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

Percentage Accurate: 99.8% → 99.9%

Time: 8.3s

Alternatives: 16

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: 99.8% 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: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0 + N[(x * N[(N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision] + t), $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. 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. Final simplification 100.0%

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

Alternative 2: 42.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+100}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-119}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-291}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-225}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-188}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-159}:\\ \;\;\;\;\frac{y}{0.2}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= t -1.12e+100)
     (* x t)
     (if (<= t -8e-119)
       (* y 5.0)
       (if (<= t -1.75e-222)
         t_1
         (if (<= t -1.25e-291)
           (* y 5.0)
           (if (<= t 1.56e-254)
             t_1
             (if (<= t 5.2e-225)
               (* y 5.0)
               (if (<= t 8.5e-188)
                 (* y x)
                 (if (<= t 1.8e-159)
                   (/ y 0.2)
                   (if (<= t 9e-34) 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 (t <= -1.12e+100) {
		tmp = x * t;
	} else if (t <= -8e-119) {
		tmp = y * 5.0;
	} else if (t <= -1.75e-222) {
		tmp = t_1;
	} else if (t <= -1.25e-291) {
		tmp = y * 5.0;
	} else if (t <= 1.56e-254) {
		tmp = t_1;
	} else if (t <= 5.2e-225) {
		tmp = y * 5.0;
	} else if (t <= 8.5e-188) {
		tmp = y * x;
	} else if (t <= 1.8e-159) {
		tmp = y / 0.2;
	} else if (t <= 9e-34) {
		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 (t <= (-1.12d+100)) then
        tmp = x * t
    else if (t <= (-8d-119)) then
        tmp = y * 5.0d0
    else if (t <= (-1.75d-222)) then
        tmp = t_1
    else if (t <= (-1.25d-291)) then
        tmp = y * 5.0d0
    else if (t <= 1.56d-254) then
        tmp = t_1
    else if (t <= 5.2d-225) then
        tmp = y * 5.0d0
    else if (t <= 8.5d-188) then
        tmp = y * x
    else if (t <= 1.8d-159) then
        tmp = y / 0.2d0
    else if (t <= 9d-34) 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 (t <= -1.12e+100) {
		tmp = x * t;
	} else if (t <= -8e-119) {
		tmp = y * 5.0;
	} else if (t <= -1.75e-222) {
		tmp = t_1;
	} else if (t <= -1.25e-291) {
		tmp = y * 5.0;
	} else if (t <= 1.56e-254) {
		tmp = t_1;
	} else if (t <= 5.2e-225) {
		tmp = y * 5.0;
	} else if (t <= 8.5e-188) {
		tmp = y * x;
	} else if (t <= 1.8e-159) {
		tmp = y / 0.2;
	} else if (t <= 9e-34) {
		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 t <= -1.12e+100:
		tmp = x * t
	elif t <= -8e-119:
		tmp = y * 5.0
	elif t <= -1.75e-222:
		tmp = t_1
	elif t <= -1.25e-291:
		tmp = y * 5.0
	elif t <= 1.56e-254:
		tmp = t_1
	elif t <= 5.2e-225:
		tmp = y * 5.0
	elif t <= 8.5e-188:
		tmp = y * x
	elif t <= 1.8e-159:
		tmp = y / 0.2
	elif t <= 9e-34:
		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 (t <= -1.12e+100)
		tmp = Float64(x * t);
	elseif (t <= -8e-119)
		tmp = Float64(y * 5.0);
	elseif (t <= -1.75e-222)
		tmp = t_1;
	elseif (t <= -1.25e-291)
		tmp = Float64(y * 5.0);
	elseif (t <= 1.56e-254)
		tmp = t_1;
	elseif (t <= 5.2e-225)
		tmp = Float64(y * 5.0);
	elseif (t <= 8.5e-188)
		tmp = Float64(y * x);
	elseif (t <= 1.8e-159)
		tmp = Float64(y / 0.2);
	elseif (t <= 9e-34)
		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 (t <= -1.12e+100)
		tmp = x * t;
	elseif (t <= -8e-119)
		tmp = y * 5.0;
	elseif (t <= -1.75e-222)
		tmp = t_1;
	elseif (t <= -1.25e-291)
		tmp = y * 5.0;
	elseif (t <= 1.56e-254)
		tmp = t_1;
	elseif (t <= 5.2e-225)
		tmp = y * 5.0;
	elseif (t <= 8.5e-188)
		tmp = y * x;
	elseif (t <= 1.8e-159)
		tmp = y / 0.2;
	elseif (t <= 9e-34)
		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[t, -1.12e+100], N[(x * t), $MachinePrecision], If[LessEqual[t, -8e-119], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, -1.75e-222], t$95$1, If[LessEqual[t, -1.25e-291], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 1.56e-254], t$95$1, If[LessEqual[t, 5.2e-225], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 8.5e-188], N[(y * x), $MachinePrecision], If[LessEqual[t, 1.8e-159], N[(y / 0.2), $MachinePrecision], If[LessEqual[t, 9e-34], t$95$1, N[(x * t), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.12e100 or 9.00000000000000085e-34 < 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. Taylor expanded in t around inf 68.3%

