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

Percentage Accurate: 99.8% → 99.9%

Time: 6.9s

Alternatives: 13

Speedup: 1.0×

• 27.2% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. fma-def 99.6%

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

   3. distribute-rgt-in 94.1%

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

   4. associate-+l+ 94.1%

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

   5. +-commutative 94.1%

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

   6. count-2 94.1%

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

   7. distribute-rgt-in 99.6%

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

   8. *-commutative 99.6%

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

   9. fma-def 99.6%

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

3. Applied egg-rr 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. fma-def 99.6%

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

   2. associate-+l+ 99.6%

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

   3. +-commutative 99.6%

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

   4. count-2 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 3: 42.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot 2\right)\\ \mathbf{if}\;y \leq -5.3 \cdot 10^{+188}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+74}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-238}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+45}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* z 2.0))))
   (if (<= y -5.3e+188)
     (* y 5.0)
     (if (<= y -2.2e+148)
       (* y (* x 2.0))
       (if (<= y -7.2e+74)
         (* y 5.0)
         (if (<= y -4.4e-19)
           t_1
           (if (<= y -2e-238)
             (* x t)
             (if (<= y 4.2e-119)
               t_1
               (if (<= y 3.1e+45) (* x t) (* y 5.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z * 2.0);
	double tmp;
	if (y <= -5.3e+188) {
		tmp = y * 5.0;
	} else if (y <= -2.2e+148) {
		tmp = y * (x * 2.0);
	} else if (y <= -7.2e+74) {
		tmp = y * 5.0;
	} else if (y <= -4.4e-19) {
		tmp = t_1;
	} else if (y <= -2e-238) {
		tmp = x * t;
	} else if (y <= 4.2e-119) {
		tmp = t_1;
	} else if (y <= 3.1e+45) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * (z * 2.0d0)
    if (y <= (-5.3d+188)) then
        tmp = y * 5.0d0
    else if (y <= (-2.2d+148)) then
        tmp = y * (x * 2.0d0)
    else if (y <= (-7.2d+74)) then
        tmp = y * 5.0d0
    else if (y <= (-4.4d-19)) then
        tmp = t_1
    else if (y <= (-2d-238)) then
        tmp = x * t
    else if (y <= 4.2d-119) then
        tmp = t_1
    else if (y <= 3.1d+45) 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 t_1 = x * (z * 2.0);
	double tmp;
	if (y <= -5.3e+188) {
		tmp = y * 5.0;
	} else if (y <= -2.2e+148) {
		tmp = y * (x * 2.0);
	} else if (y <= -7.2e+74) {
		tmp = y * 5.0;
	} else if (y <= -4.4e-19) {
		tmp = t_1;
	} else if (y <= -2e-238) {
		tmp = x * t;
	} else if (y <= 4.2e-119) {
		tmp = t_1;
	} else if (y <= 3.1e+45) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z * 2.0)
	tmp = 0
	if y <= -5.3e+188:
		tmp = y * 5.0
	elif y <= -2.2e+148:
		tmp = y * (x * 2.0)
	elif y <= -7.2e+74:
		tmp = y * 5.0
	elif y <= -4.4e-19:
		tmp = t_1
	elif y <= -2e-238:
		tmp = x * t
	elif y <= 4.2e-119:
		tmp = t_1
	elif y <= 3.1e+45:
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z * 2.0))
	tmp = 0.0
	if (y <= -5.3e+188)
		tmp = Float64(y * 5.0);
	elseif (y <= -2.2e+148)
		tmp = Float64(y * Float64(x * 2.0));
	elseif (y <= -7.2e+74)
		tmp = Float64(y * 5.0);
	elseif (y <= -4.4e-19)
		tmp = t_1;
	elseif (y <= -2e-238)
		tmp = Float64(x * t);
	elseif (y <= 4.2e-119)
		tmp = t_1;
	elseif (y <= 3.1e+45)
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z * 2.0);
	tmp = 0.0;
	if (y <= -5.3e+188)
		tmp = y * 5.0;
	elseif (y <= -2.2e+148)
		tmp = y * (x * 2.0);
	elseif (y <= -7.2e+74)
		tmp = y * 5.0;
	elseif (y <= -4.4e-19)
		tmp = t_1;
	elseif (y <= -2e-238)
		tmp = x * t;
	elseif (y <= 4.2e-119)
		tmp = t_1;
	elseif (y <= 3.1e+45)
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.3e+188], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, -2.2e+148], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e+74], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, -4.4e-19], t$95$1, If[LessEqual[y, -2e-238], N[(x * t), $MachinePrecision], If[LessEqual[y, 4.2e-119], t$95$1, If[LessEqual[y, 3.1e+45], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.29999999999999988e188 or -2.1999999999999999e148 < y < -7.19999999999999975e74 or 3.09999999999999988e45 < y

