if (y <= 6.2d-82) then
        tmp = 2.0d0 * (x * z)
    else if (y <= 1.7d-12) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x + 5.0);
	double tmp;
	if (y <= -3e-84) {
		tmp = t_1;
	} else if (y <= 4.1e-173) {
		tmp = x * t;
	} else if (y <= 6.2e-82) {
		tmp = 2.0 * (x * z);
	} else if (y <= 1.7e-12) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x + 5.0)
	tmp = 0
	if y <= -3e-84:
		tmp = t_1
	elif y <= 4.1e-173:
		tmp = x * t
	elif y <= 6.2e-82:
		tmp = 2.0 * (x * z)
	elif y <= 1.7e-12:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x + 5.0))
	tmp = 0.0
	if (y <= -3e-84)
		tmp = t_1;
	elseif (y <= 4.1e-173)
		tmp = Float64(x * t);
	elseif (y <= 6.2e-82)
		tmp = Float64(2.0 * Float64(x * z));
	elseif (y <= 1.7e-12)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x + 5.0);
	tmp = 0.0;
	if (y <= -3e-84)
		tmp = t_1;
	elseif (y <= 4.1e-173)
		tmp = x * t;
	elseif (y <= 6.2e-82)
		tmp = 2.0 * (x * z);
	elseif (y <= 1.7e-12)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e-84], t$95$1, If[LessEqual[y, 4.1e-173], N[(x * t), $MachinePrecision], If[LessEqual[y, 6.2e-82], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-12], N[(x * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000001e-84 or 1.7e-12 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 91.1%

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

   4. Taylor expanded in y around inf 70.8%

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

   if -3.0000000000000001e-84 < y < 4.0999999999999997e-173 or 6.19999999999999999e-82 < y < 1.7e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 51.0%

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

   5. Simplified 51.0%

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

   if 4.0999999999999997e-173 < y < 6.19999999999999999e-82

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 73.6%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-173}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-12}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -62000 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + 2 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -62000.0) (not (<= x 5.0)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x (+ t (+ y (* 2.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -62000.0) || !(x <= 5.0)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * 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 <= (-62000.0d0)) .or. (.not. (x <= 5.0d0))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (x * (t + (y + (2.0d0 * z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -62000.0) || !(x <= 5.0)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -62000.0) or not (x <= 5.0):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -62000.0) || !(x <= 5.0))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + Float64(2.0 * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -62000.0) || ~((x <= 5.0)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -62000.0], N[Not[LessEqual[x, 5.0]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -62000 or 5 < 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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.1%

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

   if -62000 < x < 5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 98.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -62000 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + 2 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+16} \lor \neg \left(x \leq 50000\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.05e+16) (not (<= x 50000.0)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x (+ t (+ y y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.05e+16) || !(x <= 50000.0)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	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 <= (-1.05d+16)) .or. (.not. (x <= 50000.0d0))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.05e+16) || !(x <= 50000.0)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.05e+16) or not (x <= 50000.0):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * (t + (y + y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.05e+16) || !(x <= 50000.0))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.05e+16) || ~((x <= 50000.0)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * (t + (y + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.05e+16], N[Not[LessEqual[x, 50000.0]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e16 or 5e4 < 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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.7%

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

   if -1.05e16 < x < 5e4

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 85.3%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+16} \lor \neg \left(x \leq 50000\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-15} \lor \neg \left(t \leq 2.6 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.8e-15) (not (<= t 2.6e-10)))
   (+ (* y 5.0) (* x (+ t (+ y y))))
   (+ (* y 5.0) (* (+ y z) (* x 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.8e-15) || !(t <= 2.6e-10)) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else {
		tmp = (y * 5.0) + ((y + z) * (x * 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 ((t <= (-5.8d-15)) .or. (.not. (t <= 2.6d-10))) then
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    else
        tmp = (y * 5.0d0) + ((y + z) * (x * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.8e-15) || !(t <= 2.6e-10)) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else {
		tmp = (y * 5.0) + ((y + z) * (x * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.8e-15) or not (t <= 2.6e-10):
		tmp = (y * 5.0) + (x * (t + (y + y)))
	else:
		tmp = (y * 5.0) + ((y + z) * (x * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.8e-15) || !(t <= 2.6e-10))
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(Float64(y + z) * Float64(x * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.8e-15) || ~((t <= 2.6e-10)))
		tmp = (y * 5.0) + (x * (t + (y + y)));
	else
		tmp = (y * 5.0) + ((y + z) * (x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.8e-15], N[Not[LessEqual[t, 2.6e-10]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.80000000000000037e-15 or 2.59999999999999981e-10 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 91.1%