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

   if -1.12e100 < t < -8.0000000000000001e-119 or -1.75000000000000012e-222 < t < -1.2500000000000001e-291 or 1.56e-254 < t < 5.20000000000000027e-225

   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 49.3%

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

   if -8.0000000000000001e-119 < t < -1.75000000000000012e-222 or -1.2500000000000001e-291 < t < 1.56e-254 or 1.80000000000000011e-159 < t < 9.00000000000000085e-34

   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 58.5%

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

   if 5.20000000000000027e-225 < t < 8.5000000000000004e-188

   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 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in y around inf 69.8%

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

   6. Taylor expanded in x around inf 59.1%

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

   if 8.5000000000000004e-188 < t < 1.80000000000000011e-159

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 84.1%

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

   4. Simplified 84.1%

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

      1. *-commutative 84.1%

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

      2. flip-+ 70.6%

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

      3. associate-*l/ 57.3%

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

      4. metadata-eval 57.3%

         \[\leadsto \frac{\left(\color{blue}{25} - \left(x \cdot 2\right) \cdot \left(x \cdot 2\right)\right) \cdot y}{5 - x \cdot 2} \]

      5. swap-sqr 57.3%

         \[\leadsto \frac{\left(25 - \color{blue}{\left(x \cdot x\right) \cdot \left(2 \cdot 2\right)}\right) \cdot y}{5 - x \cdot 2} \]

      6. metadata-eval 57.3%

         \[\leadsto \frac{\left(25 - \left(x \cdot x\right) \cdot \color{blue}{4}\right) \cdot y}{5 - x \cdot 2} \]

   6. Applied egg-rr 57.3%

      \[\leadsto \color{blue}{\frac{\left(25 - \left(x \cdot x\right) \cdot 4\right) \cdot y}{5 - x \cdot 2}} \]

   7. Taylor expanded in y around 0 57.3%

      \[\leadsto \color{blue}{\frac{y \cdot \left(25 - 4 \cdot {x}^{2}\right)}{5 - 2 \cdot x}} \]
   8. Step-by-step derivation

      1. associate-/l* 70.6%

         \[\leadsto \color{blue}{\frac{y}{\frac{5 - 2 \cdot x}{25 - 4 \cdot {x}^{2}}}} \]

      2. cancel-sign-sub-inv 70.6%

         \[\leadsto \frac{y}{\frac{\color{blue}{5 + \left(-2\right) \cdot x}}{25 - 4 \cdot {x}^{2}}} \]

      3. metadata-eval 70.6%

         \[\leadsto \frac{y}{\frac{5 + \color{blue}{-2} \cdot x}{25 - 4 \cdot {x}^{2}}} \]

      4. *-commutative 70.6%

         \[\leadsto \frac{y}{\frac{5 + \color{blue}{x \cdot -2}}{25 - 4 \cdot {x}^{2}}} \]

      5. cancel-sign-sub-inv 70.6%

         \[\leadsto \frac{y}{\frac{5 + x \cdot -2}{\color{blue}{25 + \left(-4\right) \cdot {x}^{2}}}} \]

      6. metadata-eval 70.6%

         \[\leadsto \frac{y}{\frac{5 + x \cdot -2}{25 + \color{blue}{-4} \cdot {x}^{2}}} \]

      7. unpow2 70.6%

         \[\leadsto \frac{y}{\frac{5 + x \cdot -2}{25 + -4 \cdot \color{blue}{\left(x \cdot x\right)}}} \]

   9. Simplified 70.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{5 + x \cdot -2}{25 + -4 \cdot \left(x \cdot x\right)}}} \]