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 53.0%

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

   4. Simplified 53.0%

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

   if -5.29999999999999988e188 < y < -2.1999999999999999e148

   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 79.9%

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

   3. Taylor expanded in x around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-*r* 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around inf 66.8%

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

      1. associate-*r* 66.8%

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

   8. Simplified 66.8%

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

   if -7.19999999999999975e74 < y < -4.3999999999999997e-19 or -2e-238 < y < 4.2e-119

   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 98.4%

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

   3. Taylor expanded in z around inf 62.1%

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

      1. associate-*r* 62.1%

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

      2. *-commutative 62.1%

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

      3. associate-*r* 62.1%

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

   5. Simplified 62.1%

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

   if -4.3999999999999997e-19 < y < -2e-238 or 4.2e-119 < y < 3.09999999999999988e45

   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 0 100.0%

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

   3. Taylor expanded in t around inf 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+188}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+74}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-238}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+45}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 4: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+187}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -8.3 \cdot 10^{+93}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e+187)
   (* y 5.0)
   (if (<= y -7e+148)
     (* y (* x 2.0))
     (if (<= y -8.3e+93)
       (* y 5.0)
       (if (<= y 7e+63)
         (* x (+ t (* z 2.0)))
         (if (<= y 1.36e+119) (* x (+ t (* y 2.0))) (* y 5.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+187) {
		tmp = y * 5.0;
	} else if (y <= -7e+148) {
		tmp = y * (x * 2.0);
	} else if (y <= -8.3e+93) {
		tmp = y * 5.0;
	} else if (y <= 7e+63) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 1.36e+119) {
		tmp = x * (t + (y * 2.0));
	} 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 (y <= (-2.8d+187)) then
        tmp = y * 5.0d0
    else if (y <= (-7d+148)) then
        tmp = y * (x * 2.0d0)
    else if (y <= (-8.3d+93)) then
        tmp = y * 5.0d0
    else if (y <= 7d+63) then
        tmp = x * (t + (z * 2.0d0))
    else if (y <= 1.36d+119) then
        tmp = x * (t + (y * 2.0d0))
    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 (y <= -2.8e+187) {
		tmp = y * 5.0;
	} else if (y <= -7e+148) {
		tmp = y * (x * 2.0);
	} else if (y <= -8.3e+93) {
		tmp = y * 5.0;
	} else if (y <= 7e+63) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 1.36e+119) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e+187:
		tmp = y * 5.0
	elif y <= -7e+148:
		tmp = y * (x * 2.0)
	elif y <= -8.3e+93:
		tmp = y * 5.0
	elif y <= 7e+63:
		tmp = x * (t + (z * 2.0))
	elif y <= 1.36e+119:
		tmp = x * (t + (y * 2.0))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e+187)
		tmp = Float64(y * 5.0);
	elseif (y <= -7e+148)
		tmp = Float64(y * Float64(x * 2.0));
	elseif (y <= -8.3e+93)
		tmp = Float64(y * 5.0);
	elseif (y <= 7e+63)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (y <= 1.36e+119)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e+187)
		tmp = y * 5.0;
	elseif (y <= -7e+148)
		tmp = y * (x * 2.0);
	elseif (y <= -8.3e+93)
		tmp = y * 5.0;
	elseif (y <= 7e+63)
		tmp = x * (t + (z * 2.0));
	elseif (y <= 1.36e+119)
		tmp = x * (t + (y * 2.0));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e+187], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, -7e+148], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.3e+93], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, 7e+63], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.36e+119], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.79999999999999989e187 or -6.9999999999999998e148 < y < -8.2999999999999997e93 or 1.35999999999999995e119 < y