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

   if -5.80000000000000037e-15 < t < 2.59999999999999981e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 96.2%

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

   5. Simplified 96.2%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-15} \lor \neg \left(t \leq 2.6 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00023 \lor \neg \left(x \leq 2.1 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.00023) (not (<= x 2.1e-46)))
   (* x (+ (* 2.0 (+ y z)) t))
   (* y (+ 5.0 (* x 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.00023) || !(x <= 2.1e-46)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = y * (5.0 + (x * 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 <= (-0.00023d0)) .or. (.not. (x <= 2.1d-46))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = y * (5.0d0 + (x * 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 <= -0.00023) || !(x <= 2.1e-46)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = y * (5.0 + (x * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.00023) or not (x <= 2.1e-46):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = y * (5.0 + (x * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.00023) || !(x <= 2.1e-46))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -0.00023) || ~((x <= 2.1e-46)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = y * (5.0 + (x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.00023], N[Not[LessEqual[x, 2.1e-46]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3000000000000001e-4 or 2.09999999999999987e-46 < 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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.2%

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

   if -2.3000000000000001e-4 < x < 2.09999999999999987e-46

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 69.9%

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

   5. Simplified 69.9%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00023 \lor \neg \left(x \leq 2.1 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{-10} \lor \neg \left(x \leq 4.4 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.25e-10) (not (<= x 4.4e-46)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x (+ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.25e-10) || !(x <= 4.4e-46)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (y + 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 <= (-3.25d-10)) .or. (.not. (x <= 4.4d-46))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (x * (y + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.25e-10) || !(x <= 4.4e-46)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.25e-10) or not (x <= 4.4e-46):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * (y + t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.25e-10) || !(x <= 4.4e-46))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.25e-10) || ~((x <= 4.4e-46)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.25e-10], N[Not[LessEqual[x, 4.4e-46]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2500000000000002e-10 or 4.4000000000000002e-46 < 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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 96.5%

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

   if -3.2500000000000002e-10 < x < 4.4000000000000002e-46

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

   4. Taylor expanded in z around 0 86.4%

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

   6. Simplified 86.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{-10} \lor \neg \left(x \leq 4.4 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+163}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -0.00024 \lor \neg \left(x \leq 0.105\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.2e+163)
   (* x y)
   (if (or (<= x -0.00024) (not (<= x 0.105))) (* x t) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.2e+163) {
		tmp = x * y;
	} else if ((x <= -0.00024) || !(x <= 0.105)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	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 <= (-5.2d+163)) then
        tmp = x * y
    else if ((x <= (-0.00024d0)) .or. (.not. (x <= 0.105d0))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.2e+163) {
		tmp = x * y;
	} else if ((x <= -0.00024) || !(x <= 0.105)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.2e+163:
		tmp = x * y
	elif (x <= -0.00024) or not (x <= 0.105):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.2e+163)
		tmp = Float64(x * y);
	elseif ((x <= -0.00024) || !(x <= 0.105))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.2e+163)
		tmp = x * y;
	elseif ((x <= -0.00024) || ~((x <= 0.105)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.2e+163], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, -0.00024], N[Not[LessEqual[x, 0.105]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2000000000000003e163

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.9%

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

   4. Taylor expanded in z around 0 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in y around inf 59.2%

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

      1. +-commutative 59.2%

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

   9. Simplified 59.2%

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

   10. Taylor expanded in x around inf 59.2%

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

       1. *-commutative 59.2%

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

   12. Simplified 59.2%

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

   if -5.2000000000000003e163 < x < -2.40000000000000006e-4 or 0.104999999999999996 < 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. Add Preprocessing