   10. Taylor expanded in x around 0 55.8%

       \[\leadsto \frac{y}{\color{blue}{0.2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+100}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-119}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-222}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-291}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-254}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-225}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-188}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-159}:\\ \;\;\;\;\frac{y}{0.2}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 3: 48.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := y \cdot \left(5 + x\right)\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+102}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))) (t_2 (* y (+ 5.0 x))))
   (if (<= t -2.05e+102)
     (* x t)
     (if (<= t -1.55e-149)
       t_2
       (if (<= t -5.6e-195)
         t_1
         (if (<= t 1.1e-299)
           t_2
           (if (<= t 6.4e-254)
             t_1
             (if (<= t 6.8e-158) t_2 (if (<= t 2.2e-33) t_1 (* x t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double t_2 = y * (5.0 + x);
	double tmp;
	if (t <= -2.05e+102) {
		tmp = x * t;
	} else if (t <= -1.55e-149) {
		tmp = t_2;
	} else if (t <= -5.6e-195) {
		tmp = t_1;
	} else if (t <= 1.1e-299) {
		tmp = t_2;
	} else if (t <= 6.4e-254) {
		tmp = t_1;
	} else if (t <= 6.8e-158) {
		tmp = t_2;
	} else if (t <= 2.2e-33) {
		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) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    t_2 = y * (5.0d0 + x)
    if (t <= (-2.05d+102)) then
        tmp = x * t
    else if (t <= (-1.55d-149)) then
        tmp = t_2
    else if (t <= (-5.6d-195)) then
        tmp = t_1
    else if (t <= 1.1d-299) then
        tmp = t_2
    else if (t <= 6.4d-254) then
        tmp = t_1
    else if (t <= 6.8d-158) then
        tmp = t_2
    else if (t <= 2.2d-33) 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 t_2 = y * (5.0 + x);
	double tmp;
	if (t <= -2.05e+102) {
		tmp = x * t;
	} else if (t <= -1.55e-149) {
		tmp = t_2;
	} else if (t <= -5.6e-195) {
		tmp = t_1;
	} else if (t <= 1.1e-299) {
		tmp = t_2;
	} else if (t <= 6.4e-254) {
		tmp = t_1;
	} else if (t <= 6.8e-158) {
		tmp = t_2;
	} else if (t <= 2.2e-33) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	t_2 = y * (5.0 + x)
	tmp = 0
	if t <= -2.05e+102:
		tmp = x * t
	elif t <= -1.55e-149:
		tmp = t_2
	elif t <= -5.6e-195:
		tmp = t_1
	elif t <= 1.1e-299:
		tmp = t_2
	elif t <= 6.4e-254:
		tmp = t_1
	elif t <= 6.8e-158:
		tmp = t_2
	elif t <= 2.2e-33:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	t_2 = Float64(y * Float64(5.0 + x))
	tmp = 0.0
	if (t <= -2.05e+102)
		tmp = Float64(x * t);
	elseif (t <= -1.55e-149)
		tmp = t_2;
	elseif (t <= -5.6e-195)
		tmp = t_1;
	elseif (t <= 1.1e-299)
		tmp = t_2;
	elseif (t <= 6.4e-254)
		tmp = t_1;
	elseif (t <= 6.8e-158)
		tmp = t_2;
	elseif (t <= 2.2e-33)
		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);
	t_2 = y * (5.0 + x);
	tmp = 0.0;
	if (t <= -2.05e+102)
		tmp = x * t;
	elseif (t <= -1.55e-149)
		tmp = t_2;
	elseif (t <= -5.6e-195)
		tmp = t_1;
	elseif (t <= 1.1e-299)
		tmp = t_2;
	elseif (t <= 6.4e-254)
		tmp = t_1;
	elseif (t <= 6.8e-158)
		tmp = t_2;
	elseif (t <= 2.2e-33)
		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]}, Block[{t$95$2 = N[(y * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e+102], N[(x * t), $MachinePrecision], If[LessEqual[t, -1.55e-149], t$95$2, If[LessEqual[t, -5.6e-195], t$95$1, If[LessEqual[t, 1.1e-299], t$95$2, If[LessEqual[t, 6.4e-254], t$95$1, If[LessEqual[t, 6.8e-158], t$95$2, If[LessEqual[t, 2.2e-33], t$95$1, N[(x * t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.05e102 or 2.20000000000000005e-33 < 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. Taylor expanded in t around inf 68.3%

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

   if -2.05e102 < t < -1.54999999999999994e-149 or -5.60000000000000007e-195 < t < 1.1e-299 or 6.4e-254 < t < 6.7999999999999999e-158

   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 0 88.6%

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

   4. Simplified 88.6%

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

   5. Taylor expanded in y around inf 61.7%

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

   if -1.54999999999999994e-149 < t < -5.60000000000000007e-195 or 1.1e-299 < t < 6.4e-254 or 6.7999999999999999e-158 < t < 2.20000000000000005e-33