   1. Initial program 98.6%

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

   2. Taylor expanded in x around 0 60.3%

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

   4. Simplified 60.3%

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

   if -2.79999999999999989e187 < y < -6.9999999999999998e148

   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 79.9%

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

   3. Taylor expanded in x around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-*r* 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around inf 66.8%

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

      1. associate-*r* 66.8%

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

   8. Simplified 66.8%

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

   if -8.2999999999999997e93 < y < 7.00000000000000059e63

   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 99.3%

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

   3. Taylor expanded in y around 0 79.4%

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

   if 7.00000000000000059e63 < y < 1.35999999999999995e119

   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 99.9%

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

   3. Taylor expanded in x around inf 76.3%

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

      1. *-commutative 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-*r* 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in z around 0 66.2%

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

      1. +-commutative 66.2%

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

      2. *-commutative 66.2%

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

      3. associate-*r* 66.2%

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

      4. *-commutative 66.2%

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

      5. associate-*r* 66.2%

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

      6. distribute-lft-out 66.2%

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

      7. *-commutative 66.2%

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

   8. Simplified 66.2%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+187}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -8.3 \cdot 10^{+93}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 5: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right) + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1e+148)
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* 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 (x <= -1e+148) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (x * (t + (z * 2.0))) + (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 <= (-1d+148)) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (x * (t + (z * 2.0d0))) + (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 <= -1e+148) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1e+148:
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1e+148)
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(z * 2.0))) + 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 <= -1e+148)
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1e+148], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1e148

   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. Taylor expanded in x around inf 99.9%

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

   if -1e148 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0 97.8%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right) + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 6: 64.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+187}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+96}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.75e+187)
   (* y 5.0)
   (if (<= y -7e+148)
     (* y (* x 2.0))
     (if (<= y -2.15e+96)
       (* y 5.0)
       (if (<= y 8e+106) (* x (+ t (* z 2.0))) (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.75e+187) {
		tmp = y * 5.0;
	} else if (y <= -7e+148) {
		tmp = y * (x * 2.0);
	} else if (y <= -2.15e+96) {
		tmp = y * 5.0;
	} else if (y <= 8e+106) {
		tmp = x * (t + (z * 2.0));
	} 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 (y <= (-2.75d+187)) then
        tmp = y * 5.0d0
    else if (y <= (-7d+148)) then
        tmp = y * (x * 2.0d0)
    else if (y <= (-2.15d+96)) then
        tmp = y * 5.0d0
    else if (y <= 8d+106) then
        tmp = x * (t + (z * 2.0d0))
    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 (y <= -2.75e+187) {
		tmp = y * 5.0;
	} else if (y <= -7e+148) {
		tmp = y * (x * 2.0);
	} else if (y <= -2.15e+96) {
		tmp = y * 5.0;
	} else if (y <= 8e+106) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.75e+187:
		tmp = y * 5.0
	elif y <= -7e+148:
		tmp = y * (x * 2.0)
	elif y <= -2.15e+96:
		tmp = y * 5.0
	elif y <= 8e+106:
		tmp = x * (t + (z * 2.0))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.75e+187)
		tmp = Float64(y * 5.0);
	elseif (y <= -7e+148)
		tmp = Float64(y * Float64(x * 2.0));
	elseif (y <= -2.15e+96)
		tmp = Float64(y * 5.0);
	elseif (y <= 8e+106)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.75e+187)
		tmp = y * 5.0;
	elseif (y <= -7e+148)
		tmp = y * (x * 2.0);
	elseif (y <= -2.15e+96)
		tmp = y * 5.0;
	elseif (y <= 8e+106)
		tmp = x * (t + (z * 2.0));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.75e+187], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, -7e+148], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e+96], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, 8e+106], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.74999999999999999e187 or -6.9999999999999998e148 < y < -2.15000000000000001e96 or 8.00000000000000073e106 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in x around 0 58.0%