   3. Taylor expanded in t around inf 39.2%

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

   5. Simplified 39.2%

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

   if -2.40000000000000006e-4 < x < 0.104999999999999996

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.0%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+163}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -0.00024 \lor \neg \left(x \leq 0.105\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00018 \lor \neg \left(x \leq 5.8 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.00018) (not (<= x 5.8e-46)))
   (* x (+ t (* 2.0 y)))
   (* y (+ x 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.00018) || !(x <= 5.8e-46)) {
		tmp = x * (t + (2.0 * y));
	} else {
		tmp = y * (x + 5.0);
	}
	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 <= (-0.00018d0)) .or. (.not. (x <= 5.8d-46))) then
        tmp = x * (t + (2.0d0 * y))
    else
        tmp = y * (x + 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.00018) || !(x <= 5.8e-46)) {
		tmp = x * (t + (2.0 * y));
	} else {
		tmp = y * (x + 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.00018) or not (x <= 5.8e-46):
		tmp = x * (t + (2.0 * y))
	else:
		tmp = y * (x + 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.00018) || !(x <= 5.8e-46))
		tmp = Float64(x * Float64(t + Float64(2.0 * y)));
	else
		tmp = Float64(y * Float64(x + 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -0.00018) || ~((x <= 5.8e-46)))
		tmp = x * (t + (2.0 * y));
	else
		tmp = y * (x + 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.00018], N[Not[LessEqual[x, 5.8e-46]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000011e-4 or 5.80000000000000009e-46 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 76.0%

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

   4. Taylor expanded in x around inf 73.2%

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

   if -1.80000000000000011e-4 < x < 5.80000000000000009e-46

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.4%

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

   4. Taylor expanded in y around inf 69.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00018 \lor \neg \left(x \leq 5.8 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-50} \lor \neg \left(y \leq 6.2 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.1e-50) (not (<= y 6.2e+46)))
   (* y (+ x 5.0))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-50) || !(y <= 6.2e+46)) {
		tmp = y * (x + 5.0);
	} else {
		tmp = x * (t + (2.0 * 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 ((y <= (-2.1d-50)) .or. (.not. (y <= 6.2d+46))) then
        tmp = y * (x + 5.0d0)
    else
        tmp = x * (t + (2.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-50) || !(y <= 6.2e+46)) {
		tmp = y * (x + 5.0);
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.1e-50) or not (y <= 6.2e+46):
		tmp = y * (x + 5.0)
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.1e-50) || !(y <= 6.2e+46))
		tmp = Float64(y * Float64(x + 5.0));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.1e-50) || ~((y <= 6.2e+46)))
		tmp = y * (x + 5.0);
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.1e-50], N[Not[LessEqual[y, 6.2e+46]], $MachinePrecision]], N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000001e-50 or 6.1999999999999995e46 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 91.3%

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

   4. Taylor expanded in y around inf 75.8%

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

   if -2.1000000000000001e-50 < y < 6.1999999999999995e46

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.0%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-50} \lor \neg \left(y \leq 6.2 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-83} \lor \neg \left(y \leq 6.9 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.2e-83) (not (<= y 6.9e+41)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-83) || !(y <= 6.9e+41)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * 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 ((y <= (-3.2d-83)) .or. (.not. (y <= 6.9d+41))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (2.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-83) || !(y <= 6.9e+41)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.2e-83) or not (y <= 6.9e+41):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.2e-83) || !(y <= 6.9e+41))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.2e-83) || ~((y <= 6.9e+41)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.2e-83], N[Not[LessEqual[y, 6.9e+41]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000001e-83 or 6.9000000000000003e41 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 81.4%

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

   5. Simplified 81.4%

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

   if -3.2000000000000001e-83 < y < 6.9000000000000003e41

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.6%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-83} \lor \neg \left(y \leq 6.9 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (x * (t + (y + (z + (y + z)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 14: 48.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00018 \lor \neg \left(x \leq 0.14\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.00018) (not (<= x 0.14))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.00018) || !(x <= 0.14)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	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 <= (-0.00018d0)) .or. (.not. (x <= 0.14d0))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.00018) || !(x <= 0.14)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.00018) or not (x <= 0.14):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.00018) || !(x <= 0.14))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -0.00018) || ~((x <= 0.14)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.00018], N[Not[LessEqual[x, 0.14]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000011e-4 or 0.14000000000000001 < 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. Add Preprocessing

   3. Taylor expanded in t around inf 39.8%

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

   5. Simplified 39.8%

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

   if -1.80000000000000011e-4 < x < 0.14000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.0%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00018 \lor \neg \left(x \leq 0.14\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.3% 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 99.9%

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

3. Taylor expanded in x around 0 35.7%

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

4. Final simplification 35.7%

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

Reproduce

herbie shell --seed 2024027 
(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)))