   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 62.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+102}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-195}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-254}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-33}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 4: 77.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot \left(y + t\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-18} \lor \neg \left(y \leq 5 \cdot 10^{-14}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x (+ y t)))))
   (if (<= y -3.6e+89)
     t_1
     (if (<= y -4.3e+54)
       (* x (* (+ y z) 2.0))
       (if (or (<= y -3.35e-18) (not (<= y 5e-14)))
         t_1
         (* x (+ t (* z 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * (y + t));
	double tmp;
	if (y <= -3.6e+89) {
		tmp = t_1;
	} else if (y <= -4.3e+54) {
		tmp = x * ((y + z) * 2.0);
	} else if ((y <= -3.35e-18) || !(y <= 5e-14)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y * 5.0d0) + (x * (y + t))
    if (y <= (-3.6d+89)) then
        tmp = t_1
    else if (y <= (-4.3d+54)) then
        tmp = x * ((y + z) * 2.0d0)
    else if ((y <= (-3.35d-18)) .or. (.not. (y <= 5d-14))) then
        tmp = t_1
    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 t_1 = (y * 5.0) + (x * (y + t));
	double tmp;
	if (y <= -3.6e+89) {
		tmp = t_1;
	} else if (y <= -4.3e+54) {
		tmp = x * ((y + z) * 2.0);
	} else if ((y <= -3.35e-18) || !(y <= 5e-14)) {
		tmp = t_1;
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (x * (y + t))
	tmp = 0
	if y <= -3.6e+89:
		tmp = t_1
	elif y <= -4.3e+54:
		tmp = x * ((y + z) * 2.0)
	elif (y <= -3.35e-18) or not (y <= 5e-14):
		tmp = t_1
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(x * Float64(y + t)))
	tmp = 0.0
	if (y <= -3.6e+89)
		tmp = t_1;
	elseif (y <= -4.3e+54)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	elseif ((y <= -3.35e-18) || !(y <= 5e-14))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (x * (y + t));
	tmp = 0.0;
	if (y <= -3.6e+89)
		tmp = t_1;
	elseif (y <= -4.3e+54)
		tmp = x * ((y + z) * 2.0);
	elseif ((y <= -3.35e-18) || ~((y <= 5e-14)))
		tmp = t_1;
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+89], t$95$1, If[LessEqual[y, -4.3e+54], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.35e-18], N[Not[LessEqual[y, 5e-14]], $MachinePrecision]], t$95$1, N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e89 or -4.29999999999999976e54 < y < -3.3499999999999999e-18 or 5.0000000000000002e-14 < 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 0 91.1%

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

   4. Simplified 91.1%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. +-commutative 83.4%

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

   7. Simplified 83.4%

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

   if -3.6e89 < y < -4.29999999999999976e54

   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 87.7%

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

   3. Taylor expanded in t around 0 87.7%

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

   4. Taylor expanded in y around 0 87.7%

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

      1. associate-*r* 87.7%

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

      2. associate-*r* 87.7%

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

      3. distribute-lft-in 87.7%

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

      4. *-commutative 87.7%

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

      5. associate-*r* 87.7%

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

   6. Simplified 87.7%

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

   if -3.3499999999999999e-18 < y < 5.0000000000000002e-14

   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 0 82.7%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+89}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + t\right)\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-18} \lor \neg \left(y \leq 5 \cdot 10^{-14}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 5: 99.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 3.5 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + \left(z + z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.5) (not (<= x 3.5e-9)))
   (* x (+ t (+ (* y 2.0) (* z 2.0))))
   (+ (* y 5.0) (* x (+ t (+ y (+ z z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 3.5e-9)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (z + 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 <= (-2.5d0)) .or. (.not. (x <= 3.5d-9))) then
        tmp = x * (t + ((y * 2.0d0) + (z * 2.0d0)))
    else
        tmp = (y * 5.0d0) + (x * (t + (y + (z + z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 3.5e-9)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (z + z))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.5) or not (x <= 3.5e-9):
		tmp = x * (t + ((y * 2.0) + (z * 2.0)))
	else:
		tmp = (y * 5.0) + (x * (t + (y + (z + z))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.5) || !(x <= 3.5e-9))
		tmp = Float64(x * Float64(t + Float64(Float64(y * 2.0) + Float64(z * 2.0))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + Float64(z + z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.5) || ~((x <= 3.5e-9)))
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	else
		tmp = (y * 5.0) + (x * (t + (y + (z + z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.5], N[Not[LessEqual[x, 3.5e-9]], $MachinePrecision]], N[(x * N[(t + N[(N[(y * 2.0), $MachinePrecision] + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + N[(z + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5 or 3.4999999999999999e-9 < 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 99.3%

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

   if -2.5 < x < 3.4999999999999999e-9

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.6%

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

   4. Simplified 99.6%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 3.5 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + \left(z + z\right)\right)\right)\\ \end{array} \]