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

   4. Simplified 58.0%

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

   if -2.74999999999999999e187 < y < -6.9999999999999998e148

   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 79.9%

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

   3. Taylor expanded in x around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-*r* 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around inf 66.8%

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

      1. associate-*r* 66.8%

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

   8. Simplified 66.8%

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

   if -2.15000000000000001e96 < y < 8.00000000000000073e106

   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 99.3%

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

   3. Taylor expanded in y around 0 76.6%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+187}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+96}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 7: 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 99.5%

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

2. Final simplification 99.5%

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

Alternative 8: 42.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot 2\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+74}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-244}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* z 2.0))))
   (if (<= y -7e+74)
     (* y 5.0)
     (if (<= y -3.6e-21)
       t_1
       (if (<= y -1.35e-244)
         (* x t)
         (if (<= y 1.45e-113) t_1 (if (<= y 4.2e+45) (* x t) (* y 5.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z * 2.0);
	double tmp;
	if (y <= -7e+74) {
		tmp = y * 5.0;
	} else if (y <= -3.6e-21) {
		tmp = t_1;
	} else if (y <= -1.35e-244) {
		tmp = x * t;
	} else if (y <= 1.45e-113) {
		tmp = t_1;
	} else if (y <= 4.2e+45) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * (z * 2.0d0)
    if (y <= (-7d+74)) then
        tmp = y * 5.0d0
    else if (y <= (-3.6d-21)) then
        tmp = t_1
    else if (y <= (-1.35d-244)) then
        tmp = x * t
    else if (y <= 1.45d-113) then
        tmp = t_1
    else if (y <= 4.2d+45) 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 t_1 = x * (z * 2.0);
	double tmp;
	if (y <= -7e+74) {
		tmp = y * 5.0;
	} else if (y <= -3.6e-21) {
		tmp = t_1;
	} else if (y <= -1.35e-244) {
		tmp = x * t;
	} else if (y <= 1.45e-113) {
		tmp = t_1;
	} else if (y <= 4.2e+45) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z * 2.0)
	tmp = 0
	if y <= -7e+74:
		tmp = y * 5.0
	elif y <= -3.6e-21:
		tmp = t_1
	elif y <= -1.35e-244:
		tmp = x * t
	elif y <= 1.45e-113:
		tmp = t_1
	elif y <= 4.2e+45:
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z * 2.0))
	tmp = 0.0
	if (y <= -7e+74)
		tmp = Float64(y * 5.0);
	elseif (y <= -3.6e-21)
		tmp = t_1;
	elseif (y <= -1.35e-244)
		tmp = Float64(x * t);
	elseif (y <= 1.45e-113)
		tmp = t_1;
	elseif (y <= 4.2e+45)
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z * 2.0);
	tmp = 0.0;
	if (y <= -7e+74)
		tmp = y * 5.0;
	elseif (y <= -3.6e-21)
		tmp = t_1;
	elseif (y <= -1.35e-244)
		tmp = x * t;
	elseif (y <= 1.45e-113)
		tmp = t_1;
	elseif (y <= 4.2e+45)
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+74], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, -3.6e-21], t$95$1, If[LessEqual[y, -1.35e-244], N[(x * t), $MachinePrecision], If[LessEqual[y, 1.45e-113], t$95$1, If[LessEqual[y, 4.2e+45], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.00000000000000029e74 or 4.1999999999999999e45 < y

   1. Initial program 99.0%

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

   2. Taylor expanded in x around 0 49.0%

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

   4. Simplified 49.0%

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

   if -7.00000000000000029e74 < y < -3.59999999999999989e-21 or -1.35e-244 < y < 1.45000000000000002e-113

   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 98.4%

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

   3. Taylor expanded in z around inf 62.1%

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

      1. associate-*r* 62.1%

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

      2. *-commutative 62.1%

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

      3. associate-*r* 62.1%

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

   5. Simplified 62.1%

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

   if -3.59999999999999989e-21 < y < -1.35e-244 or 1.45000000000000002e-113 < y < 4.1999999999999999e45