Alternative 6: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-57} \lor \neg \left(x \leq 1.48 \cdot 10^{-89}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))))
   (if (<= x -3.9e+158)
     t_1
     (if (<= x -9.6e+86)
       (* x (* (+ y z) 2.0))
       (if (or (<= x -2.5e-57) (not (<= x 1.48e-89))) t_1 (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -3.9e+158) {
		tmp = t_1;
	} else if (x <= -9.6e+86) {
		tmp = x * ((y + z) * 2.0);
	} else if ((x <= -2.5e-57) || !(x <= 1.48e-89)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (y * 2.0d0))
    if (x <= (-3.9d+158)) then
        tmp = t_1
    else if (x <= (-9.6d+86)) then
        tmp = x * ((y + z) * 2.0d0)
    else if ((x <= (-2.5d-57)) .or. (.not. (x <= 1.48d-89))) then
        tmp = t_1
    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 t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -3.9e+158) {
		tmp = t_1;
	} else if (x <= -9.6e+86) {
		tmp = x * ((y + z) * 2.0);
	} else if ((x <= -2.5e-57) || !(x <= 1.48e-89)) {
		tmp = t_1;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -3.9e+158:
		tmp = t_1
	elif x <= -9.6e+86:
		tmp = x * ((y + z) * 2.0)
	elif (x <= -2.5e-57) or not (x <= 1.48e-89):
		tmp = t_1
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (x <= -3.9e+158)
		tmp = t_1;
	elseif (x <= -9.6e+86)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	elseif ((x <= -2.5e-57) || !(x <= 1.48e-89))
		tmp = t_1;
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y * 2.0));
	tmp = 0.0;
	if (x <= -3.9e+158)
		tmp = t_1;
	elseif (x <= -9.6e+86)
		tmp = x * ((y + z) * 2.0);
	elseif ((x <= -2.5e-57) || ~((x <= 1.48e-89)))
		tmp = t_1;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+158], t$95$1, If[LessEqual[x, -9.6e+86], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -2.5e-57], N[Not[LessEqual[x, 1.48e-89]], $MachinePrecision]], t$95$1, N[(y * 5.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9e158 or -9.6000000000000001e86 < x < -2.5000000000000001e-57 or 1.48000000000000007e-89 < 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 y around inf 73.8%

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

   3. Taylor expanded in x around inf 69.3%

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

   if -3.9e158 < x < -9.6000000000000001e86

   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%

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

   3. Taylor expanded in t around 0 94.1%

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

   4. Taylor expanded in y around 0 94.1%

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

      1. associate-*r* 94.1%

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

      2. associate-*r* 94.1%

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

      3. distribute-lft-in 94.1%

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

      4. *-commutative 94.1%

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

      5. associate-*r* 94.1%

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

   6. Simplified 94.1%

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

   if -2.5000000000000001e-57 < x < 1.48000000000000007e-89

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 67.7%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-57} \lor \neg \left(x \leq 1.48 \cdot 10^{-89}\right):\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 7: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+84} \lor \neg \left(y \leq 2.7 \cdot 10^{+264}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 x))))
   (if (<= y -2.6e+92)
     t_1
     (if (<= y 1.9e-13)
       (* x (+ t (* z 2.0)))
       (if (or (<= y 2.2e+84) (not (<= y 2.7e+264)))
         t_1
         (* x (+ t (* y 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + x);
	double tmp;
	if (y <= -2.6e+92) {
		tmp = t_1;
	} else if (y <= 1.9e-13) {
		tmp = x * (t + (z * 2.0));
	} else if ((y <= 2.2e+84) || !(y <= 2.7e+264)) {
		tmp = t_1;
	} else {
		tmp = x * (t + (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) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + x)
    if (y <= (-2.6d+92)) then
        tmp = t_1
    else if (y <= 1.9d-13) then
        tmp = x * (t + (z * 2.0d0))
    else if ((y <= 2.2d+84) .or. (.not. (y <= 2.7d+264))) then
        tmp = t_1
    else
        tmp = x * (t + (y * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + x);
	double tmp;
	if (y <= -2.6e+92) {
		tmp = t_1;
	} else if (y <= 1.9e-13) {
		tmp = x * (t + (z * 2.0));
	} else if ((y <= 2.2e+84) || !(y <= 2.7e+264)) {
		tmp = t_1;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + x)
	tmp = 0
	if y <= -2.6e+92:
		tmp = t_1
	elif y <= 1.9e-13:
		tmp = x * (t + (z * 2.0))
	elif (y <= 2.2e+84) or not (y <= 2.7e+264):
		tmp = t_1
	else:
		tmp = x * (t + (y * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + x))
	tmp = 0.0
	if (y <= -2.6e+92)
		tmp = t_1;
	elseif (y <= 1.9e-13)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif ((y <= 2.2e+84) || !(y <= 2.7e+264))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + x);
	tmp = 0.0;
	if (y <= -2.6e+92)
		tmp = t_1;
	elseif (y <= 1.9e-13)
		tmp = x * (t + (z * 2.0));
	elseif ((y <= 2.2e+84) || ~((y <= 2.7e+264)))
		tmp = t_1;
	else
		tmp = x * (t + (y * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+92], t$95$1, If[LessEqual[y, 1.9e-13], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.2e+84], N[Not[LessEqual[y, 2.7e+264]], $MachinePrecision]], t$95$1, N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5999999999999999e92 or 1.9e-13 < y < 2.1999999999999998e84 or 2.7000000000000002e264 < 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 0 91.9%

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

   4. Simplified 91.9%

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

   5. Taylor expanded in y around inf 72.4%

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

   if -2.5999999999999999e92 < y < 1.9e-13

   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 0 78.9%

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

   if 2.1999999999999998e84 < y < 2.7000000000000002e264

   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 inf 91.7%

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

   3. Taylor expanded in x around inf 70.3%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+84} \lor \neg \left(y \leq 2.7 \cdot 10^{+264}\right):\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]

Alternative 8: 56.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+99}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* (+ y z) 2.0))))
   (if (<= t -1e+99)
     (* x t)
     (if (<= t 3.5e-253)
       t_1
       (if (<= t 3.5e-227)
         (* y (+ 5.0 x))
         (if (<= t 1.35e+37) 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 (t <= -1e+99) {
		tmp = x * t;
	} else if (t <= 3.5e-253) {
		tmp = t_1;
	} else if (t <= 3.5e-227) {
		tmp = y * (5.0 + x);
	} else if (t <= 1.35e+37) {
		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 (t <= (-1d+99)) then
        tmp = x * t
    else if (t <= 3.5d-253) then
        tmp = t_1
    else if (t <= 3.5d-227) then
        tmp = y * (5.0d0 + x)
    else if (t <= 1.35d+37) 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 (t <= -1e+99) {
		tmp = x * t;
	} else if (t <= 3.5e-253) {
		tmp = t_1;
	} else if (t <= 3.5e-227) {
		tmp = y * (5.0 + x);
	} else if (t <= 1.35e+37) {
		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 t <= -1e+99:
		tmp = x * t
	elif t <= 3.5e-253:
		tmp = t_1
	elif t <= 3.5e-227:
		tmp = y * (5.0 + x)
	elif t <= 1.35e+37:
		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 (t <= -1e+99)
		tmp = Float64(x * t);
	elseif (t <= 3.5e-253)
		tmp = t_1;
	elseif (t <= 3.5e-227)
		tmp = Float64(y * Float64(5.0 + x));
	elseif (t <= 1.35e+37)
		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 (t <= -1e+99)
		tmp = x * t;
	elseif (t <= 3.5e-253)
		tmp = t_1;
	elseif (t <= 3.5e-227)
		tmp = y * (5.0 + x);
	elseif (t <= 1.35e+37)
		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[t, -1e+99], N[(x * t), $MachinePrecision], If[LessEqual[t, 3.5e-253], t$95$1, If[LessEqual[t, 3.5e-227], N[(y * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+37], t$95$1, N[(x * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.9999999999999997e98 or 1.34999999999999993e37 < 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. Taylor expanded in t around inf 70.6%

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

   if -9.9999999999999997e98 < t < 3.50000000000000022e-253 or 3.5000000000000001e-227 < t < 1.34999999999999993e37