   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 0 100.0%

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

   3. Taylor expanded in t around inf 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+74}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-244}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 9: 89.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-16} \lor \neg \left(x \leq 1.18 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.4e-16) (not (<= x 1.18e-26)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.4e-16) || !(x <= 1.18e-26)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.4d-16)) .or. (.not. (x <= 1.18d-26))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.4e-16) || !(x <= 1.18e-26)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.4e-16) or not (x <= 1.18e-26):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.4e-16) || !(x <= 1.18e-26))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.4e-16) || ~((x <= 1.18e-26)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.4e-16], N[Not[LessEqual[x, 1.18e-26]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4e-16 or 1.17999999999999996e-26 < 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. Taylor expanded in x around inf 98.1%

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

   if -3.4e-16 < x < 1.17999999999999996e-26

   1. Initial program 99.1%

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

   2. Taylor expanded in t around inf 79.2%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-16} \lor \neg \left(x \leq 1.18 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 10: 88.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-21} \lor \neg \left(x \leq 4.1 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.3e-21) (not (<= x 4.1e-26)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* 2.0 (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.3e-21) || !(x <= 4.1e-26)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.3d-21)) .or. (.not. (x <= 4.1d-26))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.3e-21) || !(x <= 4.1e-26)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.3e-21) or not (x <= 4.1e-26):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (2.0 * (x * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.3e-21) || !(x <= 4.1e-26))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.3e-21) || ~((x <= 4.1e-26)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (2.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.3e-21], N[Not[LessEqual[x, 4.1e-26]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.30000000000000009e-21 or 4.0999999999999999e-26 < 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. Taylor expanded in x around inf 98.1%

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

   if -3.30000000000000009e-21 < x < 4.0999999999999999e-26

   1. Initial program 99.1%

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

   2. Taylor expanded in z around inf 81.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-21} \lor \neg \left(x \leq 4.1 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 11: 78.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+28} \lor \neg \left(y \leq 5 \cdot 10^{+51}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.1e+28) (not (<= y 5e+51)))
   (* 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 <= -2.1e+28) || !(y <= 5e+51)) {
		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 <= (-2.1d+28)) .or. (.not. (y <= 5d+51))) 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 <= -2.1e+28) || !(y <= 5e+51)) {
		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 <= -2.1e+28) or not (y <= 5e+51):
		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 <= -2.1e+28) || !(y <= 5e+51))
		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 <= -2.1e+28) || ~((y <= 5e+51)))
		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, -2.1e+28], N[Not[LessEqual[y, 5e+51]], $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 < -2.09999999999999989e28 or 5e51 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in y around inf 82.1%

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

   4. Simplified 82.1%

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

   if -2.09999999999999989e28 < y < 5e51

   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 0 100.0%

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

   3. Taylor expanded in y around 0 84.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+28} \lor \neg \left(y \leq 5 \cdot 10^{+51}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 12: 47.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-21}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-23}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.5e-21) (* x t) (if (<= x 9.5e-23) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e-21) {
		tmp = x * t;
	} else if (x <= 9.5e-23) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-9.5d-21)) then
        tmp = x * t
    else if (x <= 9.5d-23) then
        tmp = y * 5.0d0
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e-21) {
		tmp = x * t;
	} else if (x <= 9.5e-23) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.5e-21:
		tmp = x * t
	elif x <= 9.5e-23:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.5e-21)
		tmp = Float64(x * t);
	elseif (x <= 9.5e-23)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.5e-21)
		tmp = x * t;
	elseif (x <= 9.5e-23)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.5e-21], N[(x * t), $MachinePrecision], If[LessEqual[x, 9.5e-23], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4999999999999994e-21 or 9.50000000000000058e-23 < 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 0 91.6%

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

   3. Taylor expanded in t around inf 34.4%

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

      1. *-commutative 34.4%

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

   5. Simplified 34.4%

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

   if -9.4999999999999994e-21 < x < 9.50000000000000058e-23

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 60.2%

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

   4. Simplified 60.2%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-21}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-23}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 13: 31.3% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in y around 0 95.3%

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

3. Taylor expanded in t around inf 27.4%

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

   1. *-commutative 27.4%

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

5. Simplified 27.4%

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

6. Final simplification 27.4%

   \[\leadsto x \cdot t \]

Reproduce

herbie shell --seed 2023290 
(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)))