   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 inf 70.2%

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

   3. Taylor expanded in t around 0 63.7%

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

   4. Taylor expanded in y around 0 60.3%

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

      1. associate-*r* 60.3%

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

      2. associate-*r* 60.3%

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

      3. distribute-lft-in 63.7%

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

      4. *-commutative 63.7%

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

      5. associate-*r* 63.7%

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

   6. Simplified 63.7%

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

   if 3.50000000000000022e-253 < t < 3.5000000000000001e-227

   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 85.2%

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

   4. Simplified 85.2%

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

   5. Taylor expanded in y around inf 85.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+99}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 9: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-55} \lor \neg \left(x \leq 6.5 \cdot 10^{-146}\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.15e-55) (not (<= x 6.5e-146)))
   (* x (+ t (+ (* y 2.0) (* z 2.0))))
   (+ (* y 5.0) (* x (+ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.15e-55) || !(x <= 6.5e-146)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} 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 <= (-1.15d-55)) .or. (.not. (x <= 6.5d-146))) then
        tmp = x * (t + ((y * 2.0d0) + (z * 2.0d0)))
    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 <= -1.15e-55) || !(x <= 6.5e-146)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.15e-55) or not (x <= 6.5e-146):
		tmp = x * (t + ((y * 2.0) + (z * 2.0)))
	else:
		tmp = (y * 5.0) + (x * (y + t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.15e-55) || !(x <= 6.5e-146))
		tmp = Float64(x * Float64(t + Float64(Float64(y * 2.0) + Float64(z * 2.0))));
	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 <= -1.15e-55) || ~((x <= 6.5e-146)))
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	else
		tmp = (y * 5.0) + (x * (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.15e-55], N[Not[LessEqual[x, 6.5e-146]], $MachinePrecision]], N[(x * N[(t + N[(N[(y * 2.0), $MachinePrecision] + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $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 < -1.15000000000000006e-55 or 6.4999999999999999e-146 < 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 95.5%

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

   if -1.15000000000000006e-55 < x < 6.4999999999999999e-146

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 82.6%

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

      1. +-commutative 82.6%

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

   7. Simplified 82.6%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-55} \lor \neg \left(x \leq 6.5 \cdot 10^{-146}\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + t\right)\\ \end{array} \]

Alternative 10: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-53} \lor \neg \left(x \leq 2.95 \cdot 10^{-121}\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5e-53) (not (<= x 2.95e-121)))
   (* x (+ t (+ (* y 2.0) (* z 2.0))))
   (+ (* y 5.0) (* x (+ y (* z 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e-53) || !(x <= 2.95e-121)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (y + (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 ((x <= (-5d-53)) .or. (.not. (x <= 2.95d-121))) then
        tmp = x * (t + ((y * 2.0d0) + (z * 2.0d0)))
    else
        tmp = (y * 5.0d0) + (x * (y + (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 ((x <= -5e-53) || !(x <= 2.95e-121)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (y + (z * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5e-53) or not (x <= 2.95e-121):
		tmp = x * (t + ((y * 2.0) + (z * 2.0)))
	else:
		tmp = (y * 5.0) + (x * (y + (z * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5e-53) || !(x <= 2.95e-121))
		tmp = Float64(x * Float64(t + Float64(Float64(y * 2.0) + Float64(z * 2.0))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(y + Float64(z * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5e-53) || ~((x <= 2.95e-121)))
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	else
		tmp = (y * 5.0) + (x * (y + (z * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5e-53], N[Not[LessEqual[x, 2.95e-121]], $MachinePrecision]], N[(x * N[(t + N[(N[(y * 2.0), $MachinePrecision] + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(y + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5e-53 or 2.94999999999999998e-121 < 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 96.0%

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

   if -5e-53 < x < 2.94999999999999998e-121

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in t around 0 88.0%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-53} \lor \neg \left(x \leq 2.95 \cdot 10^{-121}\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + z \cdot 2\right)\\ \end{array} \]

Alternative 11: 99.8% 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 99.9%

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

2. Final simplification 99.9%

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

Alternative 12: 43.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+101}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-223}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-188}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.15e+101)
   (* x t)
   (if (<= t 1.12e-223)
     (* y 5.0)
     (if (<= t 8.5e-188) (* y x) (if (<= t 1.7e-33) (* y 5.0) (* x t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.15e+101) {
		tmp = x * t;
	} else if (t <= 1.12e-223) {
		tmp = y * 5.0;
	} else if (t <= 8.5e-188) {
		tmp = y * x;
	} else if (t <= 1.7e-33) {
		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 (t <= (-2.15d+101)) then
        tmp = x * t
    else if (t <= 1.12d-223) then
        tmp = y * 5.0d0
    else if (t <= 8.5d-188) then
        tmp = y * x
    else if (t <= 1.7d-33) 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 (t <= -2.15e+101) {
		tmp = x * t;
	} else if (t <= 1.12e-223) {
		tmp = y * 5.0;
	} else if (t <= 8.5e-188) {
		tmp = y * x;
	} else if (t <= 1.7e-33) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.15e+101:
		tmp = x * t
	elif t <= 1.12e-223:
		tmp = y * 5.0
	elif t <= 8.5e-188:
		tmp = y * x
	elif t <= 1.7e-33:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.15e+101)
		tmp = Float64(x * t);
	elseif (t <= 1.12e-223)
		tmp = Float64(y * 5.0);
	elseif (t <= 8.5e-188)
		tmp = Float64(y * x);
	elseif (t <= 1.7e-33)
		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 (t <= -2.15e+101)
		tmp = x * t;
	elseif (t <= 1.12e-223)
		tmp = y * 5.0;
	elseif (t <= 8.5e-188)
		tmp = y * x;
	elseif (t <= 1.7e-33)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.15e+101], N[(x * t), $MachinePrecision], If[LessEqual[t, 1.12e-223], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 8.5e-188], N[(y * x), $MachinePrecision], If[LessEqual[t, 1.7e-33], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.15e101 or 1.7e-33 < 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. Taylor expanded in t around inf 68.3%

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

   if -2.15e101 < t < 1.1199999999999999e-223 or 8.5000000000000004e-188 < t < 1.7e-33

   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 39.0%

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

   if 1.1199999999999999e-223 < t < 8.5000000000000004e-188

   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 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in y around inf 69.8%

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

   6. Taylor expanded in x around inf 59.1%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+101}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-223}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-188}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 13: 77.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+57} \lor \neg \left(y \leq 6.3 \cdot 10^{-15}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.3e+57) (not (<= y 6.3e-15)))
   (* 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 <= -2.3e+57) || !(y <= 6.3e-15)) {
		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 <= (-2.3d+57)) .or. (.not. (y <= 6.3d-15))) 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 <= -2.3e+57) || !(y <= 6.3e-15)) {
		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 <= -2.3e+57) or not (y <= 6.3e-15):
		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 <= -2.3e+57) || !(y <= 6.3e-15))
		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 <= -2.3e+57) || ~((y <= 6.3e-15)))
		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, -2.3e+57], N[Not[LessEqual[y, 6.3e-15]], $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 < -2.2999999999999999e57 or 6.29999999999999982e-15 < 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 75.0%

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

   4. Simplified 75.0%

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

   if -2.2999999999999999e57 < y < 6.29999999999999982e-15

   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 0 81.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+57} \lor \neg \left(y \leq 6.3 \cdot 10^{-15}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 14: 77.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+54}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e+54)
   (+ (* y 5.0) (* 2.0 (* y x)))
   (if (<= y 1.1e-13) (* x (+ t (* z 2.0))) (* y (+ 5.0 (* x 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e+54) {
		tmp = (y * 5.0) + (2.0 * (y * x));
	} else if (y <= 1.1e-13) {
		tmp = x * (t + (z * 2.0));
	} 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 (y <= (-4.8d+54)) then
        tmp = (y * 5.0d0) + (2.0d0 * (y * x))
    else if (y <= 1.1d-13) then
        tmp = x * (t + (z * 2.0d0))
    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 (y <= -4.8e+54) {
		tmp = (y * 5.0) + (2.0 * (y * x));
	} else if (y <= 1.1e-13) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = y * (5.0 + (x * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e+54:
		tmp = (y * 5.0) + (2.0 * (y * x))
	elif y <= 1.1e-13:
		tmp = x * (t + (z * 2.0))
	else:
		tmp = y * (5.0 + (x * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e+54)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(y * x)));
	elseif (y <= 1.1e-13)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	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 (y <= -4.8e+54)
		tmp = (y * 5.0) + (2.0 * (y * x));
	elseif (y <= 1.1e-13)
		tmp = x * (t + (z * 2.0));
	else
		tmp = y * (5.0 + (x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e+54], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-13], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.79999999999999997e54

   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%

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

   if -4.79999999999999997e54 < y < 1.09999999999999998e-13

   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 0 81.5%

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

   if 1.09999999999999998e-13 < 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 71.8%

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

   4. Simplified 71.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+54}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 15: 43.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+100}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.3e+100) (* x t) (if (<= t 1.8e-33) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.3e+100) {
		tmp = x * t;
	} else if (t <= 1.8e-33) {
		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 (t <= (-1.3d+100)) then
        tmp = x * t
    else if (t <= 1.8d-33) 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 (t <= -1.3e+100) {
		tmp = x * t;
	} else if (t <= 1.8e-33) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.3e+100:
		tmp = x * t
	elif t <= 1.8e-33:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.3e+100)
		tmp = Float64(x * t);
	elseif (t <= 1.8e-33)
		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 (t <= -1.3e+100)
		tmp = x * t;
	elseif (t <= 1.8e-33)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.3e+100], N[(x * t), $MachinePrecision], If[LessEqual[t, 1.8e-33], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3000000000000001e100 or 1.80000000000000017e-33 < 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. Taylor expanded in t around inf 68.3%

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

   if -1.3000000000000001e100 < t < 1.80000000000000017e-33

   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 37.5%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+100}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 16: 31.8% 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. Taylor expanded in x around 0 28.0%

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

3. Final simplification 28.0%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023293 
(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)))